1. technology and computing
2. software
3. databases

Contents
1. Design of your qPCR experiment......................................................................................................... 4
1.1. Sample maximization versus gene maximization......................................................................... 4
1.2. Replicates ..................................................................................................................................... 4
1.3. Positive and negative controls ..................................................................................................... 5
2. Data hierarchy used in qbase+ ............................................................................................................ 6
3. Calculations in qbase+.......................................................................................................................... 7
4. The analysis wizard .............................................................................................................................. 8
4.1. The Start page .............................................................................................................................. 8
4.2. The Import run page ..................................................................................................................... 9
4.2.1. Supported data formats ........................................................................................................ 9
4.2.2. Importing runs ....................................................................................................................... 9
4.3. The Sample target list page ........................................................................................................ 11
4.3.1. Data annotation................................................................................................................... 11
4.3.2. Annotating run files ............................................................................................................. 11
4.4. The Run annotation page ........................................................................................................... 13
4.5. The Aim page .............................................................................................................................. 13
4.6. The Technical quality control page............................................................................................. 14
4.6.1. Technical replicates ............................................................................................................. 14
4.6.2. Checking the quality of the data ......................................................................................... 14
4.7. Viewing flagged and excluded wells........................................................................................... 15
4.8. The Amplification efficiencies page............................................................................................ 16
4.8.1. Calculations based on amplification efficiencies................................................................. 16
4.8.2. Setting the amplification efficiency strategy ....................................................................... 16
4.8.3. Estimation of amplification efficiencies .............................................................................. 17
4.8.4. Recommendations regarding amplification efficiencies ..................................................... 17
4.9. The Normalization page ............................................................................................................. 18
4.9.1. Calculating normalized relative quantities (NRQ) ............................................................... 18
4.9.2. Defining the normalization strategy.................................................................................... 19
4.9.3. Appointing reference genes ................................................................................................ 20
4.9.4. Checking the quality of the reference genes....................................................................... 20
4.9.5. Recommendations regarding reference genes ................................................................... 21
4.10. The Scaling page ....................................................................................................................... 21
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4.11. The Analysis page ..................................................................................................................... 22
4.11.1. Single gene bar charts ....................................................................................................... 22
4.12. Leaving and returning to the analysis wizard ........................................................................... 25
5. The statistics wizard .......................................................................................................................... 26
5.1. The Goal page ............................................................................................................................. 27
5.2. The Define your groups page ..................................................................................................... 27
5.3 The Targets page ......................................................................................................................... 28
5.4 The Settings page ........................................................................................................................ 28
5.5 Statistical tests used in qbase+ for comparison of means .......................................................... 29
5.5.1. General outline of all statistical tests for comparison of the means .................................. 29
5.5.2. Parametric versus non-parametric tests ............................................................................. 31
5.5.3. How do you know if your data set comes from a normal distribution? ............................. 32
5.5.4. Assumptions of parametric tests......................................................................................... 32
5.5.5. T-test for comparing the means of two groups .................................................................. 32
5.5.6. Mann Whitney test is a non-parametric test to compare two groups ............................... 33
5.5.7. ANOVA for comparison of more than two groups ............................................................. 34
5.5.8. Follow up tests to ANOVA ................................................................................................... 35
5.5.9. Unpaired versus paired data ............................................................................................... 35
5.5.10. The paired t-test is a parametric test for comparing two groups of paired data ............. 36
5.5.11. The Wilcoxon matched pairs signed rank test is the non-parametric alternative ............ 36
5.5.12. Paired tests in qbase+ ....................................................................................................... 36
5.5.13. One-sided and two-sided p-values .................................................................................... 37
5.5.14. Multiple testing correction ................................................................................................ 37
5.5.15. Significance level versus false discovery rate .................................................................... 37
5.6. Correlation between two targets ............................................................................................... 38
5.7. Survival analysis .......................................................................................................................... 38
5.8. Analysis results ........................................................................................................................... 39
5.9. Interpretation of the output tables for statistical tests in qbase+ ............................................. 39
6. Selecting reference genes ................................................................................................................. 42
6.1. Selecting candidate reference genes in Genevestigator ............................................................ 42
6.1.1. Accessing Genevestigator and RefGenes ............................................................................ 42
STEP 1: Choose samples from a biological context similar to that of your qPCR expriment ........ 43
STEP 2: Select the gene(s) you want to measure in your qPCR experiment ................................. 44
STEP 3: Find candidate reference genes ....................................................................................... 45
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6.2. Selecting the best reference genes in your samples using qbase+ ............................................ 47
7. Export results..................................................................................................................................... 49
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For the training you can use the following account:
User: [email protected]
Password: qbptraining
1. Design of your qPCR experiment
1.1. Sample maximization versus gene maximization
The best setup for your plates is placing all samples for the same gene on the same plate. This is
called the sample maximization approach. It is counterintuitive to what most people do: they place
the same sample for all genes on the same plate, which is appropriately called the gene maximization
apprioach. The consequence of the gene maximization approach is that samples of the same gene
are placed on different plates. However, in most experiments you want to compare samples for the
same gene: see if a gene is differentially expressed in one group of samples as compared to another
group of samples. Therefore, sample maximization will greatly reduce experimental noise because
the things that you want to compare are all on the same plate so you exclude variation between
different plates. Sample maximization experiments are also easier to set up since you have to make
the master mix for each gene only once. This is why there is no need to repeat reference
(housekeeping) genes on each plate, this may even negatively influence the analysis results.
It is important to realize that sample maximization is ideal for most applications where you want to
compare between samples e.g. treated versus untreated. When you want to compare genes e.g. in
copy number variation analysis, you have to use the gene maximization approach.
1.2. Replicates
There are two types of replicates: biological and technical replicates. Biological replicates consist of
samples obtained by performing the same treatments on different subjects (patients, animals, plants,
cell cultures…). Technical replicates can be generated in many ways:



PCR replicates: the same reaction using the same cDNA is performed in two different wells.
These technical replicates should be incorporated in each run since they are used to correct
for pipetting errors.
RT replicates: uses two different cDNA preparations of the same sample instead of the same
cDNA since reverse transcription is considered the most variable step in the protocol. Should
be done once for every RT kit (so not in every run).
Repeated RNA extraction of the same sample
Importantly, technical replicates should be measured on the same plate.
Since they give information about biological variability, biological replicates are more useful than
technical replicates so it is acceptable to omit technical replicates when the sample size is sufficiently
large. When you don’t have enough money to include both types of replicates in your experiment
then choose biological replicates over technical replicates. Biogazelle recommends to use 4 biological
replicates for each sample.
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1.3. Positive and negative controls
There are three types of negative controls:



no template controls: includes all components of PCR reaction except cDNA template. In this
way you can detect PCR product contamination. In theory no product should be formed in
this reaction, if you do see a product it means that either the primers form primer dimers or
one of the components of the PCR reaction is contaminated with cDNA template. These
controls are also called blank measurements by some instruments. You should include these
controls in every run.
no RT controls: includes all components of PCR reaction except cDNA template. Instead of
cDNA template, DNase treated RNA is added to the reaction as a template. Since the primers
are designed to bind DNA no product should be formed. If you do see a product it means that
the RNA still contains genomic DNA contamination. These controls only need to be included
once for each RNA extraction that you do.
biological controls: a sample in which the gene is not expressed, healthy subject without
pathogen infection…
As positive control you can use e.g. a sample in which the gene is expressed, subject in which the
pathogen is present, sample in which the deletion is present... Sometimes synthetic templates are
used as positive controls. These synthetic templates are oligonucleotides consisting of the forward
and reverse primer and a random sequence of more than 20 nucleotides in between.
Apart from these positive and negative controls you also have normal control samples: i.e. the
samples you compare the treatment to e.g. untreated samples, healthy individuals, individuals with
normal copy number...
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2. Data hierarchy used in qbase+
Qbase+ stores your qPCR data according to a specific hierarchy: Projects < Experiments < Runs
A project contains data from one or several related qPCR experiments.
An experiment holds data from one or multiple runs on your qPCR instrument, annotations and
parameter settings used for the analysis. The data should all be related to the same biological
experiment, in which you have generated a set of biological samples. In each of the samples you
want to measure the amounts of a set of target sequences. Targets are the DNA sequences you want
quantify (genes, miRNAs…).
A run contains qPCR data coming from a single plate. The data consists of a Cq value for each well on
the plate, reflecting an amount of target sequence in a certain sample. Plates contain Cq values of
one or multiple targets in multiple samples. The software cannot work with raw fluorescence data
nor with amplification curves.
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3. Calculations in qbase+
Classic method
∆∆𝐶𝑞 = ∆𝐶𝑞𝑡𝑎𝑟𝑔𝑒𝑡 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 − ∆𝐶𝑞𝑟𝑒𝑓 𝑡𝑎𝑟𝑔𝑒𝑡
Qbase+
Limitations:
1. you assume that the amount of PCR product
doubles each PCR cycle
2. one reference gene
3. difficult to combine data from separate runs
Solutions:
1. RQ: gene-specific amplification efficiencies
2. NRQ: multiple reference genes
3. CNRQ: inter-run calibration
4. Rescale CNRQs
! Error propagation is handled by the software !
The main differences between the classical ∆∆Cq method and the method used in qbase+ are the
following:
-
Qbase+ allows to use multiple reference genes
Qbase+ takes into account gene-specific amplification efficiencies
Qbase+ allows for inter-run calibration to correct for differences between plates
The qbase+ method is based on the ∆∆Cq method so you can add the steps specific to qbase+ to the
classical ∆∆Cq method yourself in Excel but the entire calculation track becomes very complex and
mistakes are easily made.
Qbase+ analyses your qPCR data in four steps:
1. The software calculates RQs (Relative Quantities) for each gene/sample combination by comparing
the Cq of a given sample with the average Cq across all samples for that gene, taking into account
differences in PCR amplification efficiencies. Genes have different amplification efficiencies because
e.g. some primer pairs anneal better than others, the presence of inhibitors in the reaction mix (salts,
detergents…) decrease the amplification efficiency… The presence of inhibitors is not only a result of
the RNA extraction procedure but different tissues are known to exhibit different PCR efficiencies,
caused by RT inhibitors, PCR inhibitors and by variations in the total RNA fraction pattern extracted.
2. In a next step the RQ is normalized by dividing it by the geometric mean RQ of a set of selected
reference genes, which results in the NRQ (Normalized Relative Quantity). The reference genes are
chosen because they have the same expression level in all samples of the experiment.
3. If samples from different plates need to be compared to each other, an inter-run calibration step
is introduced which results in the CNRQ (Calibrated Normalized Relative Quantity). This means that if
you do not perform inter-run calibration, then CNRQ equals NRQ.
4. Finally, the CNRQ results can be rescaled according to various methods. The scaling only changes
the scale of the data, but not the fold changes between the samples. Default is scaling to the average
expression level across all samples.
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4. The analysis wizard
Most users will use the analysis wizard which guides you through the most important steps in the
analysis of your qPCR experiment:
1.
2.
3.
4.
5.
6.
7.
Creating or opening an experiment
Loading the data
Checking (and adding) sample and target names
Selecting the type of analysis you want to do
Setting quality thresholds
Checking the quality of the data
Calculating amplification efficiencies
4.1. The Start page
When you open the software, the Start page is shown. Here you can choose to


Create a new qbase+ experiment
Open an existing qbase+ experiment
If you want to create a new experiment, type a name for the new Experiment in the appropriate text
area. If the name is already in use or contains characters that are not supported by qbase+, it will
appear in red.
If you want to create a new project, click the Create new project button. Qbase+ will give your new
project a default name (e.g. Project 1) but you can change that later on.
When you want to open an existing experiment, click the name of the experiment to activate the
Next > button at the bottom. When you click the name of a project, the button will not become
active, you have to select an experiment.
When you click the Next > button, you go to the Import Run page.
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4.2. The Import run page
4.2.1. Supported data formats
Files generated by common qPCR instruments are automatically recognized and imported by qbase+.
On the Biogazelle website (https://www.biogazelle.com/import-formats) you find a list of all file
types that are supported. You have to log on to your MyBiogazelle account to access this page.
Most qPCR instruments are supported and the Excel, .csv or .txt files that they generate can be
directly imported. Alternatively, the software also accepts Excel files in qBase format, a general
format that you see below:
Well
A1
A2
A3
B1
Type
UNKN
STD
NTC
UNKN
Sample
Sample1
Standard1
Water
Sample1
Gene
Target1
Target1
Target1
Target2
Ct
Quantity
22,22
25,6
33,33
Exclusion
256
TRUE
qBase files must contain one table with a header row. The header row must contain all items shown
in the example in the same order. The header of fifth column must be Cq, Ct, Cp or TOP.
Well positions should be letter-number combinations like A1, H12, P24, or plain numbers.
Recognized sample types: UNKN (for unknowns), STD (for standards), NTC (for negative controls =
wells without template), POSITVE_CONTROL, MINUS_RT (wells without reverse transcriptase).
If you have more than 10 numbered samples use 'sample01' instead of 'sample1' because this will
result in a better alphabetical sorting in tables and figures. Samples from a dilution series should be
given different sample names.
The Ct and Quantity columns should contain numerical values or be left empty. You can use “.” or “,”
as decimal separator, the software will adapt to the settings of your computer.
The Exclusion column is left blank or contains TRUE if wells are to be excluded from calculations.
4.2.2. Importing runs
The Import run page allows you to specify and import the actual data of the experiment.
If you have created a new experiment, you have to select the run file(s) by clicking the Import runs
button. This will launch an Import run wizard supporting the import of one or multiple run files in
RDML, Excel, .txt or .csv format.
This opens the Import Run wizard, where you can select the runs you want to import.
Click the Browse button and go to the folder that contains the files. If multiple runs need to be
imported and all have the same file type, you can import them all at once (CTRL + click in Windows,
command + click in MacOSX). Click Open then Next.
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Qbase+ will try to recognize the format of the selected import files.
Quick import
If only one format matches your file(s) (in this case CFX), it will be selected and the Quick import
option will be automatically enabled. Click Finish.
Manual import
If the file format is not recognized (e.g. generic qBase files), qbase+ automatically selects the manual
import option. Click Next.
Select the correct file format (in this case qBase). Click Finish.
If you have opened an existing experiment, you will see the name of the runs that are linked to this
experiment in the list. Click the name of the data file you want to import. If necessary you can make
multiple selections at the same time by holding the Ctrl key (or command key on Mac) during the
selection.
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4.3. The Sample target list page
4.3.1. Data annotation
Run annotation consists of sample and target names, sample types and quantities for standard
samples. Both samples and targets must have a unique name. Every well should be annotated with a
sample and target name.
Samples and targets have more annotation: they also have a set of properties. These can be qbase+
specific properties (e.g. target type: target of interest or reference target) or custom properties (e.g.
age, treatment, passage number...). Some annotation is incorporated in the run files like target
names; sample names and sample types. Additional properties can be imported by means of sample
properties files.
4.3.2. Annotating run files
Once runs are imported, the software will automatically look for the sample and target names in the
run files. Normally, sample and target names are annotated on the qPCR instrument and as such run
files should contain this information.
If an annotated run (containing a sample and target name for every well that has a Cq value) is
imported, qbase+ will take over this annotation and generate a list of the target and sample names in
the Sample target list page.
However, in most experiments you need additional annotation. For instance when you have paired
samples you need to know which samples form pairs. Grouping of samples is also important
annotation: if your samples are divided into two or multiple groups like treated and untreated. This
kind of annotation is called custom sample properties in qbase+. Custom properties like grouping of
samples will be used later in the analysis for visualization, rescaling and statistics.
To add custom properties and their corresponding values in qbase+ you need to





select Add samples and targets
click Import sample list
browse to the folder that contains the samples properties file
click Open
click Next
These sample properties files have a specific format:
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name
type
description quantity normalization factor positive control quantity Pairing Treatment
Sample01 UNKN
1
Untreated
Sample02 UNKN
1
Treated
Sample03 UNKN
2
Untreated
Sample04 UNKN
2
Treated
Sample05 UNKN
3
Untreated
Sample06 UNKN
3
Treated
Sample07 UNKN
4
Untreated
Sample08 UNKN
4
Treated
Sample09 UNKN
5
Untreated
Sample10 UNKN
5
Treated
Standard1 STD
256
Standard2 STD
64
Standard3 STD
16
Standard4 STD
4
Standard5 STD
1
Water
NTC
Sample properties files can be tab delimited text, csv, xls or xlsx files. They contain one data table
starting with a header row. The header row must match the first six column headers of the example
file exactly and in the same order. Sample name and type* have to be filled in, the other four
columns can be left empty. Custom sample properties like Pairing or Treatment are provided after
these six fixed columns. Add one column per custom property, use the property name as column
header and provide values where appropriate. Do not create empty lines before the end of your list.
* The following types are recognized: UNKN (unknown), STD (standard), POSITIVE_CONTROL, MINUS_RT,
NO_AMPLIFICATION, NTC (no template control). Use UNKN for your samples of interest, use STD for samples
from a standard series. For STD samples, you have to specify the quantity (= concentration).
Now you have to tell qbase+ which sample annotation you want to import from your samples file:
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In our case we can import Quantities but this is not required since qbase+ has already read this info
directly from the run files during data import. But we definitely need to import the Custom
properties since they are not part of the run files. The Treatment property tells qbase+ which
samples belong to the group of control samples and which samples belong to the group of treated
samples.
Click Next.
4.4. The Run annotation page
All annotations can be edited after import via the Run annotation page. Editing of Cq values is
explicitly not supported by qbase+.
The run annotation can be reviewed, corrected and completed by manual editing. In cases where
runs have the same layout (for either samples or targets) as a previously annotated run, that layout
can simply be copied from the annotated run to the unannotated run.
Click Next.
4.5. The Aim page
On the Aim page you tell the software what type of analysis you want to do. Different types of
analyses require different parameters, parameter settings and different calculations. By selecting the
proper analysis type, qbase+ will only show the relevant parameters and parameter settings.
There are 5 different analysis types to choose from:


Gene expression analysis: most common analysis type. It is the quantification of mRNAs that
are the result of the transcription (expression) of genes. Quantification is done relatively
comparing mRNA levels in two or more groups of samples (typically treated versus control).
Copy number analysis: the study of copy number variation (duplication/deletion) of certain
regions in the DNA. Based on comparison with genes with known copy number.
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


Assay validation: evaluation of the performance of a qPCR assay. The success of a qPCR
depends entirely on the specificity and efficiency of the amplification. Specificity and
efficiency are measured based on samples containing known amounts of the target.
Selection of reference genes: selection of the best (most stable) references from a set of
potential reference targets. The usage of reference targets with invariant expression levels in
the studied samples is essential for doing accurate qPCR. These genes are used as internal
references for normalization (see chapter 5).
Other: any other application (e.g. ChIP-qPCR). By selecting you will exit the wizard and
continue the analysis in the fully flexible expert mode.
Click Next (or Finish if you have selected Other).
4.6. The Technical quality control page
4.6.1. Technical replicates
Technical replicates are automatically recognized by qbase+ since they are located in different PCR
wells but they have an identical sample and target name. qbase+ automatically calculates the
average Cq of technical replicates and uses this in further calculations.
4.6.2. Checking the quality of the data
On this page you can define the minimum requirements for a well to be included in the calculations:


maximum allowed difference in Cq values between technical replicates: the default is 0.5
which means that the difference in Cq value between the replicate with the highest Cq value
and the replicate with the lowest Cq value must be smaller than 0.5 cycles. A well performed
qPCR experiment should have technical replicates with very similar Cq values. Technical
replicates with variable Cq values will result in a significant bias and large error bars.
minimum allowed difference in Cq value between the sample with the highest Cq value
and the negative control with the lowest Cq value: the default is 5 which means that
negative controls should be more than 5 cycles away from the sample of interest.
Amplification in a NTC sample indicates contamination or formation of primer dimers. Such
problems can be ignored as long as the difference in Cq value between the NTC and the
samples is sufficiently large. For example, a Cq value difference of 5 corresponds to a fold
difference of 32, indicating that approximately 3% of the signal in the samples of interest
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
may be caused by contamination. This is well below the technical error on PCR replicates.
Smaller differences between NTC and samples of interest should be avoided.
allowed range of Cq values for positive controls
Wells that do not meet one of these criteria are flagged but not automatically excluded. Wells that
do not have a signal (typically negative controls) are automatically excluded. Excluded means that
the data are ignored in the calculations. You can see flagged and excluded data by ticking the Show
details… options and clicking Next.
4.7. Viewing flagged and excluded wells
If you ticked Show details and manually excluded bad replicates and Show details for positive and
negative controls, qbase+ will open the results of the quality check for the replicates and the
controls on two different tabs. These tabs show lists of samples that failed quality control.
When you open one of these tabs you can get an overview of the flagged or the excluded wells.
When the difference in Cq between technical replicates exceeds 0.5, the wells end up in the flagged
list. They are included in calculations.
If you want to exclude them from calculations you can remove the tick of the well and the well will
be moved to the list of excluded wells.
Important: replicate wells should only be excluded if there is a good reason for it (e.g. abnormal
melt curve, no sample added). When in doubt, keep all replicates! The higher replicate variability
will simply result in a larger propagated error on the final result.
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The only wells that are automatically excluded are wells without a Cq value (no tick and displayed in
grey). These data points, like those that have been manually excluded, will not be used for
calculations. In contrast to manually excluded data points they cannot be re-included in the
calculations because they don’t have a tick box. Manually excluded wells have an unticked box, by
ticking it you can re-include them in the calculations.
The wells in the list that are ticked and displayed in black are included in the calculations. If you
want to exclude them you have to remove the tick.
4.8. The Amplification efficiencies page
4.8.1. Calculations based on amplification efficiencies
Classic method
Qbase+
∑𝑛𝑖=1 𝐶𝑞𝑖
∆𝐶𝑞 = 𝐶𝑞𝑠𝑎𝑚𝑝𝑙𝑒𝐴 − 𝐶𝑞𝑠𝑎𝑚𝑝𝑙𝑒𝐵
̅̅ − 𝐶𝑞𝑠𝑎𝑚𝑝𝑙𝑒𝐴
∆𝐶𝑞 =
− 𝐶𝑞𝑠𝑎𝑚𝑝𝑙𝑒𝐴 = ̅̅
𝐶𝑞
𝑛
with n = number of samples
𝑅𝑄𝐴 𝑣𝑠 𝐵 = 2−∆𝐶𝑞
𝑅𝑄𝐴 = 𝐸 ∆𝐶𝑞
In the classic method ∆Cq is the difference in Cq values between two samples, typically control and
treated. The Relative Quantity (RQ) is then calculated assuming 100% amplification efficiency (E = 2)
for each gene. The formula of the RQ uses -∆Cq instead of ∆Cq because in this way higher expression
in sample A compared to sample B will result in a high RQ (RQ > 1) while lower expression in sample
A compared to sample B will result in a small RQ (RQ < 1).
Qbase+ calculates the amplification efficiency (E) for each gene. These gene-specific amplification
efficiencies are used to calculate an RQ for each gene in each sample by comparing the Cq of a given
sample with the average Cq across all samples for that gene. So in qbase+ ∆Cq is the difference
between the Cq value of a gene in a given sample and the average Cq value of that gene across all
samples. The Cq is subtracted from the average because in this way high expression will result in a
positive ∆Cq and low expression in a negative ∆Cq.
4.8.2. Setting the amplification efficiency strategy
In the amplification efficiencies section you can choose between two strategies:
1. All target genes have the same amplification efficiency
By default the amplification efficiency is set to 2 (with a standard error of 0) but the user can change
these values. These are the values that are used in the classic ∆∆Cq method, which assumes that all
target genes amplify with the same optimal PCR efficiency of 100%.
When you change the value, note that you to have to enter the amplification efficiency as an
efficiency value + 1, e.g. an E value of 1.95 for 95% or 0.95 efficiency.
2. Target gene specific amplification efficiencies
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When you choose this option, you can either let qbase+ calculate target specific amplification
efficiencies if serial dilutions included for all the targets as is the case in our example. The serial
dilution allow to generate a standard curve, and the slope of this curve gives an estimate of the
amplification efficiency. The calculated efficiencies and corresponding errors are immediately shown
in the table. This is what you normally do the first time that you use a primer pair for detecting a
target.
In all following experiments, you can then manually enter these efficiencies as custom efficiencies.
You can manually enter an efficiency value and a standard error for each target.
4.8.3. Estimation of amplification efficiencies
The gold standard method for PCR efficiency estimation is a serial dilution of representative
template, preferably a mixture of cDNA from all your samples. The Cq values of the dilution series
are plotted against the quantity of template used in the PCR reaction. Linear regression is used to
fit a standard curve to the data. The slope of the standard curve for a specific gene is calculated.
The PCR efficiency E is calculated from the slope of the standard curve as follows:
E = 10 (-1/slope)
with an E of 2 being perfect, indicating 100% efficiency.
The linear regression also calculates the error on the estimated amplification efficiency and the
software will propagate these errors during conversion of Cqs to RQs.
4.8.4. Recommendations regarding amplification efficiencies
Including a dilution series is only required the first time that you use a primer pair for a target. You
calculate the efficiency based on this dilution series and use the same efficiency in all following runs.
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Use a representative template to create the dilution series, preferably a mixture of cDNA from all
your samples to ensure that you have signals for each gene. If you use a single sample, some of the
genes might not be expressed in this sample. If one of the genes has low expression levels in all
samples, you can use a synthetic template, which can be abundantly generated.
It is recommended to aim for E values in the range of 1.90 – 2.10 with standard errors typically
below 0.01. When the efficiencies of all genes fall in this range, it is not necessary to take them into
account: you can then use the same efficiency for all genes (E = 2 and SE = 0). If the efficiency is
below 1.9 you have to either use that efficiency in the next runs or design a new, more efficient
primer pair.
Do make sure that in the next runs you use cDNA concentrations that fall within the standard curve
otherwise the calculated efficiencies will not be representative.
There is a free algorithm, LinRegPCR, that provide a reliable estimate of the amplification efficiency
directly based on the amplification curve (without the use of a dilution series). However, most other
algorithms fail in this respect. If you want to use LinRegPCR, export the estimated efficiencies to an
RDML file. You can import this file in qbase+ and use the amplification efficiencies for RQ calculations.
4.9. The Normalization page
4.9.1. Calculating normalized relative quantities (NRQ)
Several factors are responsible for variability that has no biological relevance (noise) between
samples in qPCR experiments e.g. differences in:
- amount of cDNA
- RNA integrity
- enzyme efficiencies
Qbase+ uses housekeeping genes for normalization. Housekeeping genes are genes with constant
expression levels in all cell types, tissues and conditions that are studied in the experiment. In qbase+
these housekeeping genes are called reference targets.
Classic method
Qbase+
𝑅𝑄𝐴 𝑣𝑠 𝐵 = 2−∆𝐶𝑞
𝑅𝑄𝐴 = 𝐸 ∆𝐶𝑞
𝑁𝑅𝑄 = 2−∆∆𝐶𝑞 =
2
∆𝐶𝑞𝑟𝑒𝑓
2∆𝐶𝑞𝑡𝑜𝑖
with toi: target of interest
ref: reference target
𝑅𝑄
= 𝑅𝑄 𝑡𝑜𝑖
𝑟𝑒𝑓
∆𝐶𝑞𝑡𝑜𝑖
𝑁𝑅𝑄 =
𝐸𝑡𝑜𝑖
∆𝐶𝑞
𝐸𝑟𝑒𝑓 𝑟𝑒𝑓
=
𝑅𝑄𝑡𝑜𝑖
𝑅𝑄𝑟𝑒𝑓
For multiple reference genes:
𝑅𝑄𝑡𝑜𝑖
𝑁𝑅𝑄 =
𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑚𝑒𝑎𝑛 (𝑅𝑄𝑟𝑒𝑓𝑠 )
𝑁𝐹 =
1
𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑚𝑒𝑎𝑛 (𝑅𝑄𝑟𝑒𝑓𝑠 )
The housekeeping genes are measured in all samples along with the genes of interest. In theory (if
there was no variability), each housekeeping gene should have identical RQ values in all samples. In
18
reality, the factors listed above are responsible for variation in the expression levels of the
housekeeping genes. However, this variation is a direct measure of the noise between the samples
and can be used to calculate a normalization factor (NF = factor to be multiplied to the observed RQ
values so that the expression levels of the housekeeping genes are equalized across samples) for
each sample. These normalization factors are then used to adjust the RQ values of the genes of
interest accordingly so that the variability is eliminated.
As you can see, qbase+ uses the geometric mean instead of the arithmetic mean, as the geometric
mean controls better for expression differences between genes. The geometric mean is based on the
product of the individual values (as opposed to the arithmetic mean which uses their sum).
3
Geometric mean of 3 reference genes = √(𝑅𝑄1 𝑥 𝑅𝑄2 𝑥 𝑅𝑄3 )
Arithmetic mean of 3 reference genes =
𝑅𝑄1 + 𝑅𝑄2 + 𝑅𝑄3
3
A geometric mean is better to compare items that have different numeric ranges. For example, the
geometric mean can give a meaningful "average" to compare two genes, one with a RQ between 1
and 1.1 in different samples and one with a RQ between 1 and 4. If an arithmetic mean is used, the
second gene is given more weight because its numeric range is larger.
4.9.2. Defining the normalization strategy
You can specify the normalization strategy you want to use on the Normalization method page:
The Reference genes normalization strategy is doing the normalization based on the RQ values of the
housekeeping genes (see section 3.9.6. for a description of how to choose the ideal housekeeping
genes).
The Global mean normalization strategy calculates normalization factors based on the RQ values of
all genes instead of only using the reference genes. This strategy is recommended for experiments
with more than 50 random genes. Random means that the genes are randomly distributed over all
biological pathways: so they do not belong all to the same pathway, nor do they all encode proteins
with a similar function. In experiments where more than 50 random genes are measured, global
mean normalization outperforms reference gene normalization. The Only samples detected in all
samples option performs normalization based of the RQs of all genes that are measured in all
19
samples (i.e. that the samples have in common). It is a variant on the global mean normalization
strategy and should be used for the same type of experiments (more than 50 random genes are
measured).
The Custom value normalization is used for specific study types. This strategy allows users to provide
custom normalization factors such as for example the cell count.
None means that you choose to do no normalization at all. This option should only be used for single
cell qPCR. In all other cases it is strongly recommended to normalize your data.
4.9.3. Appointing reference genes
Before you can use them for normalization you have to indicate which targets should be used as
reference genes (upon import qbase+ treats all genes as targets of interest unless you explicitly mark
them as reference genes) on the Normalization method page:
4.9.4. Checking the quality of the reference genes
For each appointed reference gene, qbase+ calculates two indicators of expression stability
 M (geNorm expression stability value): calculated based on the pairwise variations of the
reference genes. For every combination of two reference genes, log2-transformed ratios of
RQs are calculated for each sample. The pairwise variation (V) for each combination of two
reference genes is the standard deviation of these log2 RQ ratios.

The M-value of a reference gene is then calculated as the arithmetic mean of all pairwise
variations of all combinations in which this reference gene participates.
CV (coefficient of variation): the ratio of the standard deviation of the NRQs of a reference
gene over all samples to the mean NRQ of that reference gene.
The default limits for M and CV were determined by checking M-values and CVs for established
reference genes in 85 samples belonging to 5 different human tissue groups in a pilot experiment
that was done by Biogazelle. The results showed that CV and M-values lower than 0.2 and 0.5
respectively are typical for stably expressed reference genes in homogeneous samples. These are the
values that were chosen as the limits for CV and M in qbase+.
However, for more heterogeneous sets of samples, the mean CV and M-values can increase to 0.5
and 1 respectively. So if you have heterogeneous samples it is acceptable to increase the limits for CV
and M to these values. Furthermore, it was shown that the variability in fly and plant samples is
20
higher than in samples from other organisms. So for fly and plants it is recommended to use 1 and
0.5 as the default limits for M and CV. These are the final limits for M and CV though, Biogazelle
advises strongly against increasing the limits for M and CV above 1 and 0.5.
M and CV values of the appointed reference genes are automatically calculated by qbase+ and shown
on the Normalization method page:
The red color indicates that the M-values and the CVs are too high (compared to the limits set by
Biogazelle) for all reference targets. In such cases it is advised to exclude the worst reference target
(the one with the highest M value) from the analysis by unticking the box in front of its name.
If the M and CV values of reference genes are lower than the limits they are highlighted in green.
Note that CV and M-values will not be calculated if there are samples that have missing data for one
of the reference genes: reference genes have to be expressed in all samples! If you have missing data
for reference genes either delete the sample(s) or untick the reference gene.
4.9.5. Recommendations regarding reference genes
It is recommended to use at least three reference genes. In theory, two reference genes are
sufficient but it’s always good to a have a backup in case something goes wrong. If you use only one
reference gene then you cannot check its stability.
You can place the reference genes on other plates than the genes of interest.
The best way of choosing reference genes is to choose a set of 10 candidate reference genes in
Genevestigator and perform a geNorm pilot experiment to select the most stable genes among
these candidates (see section 5).
4.10. The Scaling page
Qbase+ allows you to rescale the NRQ values according to various methods. Rescaling means that
you calculate NRQ values relative to a specified reference level. The scaling only changes the scale
of the data (so the numbers will be different), but not the fold changes between the samples.
However, the choice of reference does have a clear effect on the error bars. The default scaling
method uses the average expression level of a gene across all samples and this is also the method
that will result in the smallest error. Alternative methods are scaling to:

lowest expression level of a gene
21





average expression level of a gene across all samples
highest expression level of a gene
expression level of a specific sample (e.g. untreated control)
average expression level of a certain group (e.g. all control samples): this is often how people
want to visualize their results. If this is what you want you have to indicate which group is to
be used for the scaling.
positive control is a scaling strategy that is only used for copy number analysis, not for gene
expression analysis. The positive control is a calibrator: a sample with known copy number.
Scaling works as follows: if you scale to a sample you will see that the rescaled expression level of
that sample equals 1. Similarly, if you scale to a group, the average rescaled expression level
across all samples of that group will equal 1.
4.11. The Analysis page
On this page you can choose to:




View the relative expression levels (= scaled NRQs) of each gene separately (recommended)
in a bar chart per gene
View the relative expression levels of all genes of interest on the same bar chart. You have
to realize, however, that you can use this view to see if these genes show the same
expression pattern but you cannot directly compare the heights of the different genes
because each gene is independently rescaled!
Export the rescaled NRQs for further analysis outside qbase+ (e.g. in GraphPad Prism)
Start the Statistics wizard to statistically analyze the data
Make your choice and click the Finish button at the bottom of the page.
4.11.1. Single gene bar charts
The Target select box allows you to select the gene you want to view the expression levels of.
Relative expression levels are shown for each sample separately. Error bars are shown and represent
a combination of the errors generated in each step in the analysis:
22


Difference between technical replicates
Errors on amplification efficiencies: these errors represent how much the actual data of the
standard dilution series deviates from the standard curve that is calculated by linear
regression.
These errors are then propagated in the next steps of the analysis. The error bars represent the
technical noise in the experiment. Large error bars, e.g. Sample05, mean that you cannot be sure
that the expression level that you see here is the real expression level of the Palm gene in this
sample. The two replicates of this sample had very different Cq values and there is no way to choose
which of the two replicates is correct. These errors are not used for the statistical analysis.
If a grouping property was specified, it is possible to group the results in the bar charts. This
functionality facilitates visual interpretation of results when multiple groups need to be compared.
After grouping the samples you can plot individual samples as shown above but you can also choose
to plot the average expression levels of each group as shown below. The error bars that you see in
the latter plot represent biological variation. The errors of the individual samples, which you saw in
the former bar charts are not used on this chart since they represent technical variation. The error
bars of the group averages are calculated based on the expression levels of the biological replicates
and represent the range that will contain with 95% certainty the real average expression level in this
group of samples.
23
The nice characteristic of 95% confidence intervals is the following:
 if the 95% confidence intervals of the two groups do not overlap you are sure that the
expression levels in the two groups are significantly different, in other words that the gene is
differentially expressed.
 You can, however, not reverse this rule: if the confidence intervals do overlap you cannot say
that you are sure that the expression levels are the same. You simply don’t know if the gene
is differentially expressed or not.
These rules only apply when error bars represent 95% confidence intervals as they do here.
Switching the Y-axis to Logarithmic only changes the scale of the Y-axis, not the expression levels so
setting the Y-axis in logarithmic scale does not mean that you log transform the NRQs ! Switching
the Y-axis to a logarithmic scale can be helpful if you have very large differences in expression
between different samples.
24
4.12. Leaving and returning to the analysis wizard
Once you have created target bar charts you have quit the wizard and you are in the regular qbase+
version. If you want to return to the wizard e.g. to repeat the analysis on the data of another qPCR
experiment, you simply click the Launch wizard button in the top tool bar.
If you’re in the wizard and you want to leave it to do some steps in the regular qbase+ interface click
the Close wizard button in the top tool bar
25
5. The statistics wizard
Once you generate target bar charts you leave the Analysis wizard and you go to the regular qbase+
interface. Suppose that you want to perform a statistical test to prove that the difference in
expression that you see in the target chart is significant.
In that case you have to open the Statistics wizard. You can open it from the Analysis wizard by
selecting Perform statistical analysis
But you can also open it in the regular qbase+ interface. In the Project Explorer (window at the left):
 expand the project you want to work in (in the example: Project1)
 expand the Experiments folder in the project
 expand the experiment you want to analyze (in the example: GeneExpression)
 expand the Analysis section
 expand the Statistics section
 double click Stat wizard
In most cases the experiment and the project you want to analyze are the ones you are working in,
e.g. the experiment for which you generated a target bar chart. Then they will already be expanded
and you only have to perform the two last steps (Statistics -> Stat wizard).
Double clicking Stat wizard will open the Statistics wizard.
The Statistics wizard will choose the appropriate test for analyzing your data (= the CNRQs that you
have generated in qbase+).
26
5.1. The Goal page
First you have to specify the goal of your analysis:
Choose mean comparison to compare groups of samples e.g. to see if gene expression is altered by a
certain treatment.
Target correlation allows you to identify genes that show similar expression patterns (high
expression in the same samples, low expression in the same samples.
Survival analysis allows you to assess to effect of gene expression on the occurrence of an event e.g.
death, injury, sickness, recovery from sickness.
In gene expression analysis, we almost always want to compare groups of samples. So in most cases
the mean comparison goal is chosen. The selected goal guides you to the statistical test that will be
applied by the wizard. At the right you see list of possible statistical tests that can be used for the
goal that you have selected. A further description of your data will help the wizard decide which of
these tests is the most appropriate.
5.2. The Define your groups page
You have to tell qbase+ which groups you want to compare by selecting the appropriate grouping
property. The direction of the comparison (A/B or B/A) can be altered by changing the Target scaling
options. The group that is chosen as a reference for scaling (the group whose average expression is
set to 1 by the scaling) will be used as denominator in the comparison.
At this point qbase+ knows how many groups you want to compare. The number of groups
determines the statistical tests you can use to compare the means of the groups:

2 groups: t-test, Mann-Whitney, Wilcoxon signed rank test
27

more than 2 groups: ANOVA
5.3 The Targets page
You have to indicate which genes you want to include in the analysis, i.e. for which genes you want
to know if they are differentially expressed or not. Typically you only want to test the targets of
interest.
5.4 The Settings page
On this page you have to describe the characteristics of your data sets, allowing qbase+ to choose
the appropriate test for your data.
28
5.5 Statistical tests used in qbase+ for comparison of means
Mean comparison allows you to compare the mean expression levels of one or more target genes in
different groups of samples, e.g. you have a group of treated samples and a group of untreated
samples and you want to assess which of your target genes are differentially expressed (DE). A gene
is called DE if the mean expression level of the gene in the treated samples is significantly different
from its mean expression level in the untreated samples.
The Mean comparison goal leads you to the following tests:
• Unpaired t-test
• Paired t-test
• Mann-Whitney test
• Wilcoxon signed rank test
• One-way ANOVA
5.5.1. General outline of all statistical tests for comparison of the means
As you can see in the list above, you can do various statistical tests to identify DE genes. The test you
choose depends on the characteristics of your data. For each gene you perform a separate statistical
test.
All statistical tests that are described in this section follow the same pattern:
1. Generate 2 hypotheses:
Null hypothesis H0 which always states that there is no effect / no difference
Alternative hypothesis Ha which always states that there is an effect / difference
2. To check if H0 is true, you calculate a statistic using your data. Depending on the statistical test
that you are doing, the formula for the statistic will differ but in any case the formula will use your
data as input and generate a value as output.
In most tests: the higher the difference -> the more the value of the statistic deviates from 0
3. Choose the significance level (typically α = 0.05) to determine how confident you want to be about
the outcome of the test. The significance level represents the probability that you reject H0, saying
that there is a difference while in reality there is not (= false positive). So if you choose α = 0.05, it
means that you allow a 5% chance of incorrectly rejecting H0.
4. Taking into account the significance level and the degrees of freedom (=n-1 in most cases), you can
convert the value of the statistic into a p-value. Each statistic follows a certain distribution. Software
29
is able to calculate the distribution of a statistic with certain degrees of freedom. Below you see the
distribution of the t-statistic (calculated in a t-test) given H0 is true, for different degrees of freedom:
You see that the degrees of freedom have a substantial impact on the shape of the distribution.
The t-statistic is plotted on the X-axis, the probability that the t-statistic comes from this distribution
is plotted on the Y-axis. When H0 is true the t-statistic equals 0, so this is the center of the
distribution, the value with the highest probability. The more the t-statistic deviates from 0 (the
further it is located on the X-axis), the less likely it is that it comes from this distribution (the lower
the value on the Y-axis), this distribution being the distribution that assumes that H0 is true. So the
lower the probability, the less likely it is that H0 is true.
The significance level is the sum of the probabilities of t-statistics that are located in the tails of this
distribution, giving a total probability of 0.05 if you choose α = 0.05. These t-statistics are far away
from the center: if your t-statistic falls in this range it is probably coming from a different distribution
(where H0 is not true) but there still is a small chance that it is coming from this distribution and that
you’re making a mistake.
Software can compute the corresponding thresholds for the t-statistic. For instance, for 15 degrees
of freedom and α = 0.05, the threshold values (the boundaries between H0 and Ha) for the t-statistic
are 2.132 and -2.132. In 95% of the cases where H0 is true the t-statistic will fall in this range.
30
If the t-statistic that you have calculated falls between the thresholds, you have no evidence to reject
H0. If the t-statistics falls out of this range, you can reject H0 and accept Ha but there is a 5% chance
that you are wrong.
Similarly, software can link a t-statistic to a p-value by calculating the area under the curve.
P-values reflect to what extent the statistic is higher than you would expect if H0 were true.
5. Interpret the p-value.
p < α: the value of the statistic that you calculated is very different from the value you would expect
if H0 were true i.e. there is no effect. This means that you have a good argument for rejecting H0 and
saying that there is an effect.
! The effect may be statistically significant but this doesn’t necessarily mean that it’s biologically
relevant.
p > α: you have no good arguments to reject H0, to say that there is an effect.
! This doesn’t necessarily mean that there is no effect you just don’t have sufficient data to prove
that there is.
5.5.2. Parametric versus non-parametric tests
The distribution (log-normal or not) is a very important characteristic to select the proper statistical
test. Log normal means that the data is normally distributed when log-transformed.
Data can be normally distributed or non-normally distributed. Plotting normally distributed data as
a histogram with ranges of data values on the X- axis and the number of data values that fall in each
range on the Y-axis, creates a bell-shaped curve when the data comes from a normal distribution.
http://www.mathsisfun.com
The fact that this bell-shape is nicely symmetrical has important implications for the data, e.g. the
mean is a good representative of the center of the data set and the standard deviation is a good
representative for the spread of the data. In non-normal distributions this is not the case.
The t-statistic of a t-test is calculated based on the mean and the standard deviation of the data. As a
result, t-test are only appropriate to test data that comes from a normal distribution. If the data
comes from a non-normal distribution you have to use a non-parametric test. Non-parametric tests
make a ranking of the data, ordering the data values from smallest to largest or vice versa and
calculate a statistic based on this ranking. This means that they make no assumptions regarding the
distribution of the data and can be used on any kind of data set. The non-parametric alternative of a
t-test is the Mann-Whitney test.
31
Data that comes from a non-normal distribution may be transformed in such a way that the
transformed data do follow a normal distribution. One of the most used transformations for this is
the log transformation. Therefore, qbase+ will automatically log10 transform the NRQs prior to doing
statistics. For easy interpretation of the results, values are re-transformed to linear scale by taking
the anti-logarithm.
5.5.3. How do you know if your data set comes from a normal distribution?
In most cases you don’t know but there is one simple rule you can follow.
When you have measured many biological replicates (minimal 24 for each group), you may
automatically assume that the data comes from a normal distribution and perform a t-test.
For sample sizes in the range of 7-23 biological replicates per group, you may not assume that the
data comes from a normal distribution. There are statistical tests to check whether data is normally
distributed, e.g. the Shapiro Wilk test or the D’Agostino Pearson omnibus test, but they assume a
minimum of 7 biological replicates per group and they are not implemented in qbase+. However, you
can export the log NRQs and do these tests in GraphPad Prism to check normality of the data. There
are several exercises on the wiki that perform this kind of analysis. Check out the statistical analysis
section in http://wiki.bits.vib.be/index.php/Analyzing_gene_expression_data_in_qbase%2B and the
analyzing the data section in http://wiki.bits.vib.be/index.php/Copying_data_annotation.
For sample sizes in the range of 4-6 biological replicates per group, you cannot check the normality
of the data. If you use assume that they are normally distributed and you use a parametric test while
in fact the data are drawn from a non log-normal distribution, the p-value will be too low. In other
words you will generate false positives, saying the genes are DE while in reality they are not. On the
other hand, if you assume that the data are not coming from a normal distribution and use a
nonparametric test while in the fact the data does come from a normal distribution, the p values will
be too high. Your test will be too stringent saying that some genes are not DE while in fact they are
(false negatives). In most cases, scientists prefer false negatives over false positives. Therefore, if
you’re not sure if the data is log-normal distributed or not, it is safer to choose a non-parametric
test. It can be too stringent if the data is normally distributed but it’s generally considered better to
be too stringent than to generate false positives.
For sample sizes smaller than 4 biological replicates per group, there is only one valid option: a ttest. Non-parametric tests for sample sizes smaller than 4 will always result in a p-value > 0.05.
5.5.4. Assumptions of parametric tests
Data are drawn from a normal distribution. If data are not normally distributed and you can’t find a
transformation to make them normally distributed, you use the non-parametric Mann Whitney test.
The means of both distributions can be different (this is what you test) but the variance is assumed
the same between the two groups. However, in the qbase+ implementation of the t-test no equal
variances are assumed (for more information: http://wolfweb.unr.edu/~ldyer/classes/396/PSE.pdf).
5.5.5. T-test for comparing the means of two groups
If you want to compare the means of two different groups of samples, e.g. a group of wild type
samples and a group of mutant samples, you need a two-sample t-test.
32
Hypotheses
H0 : µwt = µmut (no difference) versus Ha : µwt ≠ µmut (difference)
t-statistic
𝑡=
̅̅̅̅̅̅̅̅̅̅̅̅
(𝑁𝑅𝑄
𝑁𝑅𝑄𝑤𝑡 )
𝑚𝑢𝑡 − ̅̅̅̅̅̅̅̅̅̅
𝑠𝑡𝑒
with 𝑠𝑡𝑒 = √ 𝑠 2 (
𝑛
1
𝑚𝑢𝑡
+
1
𝑛𝑤𝑡
) and 𝑑 = 𝑛𝑚𝑢𝑡 + 𝑛𝑤𝑡 − 2 degrees of freedom
𝑠 2 : variance of mutant or wt group (remember that the variances of both groups are assumed equal)
nmut and nwt are the number of subjects in each group
̅̅̅̅̅̅̅̅̅̅
̅̅̅̅̅̅̅̅̅̅̅
If H0 is true (𝑁𝑅𝑄
𝑚𝑢𝑡 = 𝑁𝑅𝑄𝑤𝑡 ) then t = 0. So the more t deviates from 0, the less likely H0 is.
5.5.6. Mann Whitney test is a non-parametric test to compare two groups
Hypotheses
H0: the probability distributions of both groups are equal
Ha: the probability distributions of both groups are not equal
U statistic
The Mann Whitney test uses the following procedure:
1. the data values of the two groups are combined in one big data set
2. the data values are ordered from smallest to highest (value column)
3. each value gets a rank that reflects the order e.g. the smallest value gets rank 1, the
smallest but one gets rank 2… (rank column)
4. you do keep track of the group a value comes from (group column)
Let’s start from a simple example of gene expression levels:
wt
2
1.6
1.2
mutant
4
3.6
3.2
For each gene separately, all data values are ranked:
rank
1
2
3
4
5
6
value
1.2
1.6
2
3.2
3.6
4
group
wt
wt
wt
mut
mut
mut
Next, scores are added. Every wt is given one point for every mut that is above it. Every mut is given
one point for every wt group that is above it.
33
rank
1
2
3
4
5
6
value
1.2
1.6
2
3.2
3.6
4
group
wt
wt
wt
mut
mut
mut
score
0
0
0
3
3
3
Scores for mut and wt are added and the smallest of those two values is taken. This value is called U.
Uwt = 0 + 0 + 0 = 0
Umut = 3 + 3 + 3 = 9
U=0
H0 is not true (the distributions are not equal as in the example above) => U is 0
So the more U deviates from 0, the more likely H0 is.
Note: when you do a Mann Whitney test on multiple data sets that are based on a low number of
samples, you will often see exactly the same p-values popping up. That’s normal because when
there are a low number of samples, there are not that many possible ranking scenarios and different
data sets can easily lead to the same ranking.
5.5.7. ANOVA for comparison of more than two groups
To compare three or more groups you use ANOVA. If you have more than two groups, it is not ok to
do multiple pairwise comparisons with a t-test. You have to analyze all the groups at once with oneway ANOVA and after that you can do pairwise comparisons using special follow-up tests.
Hypotheses
H0 : no difference between the means versus Ha : at least two means are different
F-statistic
The ANOVA compares the difference between the groups to the variability within the groups. To this
end, the F-statistic is calculated: the ratio of the variance between the means of the groups to the
variance within the groups:
𝐹=
𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑔𝑟𝑜𝑢𝑝𝑠 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛
𝑤𝑖𝑡ℎ𝑖𝑛 𝑔𝑟𝑜𝑢𝑝𝑠 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛
=
̅̅̅̅̅̅̅̅̅ ̅̅̅̅̅̅̅ 2
∑𝑘
𝑖=1 𝑛𝑖 (𝑁𝑅𝑄𝑖 − 𝑁𝑅𝑄 )
(𝑘−1)
2
𝑘,𝑛𝑖
̅̅̅̅̅̅̅̅̅𝑖 )
∑
(𝑁𝑅𝑄𝑖𝑗 − 𝑁𝑅𝑄
𝑖=1,𝑗=1
(𝑁−𝑘)
where
̅̅̅̅̅̅̅
𝑁𝑅𝑄𝑖 is the sample mean in the ith group
ni is the number of observations in the ith group
̅̅̅̅̅̅
𝑁𝑅𝑄 is the overall mean of the data (over all groups)
k is the number of groups
N is the total number of data points (over all groups)
If the groups are drawn from populations with the same mean, the variance between the groups
should be lower than or equal to the variance within the groups so F would be close to 1. A high Fstatistic therefore implies that the groups are drawn from populations with different means.
34
5.5.8. Follow up tests to ANOVA
Note that the ANOVA will only indicate if there is a difference between the groups but not which
group differs from which, you need to do an additional test, called a post test e.g. the Tukey-Kramer
post-test. This test will find means that are significantly different from each other by comparing all
possible pairs of means. The differences between post tests and a regular t-test are the following:


the post tests take into account the scatter in all groups. A t-test only uses the variation of
the two groups it compares. The former gives you a more precise value for the variation,
which is reflected in more degrees of freedom and thus more power to detect differences.
the post tests perform a multiple testing correction, making the significance level apply for
the whole set of comparisons. The t-test uses a significance level that only applies for each
comparison individually, which will lead to a much higher number of false positives (= the
test concludes that two groups are different while in fact they are not)
The Tukey-Kramer test will compare all possible pairs of means.
Assumptions: data are drawn from a normal distribution
groups have equal variances
Statistic:
Tukey's test calculates a q statistic
𝑞=
̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
𝑁𝑅𝑄𝑔𝑟𝑜𝑢𝑝𝑏 )
(𝑁𝑅𝑄
𝑔𝑟𝑜𝑢𝑝𝑎 − ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
𝑠𝑡𝑒
where
̅̅̅̅̅̅̅̅̅̅̅̅̅̅
𝑁𝑅𝑄𝑔𝑟𝑜𝑢𝑝𝑎 the larger of the two means being compared
̅̅̅̅̅̅̅̅̅̅̅̅̅̅
𝑁𝑅𝑄𝑔𝑟𝑜𝑢𝑝𝑏 the smaller of the two means being compared
1
1
2
𝑛𝑎
𝑠𝑡𝑒 = √(𝑤𝑖𝑡ℎ𝑖𝑛 𝑔𝑟𝑜𝑢𝑝𝑠 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛 ( (
+
1
𝑛𝑏
))) =
√
𝑘,𝑛
2 1
2
𝑖
̅̅̅̅̅̅̅𝑖 ) ( (
∑𝑖=1,𝑗=1
(𝑁𝑅𝑄𝑖𝑗 − 𝑁𝑅𝑄
1
1
+ ))
𝑛𝑎 𝑛𝑏
𝑁−𝑘
na and nb are the number of samples in each group
N is the total number of samples and k is the number of groups
5.5.9. Unpaired versus paired data
In an unpaired experiment, you have two separate sets of samples from different individuals
e.g. samples from 20 patients. At the start of the experiment you randomly pick 10 patients to
receive treatment and 10 patients to receive placebo. You sample all patients two weeks after
treatment. For such experiments you need an unpaired t-test.
In a paired experiment, you use the same individuals for all experimental conditions e.g. samples
from 20 patients. This time you sample all patients before treatment and after two weeks treatment.
Other examples of paired data: you measure multiple tissues of the same individual (e.g. right eye
and left eye…), you measure individuals that belong to the same group (e.g. persons belonging to the
same family, patients going to the same doctor…). The benefit of this approach is that the variability
among subjects has less influence on the outcome of the test. The downside is that such data have to
be analyzed by specific statistical tests that take the pairing into account, like the paired t-test or a
Wilcoxon signed rank test.
35
These tests will not calculate a statistic based on the data but on pairwise differences of data values
coming from the same or related individuals.
5.5.10. The paired t-test is a parametric test for comparing two groups of paired data
Assumptions of the paired t-test
The test assumes that the differences between pairs follow a normal distribution. The paired t-test
does not assume that the two groups of data are sampled from populations with equal variances!
Hypotheses
H0: the mean difference between the pairs is equal to 0
Ha: the mean difference between the pairs is not equal to 0
t-statistic
Statistics are calculated in the same way as in a one-sample t-test but instead of a mean, the mean
difference between the pairs is used.
5.5.11. The Wilcoxon matched pairs signed rank test is the non-parametric alternative
The Wilcoxon matched pairs signed rank test ranks the differences between the pairs.
Hypotheses
H0: the median difference between the pairs is equal to 0
Ha: the median difference between the pairs is not equal to 0
W-statistic
Suppose our example comes from a paired experiment:
before
1.2
1.6
2
after
4
3.6
3.2
difference
2.8
2
1.2
The absolute values of the differences between observations are ranked from smallest to largest:
rank
sign
absolute value of the difference
1
+
1.2
2
+
2
3
+
2.8
The ranks of all differences in one direction are summed, and the ranks of all differences in the other
direction are summed. The smaller of these two sums is the test statistic, W.
Wup = 6
Wdown = 0
W=0
If H0 is not true (mean differences between pairs are not equal to 0) then W is 0
So the more W deviates from 0, the more likely H0 is.
5.5.12. Paired tests in qbase+
For a paired analysis (Paired t-test or Wilcoxon signed rank test), two sample properties are required:
a grouping property (to define the groups to compare like in the unpaired statistical analyses) and a
36
pairing property. A pairing value can be a number or a letter combination, and must be identical and
unique for the pair.
5.5.13. One-sided and two-sided p-values
Only if you know the direction of the observed effect (lower or higher in one group compared to the
other) prior to generating the data and performing the statistical test, you can use a one-sided pvalue.
In this case you will test H0 : µwt = µmut (not DE) versus Ha : µwt < µmut (upregulated in mutant)
If you use a significance level (α) of 0.05, a two-sided test allots half of α to test the statistical
significance in one direction and half of α to test statistical significance in the other direction. This
means that .025 is in each tail of the distribution of the t-statistic.
If you are using a significance level of .05 in a one-sided test, all of α is allotted to test the statistical
significance in the direction of interest. This means that .05 is in one tail of the distribution of the tstatistic.
two-sided test
one-sided test
The threshold for rejecting H0 will be lower in the one-sided test than in the two-sided test making
the one-sided test less stringent. That’s why many people prefer the one-sided test (it’s easier to
reach significance) but if you don’t know the observed effect before you generate the data (that is in
almost all cases), a two-sided test is recommended.
5.5.14. Multiple testing correction
You always have to do a correction when you perform multiple tests on the same data set:
 You compare more than two groups
 You have data for multiple genes coming from the same experiment and you want to analyze
each gene individually e.g. checking for differential expression
In these cases you have to correct the calculated p-values to control the false positive rate.
5.5.15. Significance level versus false discovery rate
The significance level α reflects the probability of rejecting H0 while in fact H0 is true. It corresponds to
the number of tests incorrectly rejecting H0 divided by the total number of tests.
By choosing α = 0.05 you allow a 5% chance of saying that there is a difference while in reality there
is not. The more tests you do the more likely it will be that you actually will make that mistake. When
you do 3 tests (each with α = 0.05) the chance of incorrectly rejecting H0 increases from 5% to 14%.
This is why you have to correct for doing multiple tests.
37
The false discovery rate or FDR is the number of tests incorrectly rejecting H0 divided by the total
number of tests rejecting H0. This metric is important when you do many tests on the same data set.
There are two main ways to correct for multiple comparisons: Bonferroni correction or FDR-based
methods. Bonferroni correction simply multiplies the p-values by the number of tests, enlarging the
p-values and making it less likely that they will be smaller than 0.05. However, when you do a large
number of tests this correction becomes too conservative and you have to use one of the FDR-based
methods. Since FDR is the number of tests incorrectly rejecting H0 divided by the total number of
tests rejecting H0 it is a better metric for multiple comparisons. Suppose you set the FDR to 0.05 and
you do 100 tests. The number of tests that are wrong now depends on the number of tests that
reject H0, which will always be a small fraction of the 100 tests. Even if 20 of the 100 tests reject H 0,
still only 1 of them will actually be wrong.
In qbase+, the false discovery rate (FDR) based correction method of Benjamini and Hochberg that is
described in the previous section is implemented.
5.6. Correlation between two targets
Choose the Target correlation goal if you want to assess whether two target genes have similar
expression patterns. You want to test if the two genes have correlated expression patterns, meaning
that their expression changes simultaneously. For instance, if the expression of gene 2 increases
when the expression of gene 1 increases, both genes are positively correlated. If, on the other hand,
expression of gene 2 decreases with an increase in expression of gene 1, both genes are negatively
correlated.
The Target correlation goal leads to the calculation of one of the following measures of correlation:
 Pearson correlation
 Spearman correlation
The Spearman correlation is the non-parametric version of the Pearson correlation.
The correlation always lies between -1 and 1.
 1: perfect positive linear correlation between the genes
They go up in the same samples, they go down in the same samples
 -1: perfect negative linear correlation between the genes
When one gene goes up, the other goes down
 When there is no relation between the genes: the correlation = 0
5.7. Survival analysis
Survival analysis studies the occurrence of events in time. Events are in most cases binary (yes or no)
like death, failure, injury, sickness, recovery from sickness, exceeding a threshold…
Survival analysis answers questions like: How many out of 100 people will survive until 86 years?
What’s a person’s chance of surviving past 20 years? Are there environmental factor that increase or
decrease the death rate... Therefore, qPCR data can be analyzed by survival analysis e.g. the effect of
38
the expression of a gene on the incidence of coronary heart diseases, the effect of gene copy number
on the mortality after myocardial infarctions…
The Survival analysis choice leads to the calculation of Cox proportional hazard, which represents the
relationship between the expression of a gene and a patient’s survival.
5.8. Analysis results
Each analysis is saved in the Statistics section of the Project Explorer with a unique name containing
the type of statistical analysis followed by a serial number. These results can be deleted, renamed
and exported (CSV, XLS or XLSX format). Upon opening a stat result, results are recalculated
instantaneously. Hence, if data have changed, results will reflect that change (e.g. more samples
were added to the experiment, or calculation settings were modified). Dramatic changes (e.g.
removal of a target for which results were previously calculated) can result in a conflict, whereby an
alert will be shown that results cannot be recalculated. In this situation, you need to restart the
wizard and complete a new analysis.
A stat result window contains 3 tabs at the bottom.
Table contains the calculated p-values and associated values, Chart provides a graphical
representation of the results, and Settings summarizes the input provided and options selected using
the stat wizard. Double clicking on a target or target pair in the Table tab may bring you to the
corresponding graph, depending on the statistical test. Chart also has a dropdown list, for quick
browsing through all results.
5.9. Interpretation of the output tables for statistical tests in qbase+
Unpaired t-test, Mann-Whitney
Column header Interpretation
Target
name of the target
p
p-value, multiple testing corrected (if this option was selected)
Property
sample property used to define the subgroups: e.g. Treatment
39
Comparison
the 2 values for this sample property: e.g. yes - no
Ratio Fold
change between the two subgroup
95% CI low
lower value of the 95% confidence interval of the ratio
95% CI high
upper value of the 95% confidence interval of the ratio
Value sample property value used to define one of the subgroups
Mean
mean value of the sample subgroup
95% CI low
lower value of the 95% confidence interval of the mean value
95% CI high
upper value of the 95% confidence interval of the mean value
Datapoints
number of datapoints per subgroup
Non-symmetrical CIs are obtained because statistical analysis is performed on log transformed data.
Paired t-test, Wilcoxon signed rank
Column header Interpretation
Target
name of the target
p
p-value, multiple testing corrected (if this option was selected)
Property
sample property used to define the subgroups
Comparison
2 values from this sample property used to define the 2 subgroups
Ratio Fold
change between the two subgroups
95% CI low
lower value of the 95% confidence interval of the ratio
95% CI high
upper value of the 95% confidence interval of the ratio
Pairs
number of data pairs
ANOVA
Column header Interpretation
Target
name of the target
p
Two-sided p-value, multiple testing corrected (if this option was selected)
r2
Fraction of the overall variance (of all the data, pooling all the groups) attributable to
differences among the subgroup means
Property
sample property used to define the subgroups
Comparison
all combinations of 2 values from the grouping property
Ratio Fold
change between each combination of two subgroups
95% CI low
lower value of the 95% confidence interval of the ratio
95% CI
high upper value of the 95% confidence interval of the ratio
Significant
indication if 2 subgroups are statistically significantly different (p<0.05)
Value
sample property value used to define one of the subgroups
Mean
mean value of the sample subgroup
95% CI low
lower value of the uncorrected 95% confidence interval of the mean value
95% CI high
upper value of the uncorrected 95% confidence interval of the mean value
Datapoints
number of datapoints per subgroup
Spearman correlation, Pearson correlation
Column header Interpretation
Target X
name of the target in the X-axis
Target Y
name of the target in the Y-axis
r
correlation coefficient
p
p-value
Switching target between X and Y axis has no effect on p and r value.
Cox proportionzal hazards
Column header Interpretation
40
Target
p
HR
95% CI low
95% CI high
Datapoints
name of the target
p-value
hazard ratio, increase (or decrease if HR < 1) in risk per log10 unit (equals 10-fold
difference) increase in CNRQ value
lower value of the 95% confidence interval of the HR
upper value of the 95% confidence interval of the HR
number of datapoints used in the Cox model
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6. Selecting reference genes
Since normalization of qPCR data is based on the assumption that the reference genes have the
same expression level in all samples, it is crucial that the expression of the chosen reference genes
really is stable in your samples.
In many labs, classical reference genes such as GAPDH, HPRT, tubulin or actin are routinely used to
normalize qPCR data. Unfortunately, in many cases these commonly used reference genes are
inappropriate for normalization because their expression is not always stable. For instance, it has
been reported in several independent studies that GAPDH is a poor normalizer in certain conditions.
Ideally, reference genes have to fulfill another condition apart from stability of expression: their
overall expression level should preferably be similar to that of the genes of interest.
The best way of choosing reference genes is to choose a set of 10 candidate reference genes in
Genevestigator that have very stable expression levels in microarray experiments on the same tissue
and organism as you will be using in your qPCR experiment. Once you have the candidates, you can
perform a qPCR pilot experiment on a representative set of your samples to select those candidates
that are the most stable in your samples using qbase+.
6.1. Selecting candidate reference genes in Genevestigator
Genevestigator contains manually curated public microarray data from thousands of experiments.
Each microarray experiment consists of a set of samples, grown in a certain condition and in which
gene expression levels were measured. Genevestigator offers multiple tools to analyze the data. One
of these tools is RefGenes that can fulfill both conditions for finding reference genes.
RefGenes allows you to identify the genes with the most stable expression in samples collected in
biological conditions that are identical/very similar to the conditions you study in your experiments.
It works in a three step process:



STEP 1: choose from thousands of experimental conditions those that are close to the
conditions that you applied in your experiment
STEP 2: obtain the optimal range of transcript levels by searching the transcript levels of your
genes of interest
STEP 3: Refgenes creates a data set of expression values for all genes with expression levels
in the same range as your target genes. RefGenes computes the variance of expression for
each gene across the chosen conditions and selects the 25 genes with the lowest variance.
All VIB scientists have free access to the commercial version of Genevestigator.
6.1.1. Accessing Genevestigator and RefGenes
To access the commercial version of Genevestigator, you need a VIB email address. Check your VIB
email address on the Who's Who page of VIB (http://www.vib.be/en/whoiswho/Pages/default.aspx).
42
Follow the instructions on the BITS website (https://www.bits.vib.be/index.php/softwareoverview/genevestigator) to access the software. Note that you have to log on to the page on the
BITS page using your VIB account to be able to see the content.
Open the RefGenes tool by clicking its icon in the Further tools section:
STEP 1: Choose samples from a biological context similar to that of your qPCR expriment
Don't make a too general selection, e.g. all human samples: you might end up with genes that are
stable in many conditions but not in yours.
Don't make a very specific selection either, e.g. human heart samples from patients taking the same
medication as yours. If you want to broaden your study later with samples from other patients, your
reference genes might not be valid anymore.
Do the selection on the level of organism and tissue. So select all samples from the same organism
and the same/similar tissue type as the one that you use in your experiments e.g. mouse liver,
human fibroblasts... provided that this selection consists of at least 50 microarrays from at least 3
independent experiments. You need to search in a sufficiently large set of microarrays: if that is not
possible, just broaden the context and incorporate other but related/similar tissues.
To select the samples that you want to use for the RefGenes analysis click the New button in the
Sample Selection panel. The selection of samples defines which data are used for the analysis.
This opens the Sample Selection window where you:


Select the organism you're interested in
Select the array type you want to analyze. Genevestigator contains data from multiple types
of microarrays e.g. different generations of Affymetrix chips. On each array type, genes are
represented by different sets of probes. To keep the analysis results easily interpretable, data
from different array types are not mixed.
43

Click the Select particular conditions button to select all samples with a certain annotation
Select the type of conditions you want to base your selection on (in this example: Anatomy). For each
type of conditions you can browse the corresponding ontologies and select the desired conditions (in
this example: cardiac muscle). Note that you can select multiple tissues.
STEP 2: Select the gene(s) you want to measure in your qPCR experiment
This step is not essential, you can look for reference genes without specifying your genes-of-interest.
By specifying target genes (those you want to amplify by qPCR) you can focus the RefGenes search on
candidate reference genes that have a similar expression levels.
If you want to select genes-of-interest, click the New button in the Gene Selection panel.
Enter the names of your target genes in the text area and click OK. You can enter as many names as
you want.
Now you get a list of probe set IDs for each gene you have entered. Some genes have multiple probe
set IDs because they are represented by multiple probe sets on the array.
44
It is important to realize that Affymetrix probe set IDs have a certain meaning: what comes after the
underscore is an indication of the quality of the probes:




_at means that all the probes of the probe set hit one transcript. This is what you want:
probes specifically targeting one transcript of one gene.
_a_at means that all the probes in the probe set hit alternate transcripts from the same
gene. This is still ok: the probes bind to multiple transcripts but at least the transcripts come
from the same gene (splice variants).
_s_at means that all the probes in the probe set hit transcripts from different genes. This is
not what you want: the expression levels represent a mixture of genes
_x_at means that some of the probes hit transcripts from different genes. This is still not
what you want: the expression level is based on a combination of the signals of all the
probes in a probe set so also of the probes that bind to multiple genes.
Ignore probe sets with _s or _x. If you have two specific probe sets for a gene, they should more or
less give similar signals. If this is not the case, base your choice upon the expression level that you
expect for that gene based on previous qPCR results.
The expression behavior of the genes of interest is now displayed in the Target genes section:
STEP 3: Find candidate reference genes
To find reference genes click the Run button at the top of the RefGenes tool.
You can specify the Range yourself if you have not selected any target genes. Since most genes have
low or medium expression levels, use this range (6 to 11) also for the reference genes.
45
If you have specified target genes, the tool will automatically fill in their range.
RefGenes will show the top 20 most stable genes, i.e. the genes with the lowest Standard Deviation
(SD) with expression levels that fall in the selected range:
In the selected example all candidate reference genes have low expression levels since these were
the most stable ones. If you want to change the range you can either do it manually by typing a range
or you can exclude BRCA2 from the target genes using the tick boxes in the Gene selection panel:
This changes the range to search in and thus the suggested candidate reference genes:
46
6.2. Selecting the best reference genes in your samples using qbase+
In a qPCR pilot experiment you analyze a set of candidate reference genes (preferentially more than
8, identified by Genevestigator) in a representative set of samples that you want to test in your
final qPCR experiment (typically 10 independent samples). It is important that the samples are
representative for the final experiment: if you work with treated and untreated samples, an equal
number of samples from both subgroups should be studied.
Like in all qPCR analyses, place all samples that measure the same gene in the same plate. The only
two differences between this analysis and the analysis for finding differentially expressed genes that
was outlined in Section 4 are the following:


Choose Selection of reference genes (geNorm) as the aim of your experiment
Appoint all genes as reference genes on the Normalization page
The software uses the geNorm method to determine the most stable reference genes. The window
consists containing the results of the geNorm analysis consists of three tabs : geNorm M, geNorm V
and Interpretation.
The geNorm M tab shows a ranking of the candidate reference genes according to their stability,
expressed in M values, from the most unstable genes at the left (with the highest M values) to the
best reference genes at the right (with the lowest M values). In this way, you can choose the genes at
the right = the genes that vary the least over your samples: in the example shown below these are
EDN3, MUSK and Gm16845.
Now you know the most stable candidates in your samples but you don’t know how many of these
reference genes you need in your study. This is what the second tab, geNorm V, tells you. This tab
shows a bar chart that helps determining the optimal number of reference genes to be used in
subsequent analyses. A Vn/n+1 value is shown for every comparison between two consecutive
numbers (n and n+1) of candidate reference gene, e.g. V3/4 represents the added value of adding a
fourth reference gene to the set that consists of the three best reference genes. As a general
guideline it is stated that the benefit of using an extra reference gene is limited as soon as the
Vn/n+1 value drops below 0.15 threshold. In the example shown below, using two reference genes
(EDN3 and MUSK) is in theory sufficient since V2/3 is below 0.15. However, Biogazelle recommends
to always use a minimum of three reference genes.
47
If in a later stage you want to analyze additional samples, you have to repeat the qPCR pilot
experiment on a representative set of samples including the new samples and run the geNorm
analysis again.
48
7. Export results
You can export all sorts of data: experiments, samples, targets, normalization factors, results
(CNRQ)… using different formats by clicking the upward pointing arrow in the qbase+ toolbar. For
instance to save the results:
Click upward pointing arrow -> Export Result Table (CNRQ)
You will be given the choice to export results only (CNRQs) or to include the errors (standard error of
the mean) as well. The scale of the Result table can be linear or logarithmic (base 10).
To export the data to your ELN, export in Excel format. For publication export the experiment in
RDML format.
Images can be saved by right clicking and choosing Save as. If you want to process the images in a
later stage, save them in svg format.
49