What Is A Statistical Analysis T-Test And How To Perform One Using Flow Cytometry Data

Designing an antibody panel and running samples on a flow cytometer are not the only steps in a flow cytometry experiment.

After you run your experiment, you have to analyze the data. In particular, you need to perform statistical analyses of the data. This is especially true if you’re hoping to publish your data.

Once all the experiments are concluded and the preliminary analysis of the data performed, you must perform statistical analyses on the data to determine if there is significance in the data.

There are several different statistical tests that can be performed depending on the type of data and the comparisons being made. In the case of either making a comparison against a hypothetical mean, or comparison between two populations, the gold standard test is the Student’s T-Test.

What Is A Statistical T-Test?

The T-Test was developed by chemist William Sealy Gosset, who developed the test while working at the Guinness Brewery as a way to monitor the production of their most famous product.

Since he wasn’t allowed to publish his work directly, the paper was published under a pseudonym in the journal, Biometrika.

Before getting into the details of how the T-Test is performed and how the results are interpreted, there are several factors that need to be kept in mind…

The T-Test makes several assumptions about the data:

  • The data is from a Gaussian distribution
  • The data is continuous
  • The sample is a random sample of the population
  • The variance of the populations is equal (If not, there are variations on the theme to address this.)

There are three major variations on the T-Test:

  • One-sample T-Test – compares the mean of the experimental sample to a hypothetical mean.
  • Unpaired T-Test – compares the mean of the control and experimental samples.
  • Paired T-Test – compares the mean of two samples where the observations in one sample can be related to the observation in the second sample. (For example, the effects of treatment on patients where there is a before treatment and after treatment measurement.)

The three pieces of information needed to perform a T-Test:

  • The mean of both samples
  • The standard deviation of both samples
  • The number of observations

The T-Test compares the differences between the means of two populations to determine if the null hypothesis should be rejected. At a minimum, to perform the T-Test, one needs the means and standard deviations of both populations, and the number of measurements.

The researcher also needs to set the threshold value, also termed the α. We will compare this threshold to the P-value. If the P-value is greater than the α, there is no significance in the data. However, if the P-value is less than the α, there is significance in the data.

What Is A Null Hypothesis (HO)?

Simply stated, this is a statement about the relationship of the above two populations.  Mathematically, this can be expressed as:

μA = μB

The null hypothesis makes the assumption that our experimental results are from random variation. If, during the statistical analysis, the data is sufficient to show that random variation is not a sufficient explanation for the data, the alternative hypothesis (HA) must be accepted.

A One-Tailed Versus A Two-Tailed T-Test

A T-Test can either be one-tailed or two-tailed. The above example would be an appropriate null hypothesis for a two-tailed T-Test—that is, when the investigators do not know if the treatment will cause an increase or decrease in the measurement. If the investigators expect the treatment will cause an increase OR a decrease, a one-tailed T-Test is more appropriate.

How To Run A T-Test

In the following example, the researchers sought to determine if the percentage of CD4+ T-cells in patients who had Irumodic Syndrome was increased after treatment with Byphodine.

The percentage of CD4+ T-cells was measured on PBMCs before treatment and one week after treatment. Considering this information, this is how you would proceed to run a T-Test…

1. Establish the null hypothesis.

“In patients with Irumodic Syndrome, treatment by Byphodine either decreased or caused no change in the percentage of CD4+ T-cells.”

In this case, since the researchers are not concerned if the treatment causes a decrease in the CD4+ cell, a one-tailed T-test will be performed, and can be written as:

μA ≥ μB

2. Determine the alternate hypothesis.

“In patients with Irumodic Syndrome, treatment by Byphodine increases the percentage of CD4+ T-cells.”

3. Establish the threshold.

By convention, the α is typically set to 0.05. This comes from work by R.A. Fisher who stated in his work Statistical Methods for Research Workers (13th Edition):

The value for which P=0.05, or 1 in 20, is 1.96 or nearly 2; it is convenient to take this point as a limit in judging whether a deviation ought to be considered significant or not. Deviations exceeding twice the standard deviation are thus formally regarded as significant.

There are cases where the threshold can be changed. Increasing the α makes it easier to show significance at the expense of committing a Type I statistical error (false positive). Decreasing the α makes it hard to show significance, and increases the chance of committing a Type II statistical error (false negative). Care must be taken, however, to ensure that the reason for the change is well-documented and spelled out.

For this example, we will set the α to 0.05.

4. Collect the flow cytometry data.

Following all best practices, with a well-controlled instrument, all appropriate gating and reference controls used to generate the data table below.

Table of %CD4+ PBMCs

Pre-treatmentPost-treatment
18.526.7
20.122.2
25.234.5
16.523.6
23.329.6
22.629.1
18.040.1
19.335.3
17.439.5
19.931.4

Once this data is entered into our statistical analysis package of choice (we personally use Graphpad Prism), we can generate an appropriate graph:

t-test statistical analysis of flow cytometry data | Expert Cytometry | t-test formula for data analysis

In the above case, the data is plotted, with the mean and standard deviation plotted.

When the one-way T-Test is calculated, the P-value is 0.0003, which is lower than the threshold. Therefore, the null hypothesis is rejected, and the alternate hypothesis is accepted. As a result, this data supports the conclusion.

The use of the T-Test makes the assumption that the data follows a normal distribution.  If this is not the case, there are non-parametric tests that will allow for the statistical analysis similar to the T-Test. These include the Wilcoxon test and the Mann-Whitney test. In non-parametric tests, the data is ranked according to the value (from lowest to highest), regardless of where the data comes from.

Non-parametric tests test the null hypothesis that the data is distributed at random, with the alternate hypothesis being that the data is not randomly distributed, but one population has larger values than the other.

The Student’s T-Test is an essential tool in the researcher’s toolkit to confirm that the data generated in the course of the investigation supports the hypothesis driving the research. Proper application of the T-Test (and related non-parametric tests) to determine statistical significance in the data will improve confidence in the conclusions of any published work. Following the steps outlined above will allow the researcher to correctly apply the proper statistical tool for their data.

To learn more about getting your flow cytometry data published and to get access to all of our advanced materials including 20 training videos, presentations, workbooks, and private group membership, get on the Flow Cytometry Mastery Class wait list.

Join Expert Cytometry's Mastery Class
Tim Bushnell, PhD
Tim Bushnell, PhD

Tim Bushnell holds a PhD in Biology from the Rensselaer Polytechnic Institute. He is a co-founder of—and didactic mind behind—ExCyte, the world’s leading flow cytometry training company, which organization boasts a veritable library of in-the-lab resources on sequencing, microscopy, and related topics in the life sciences.

Similar Articles

3 Must-Have High-Dimensional Flow Cytometry Controls

3 Must-Have High-Dimensional Flow Cytometry Controls

By: Tim Bushnell, PhD

Developments such as the recent upgrade to the Cytobank analysis platform and the creation of new packages such as Immunocluster are reducing the computational expertise needed to work with high-dimensional flow cytometry datasets. Whether you are a researcher in academia, industry, or government, you may want to take advantage of the reduced barrier to entry to apply high-dimensional flow cytometry in your work. However, you’ll need the right experimental design to access the new transformative insights available through these approaches and avoid wasting the considerable time and money required for performing them. As with all experiments, a good design begins…

The Fluorochrome Less Excited: How To Build A Flow Cytometry Antibody Panel

The Fluorochrome Less Excited: How To Build A Flow Cytometry Antibody Panel

By: Tim Bushnell, PhD

Fluorochrome, antibodies and detectors are important. The journey of a thousand cells starts with a good fluorescent panel. The polychromatic panel is the combination of antibodies and fluorochromes. These will be used during the experiment to answer the biological question of interest. When you only need a few targets, the creation of the panel is relatively straightforward. It’s only when you start to get into more complex panels with multiple fluorochromes that overlap in excitation and emission gets more interesting.  FLUOROCHROMES Both full spectrum and traditional fluorescent flow cytometry rely on measuring the emission of the fluorochromes that are attached…

Flow Cytometry Year in Review: Key Changes To Know

Flow Cytometry Year in Review: Key Changes To Know

By: Meerambika Mishra

Here we are, at the end of an eventful year 2021. But with the promise of a new year 2022 to come. It has been a long year, filled with ups and downs. It is always good to reflect on the past year as we move to the future.  In Memoriam Sir Isaac Newton wrote “If I have seen further, it is by standing upon the shoulders of giants.” In the past year, we have lost some giants of our field including Zbigniew Darzynkiwicz, who contributed much in the areas of cell cycle analysis and apoptosis. Howard Shapiro, known for…

What Star Trek Taught Me About Flow Cytometry

What Star Trek Taught Me About Flow Cytometry

By: Tim Bushnell, PhD

It is no secret that I am a very big fan of the Star Trek franchise. There are many good episodes and lessons explored in the 813+ episodes, 12 movies (and counting). Don’t worry, this blog is not going to review all 813, or even 5 of them. Instead, some of the lessons I have taken away from the show that have applicability to science and flow cytometry.  “Darmok and Jalad at Tanagra.”  (ST:TNG season 5, episode 2) This is probably one of my favorite episodes, which involves Picard and an alien trying to establish a common ground and learn…

5 Flow Cytometry Strategies That Sun Tzu Taught Me

5 Flow Cytometry Strategies That Sun Tzu Taught Me

By: Tim Bushnell, PhD

Sun Tzu was a Chinese general and philosopher. His most famous writing is ‘The Art of War’, and has been studied by generals and CEOs, to glean ideas and strategies to help their missions. I was recently rereading this work and thought to myself if any of Sun Tzu’s lessons could apply to flow cytometry.  So I have identified 5 points that I think lend themselves to thinking about flow cytometry.  “Quickness is the essence of the war.” In flow cytometry, speed is of the essence. The longer the cells are out of their natural environment, the less happy they…

A Basic Guide To Flow Cytometry (3 Foundational Concepts)

A Basic Guide To Flow Cytometry (3 Foundational Concepts)

By: Meerambika Mishra

Mastering foundational concepts are imperative for successfully using any technique or system.  Robert Heinlein introduced the term ‘Grok’  in his novel Stranger in a Strange Land. Ever since then it has made its way into popular culture. To Grok something is to understand it intuitively, fully. As a cytometrist, there are several key concepts that you must grok to be successful in your career. These foundational concepts are the key tools that we use day in and day out to identify and characterize our cells of interest.  Cells Flow cytometry measures biological processes at the whole cell level. To do…

Which Fluorophores To Use For Your Microscopy Experiment

Which Fluorophores To Use For Your Microscopy Experiment

By: Heather Brown-Harding, PhD

Fluorophore selection is important. I have often been asked by my facility users which fluorophore is best suited for their experiments. The answer to this is mostly dependent on whether they are using a widefield microscope with set excitation/emission cubes or a laser based system that lets you select the laser and the emission window. Once you have narrowed down which fluorophores you can excite and collect the correct emission, you can further refine the specific fluorophore that is best for your experiment.  In this blog  we will discuss how to determine what can work with your microscope, and how…

4 No Cost Ways To Improve Your Microscopy Image Quality

4 No Cost Ways To Improve Your Microscopy Image Quality

By: Heather Brown-Harding, PhD

Image quality is critical for accurate and reproducible data. Many people get stuck on the magnification of the objective or on using a confocal instead of a widefield microscope. There are several other factors that affect the image quality such as the numerical aperture of the objective, the signal-to-noise ratio of the system, or the brightness of the sample.  Numerical aperture is the ability of an objective to collect light from a sample, but it contributes to two key formulas that will affect your image quality. The first is the theoretical resolution of the objective. It is expressed with the…

What Is Total Internal Reflection Fluorescence (TIRF) Microscopy & Is It Right For You?

What Is Total Internal Reflection Fluorescence (TIRF) Microscopy & Is It Right For You?

By: Heather Brown-Harding, PhD

TIRF is not as common as other microscopy based techniques due to certain restrictions. We will discuss these restrictions, then analyze why it might be perfect for your experiment.  TIRF relies on an evanescent wave, created through a critical angle of coherent light (i.e. laser) that reaches a refractive index mismatch.  What does it mean in practice?  A high angle laser reflects off the interface of the coverslip and the sample. Although the depth that this wave penetrates is dependent on the wavelength of the light, in practice it is approximately 50-300nm from the coverslip. Therefore, the cell membrane is…

Top Technical Training eBooks

Get the Advanced Microscopy eBook

Get the Advanced Microscopy eBook

Heather Brown-Harding, PhD

Learn the best practices and advanced techniques across the diverse fields of microscopy, including instrumentation, experimental setup, image analysis, figure preparation, and more.

Get The Free Modern Flow Cytometry eBook

Get The Free Modern Flow Cytometry eBook

Tim Bushnell, PhD

Learn the best practices of flow cytometry experimentation, data analysis, figure preparation, antibody panel design, instrumentation and more.

Get The Free 4-10 Compensation eBook

Get The Free 4-10 Compensation eBook

Tim Bushnell, PhD

Advanced 4-10 Color Compensation, Learn strategies for designing advanced antibody compensation panels and how to use your compensation matrix to analyze your experimental data.