Statistical Analysis of Biological Experiments

Exam: 2021-22

Fluorescence Data from FACS Analysis

Given was a table with fluorescence data derived from FACS with 2 columns for two cell subsets A and B. The single entries were cell numbers having a certain value for the fluorescence.

a) Should the mean or the median be calculated for the data? Explain your choice.

b) How can you estimate the medians for both cell subsets? Describe the method step-by-step.

c) To plot a histogram, error bars are needed. How can you get error bars for the single histogram bars? Calculate the error bar for 1 ≤ F ≤ 10 for the cell subset A (the value in the table was 28).

d) Next, we want to perform a statistical test. Can the t-test be used to compare cell subsets A and B? Explain your answer.

e) What can be said about the standard deviation of cell subsets A and B? (single choice)
□ sigma_A ≫ sigma_B
□ sigma_A ≈ sigma_B
□ sigma_A ≪ sigma_B

no idea

Exam: SS 15

Statistical Test for Obesity in Genetically Modified Mice

In an experiment, scientists would like to investigate the possible genetic preference for obesity. Therefore, 16 mice were genetically modified, and their mass was measured after 30 days. The mean mass was determined to be 21 units with a standard deviation of 4 units, whereas the control group (12 mice) had a mean mass of 15 units and a standard deviation of 6 units.

Do the genetically modified mice exhibit a significantly higher mass? Perform an appropriate statistical test.

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WS 16-17

Statistical Analysis of CD8SP T Cells in Mice

The folder exercise contains the file mouse.mat. Rename the folder with your name and surname. The file, a data frame, contains data from blood samples of treated (TR) and untreated (WT) mice. One field of the data frame contains the amount of CD8SP T cells for WT and TR, respectively, measured in arbitrary units.

a) Write a short code that performs the following steps:

• Loading the data set

• Extracting the corresponding data from the data frame

• Creating a bar plot from a histogram for WT and TR (six bins each) in the same figure with semi-transparent bars

• Labeling the axes and the legend accordingly (the figure should look like the given example)

• Save the code and the figure as a PDF in the folder (one extra point if the figure is saved automatically within the code).

b)
Does the amount of CD8SP T cells of the treated sample significantly differ from the untreated on a 5% confidence level? Perform an appropriate statistical test within the function you wrote in a). Assume that the data is normally distributed and that both samples do not necessarily have the same variance. The p-value has to be an output of your function. What is your conclusion? Formulate H0 and H1.

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WS 18-19

Distribution of Blood Types in a Sample Population

Blood types occur in a distribution 41:x:y:6 (0 : A:B : AB), where x and y were values such that they added up to 100.

a) What is the probability of picking 10 persons out of 20 that have blood type 0?

b) Calculate the mean and standard deviation of the distribution.

c) How many persons have to be chosen so that someone amongst them has blood type AB with a probability of 90%?

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SS 17 Retest

Statistical Analysis of Binding Affinity

Suppose you like to measure the binding affinity of a receptor R for its ligand L and you find that the probability that the receptor will be occupied by its ligand is

p_bound = [LR] / ([R] + [LR]

a) Derive an equation for the relative error of p_bound, given the errors of the concentrations [LR] and [R], respectively.

b) What is the condition that such a calculation is valid?

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SS 17

Statistical Test on Cancer Diagnosis Age by Genotype

he folder examination contains the file example cancer.xlsx. The data was derived from a medical study about the onset of breast cancer (Parl et al.; 1989) depending on genotype. The first column contains the patient number, the second column the age of diagnosis (in years), and the third column contains the genotype (enumerated by 1, 2, and 3).

Write a short code that performs the following steps:

• Load the data file example cancer.xlsx (e.g., with xlsread) as a variable input of the function.

• Create a bar plot (derived from a histogram) including labeling, legend, and semi-transparent bars.

• Apply an appropriate statistical test (that also creates another figure, including labeling) to judge whether the age of diagnosis depends significantly on the genotype.

• Provide the p-value as output.

Formulate H0 and H1. Which hypothesis is supported by the data and why?

WS 18-19

Bootstrapping and Confidence Intervals

a) Describe how bootstrapping can be used to calculate a 95% confidence interval for a given dataset where r=log⁡2(N1/N2)) and N1​ is measured in repeated experiments.

b) Given a measured value r=0.8r = 0.8r=0.8 with a 95% confidence interval ranging from -0.1 to 1.7, answer the following multiple-choice questions:

• What does the 95% confidence interval indicate?

• What can be concluded from this result?

WS 15-16 Retest

p-value Adjustment for Multiple Testing

a) Describe briefly one method of p-value adjustment for multiple hypothesis testing.

b) Under what condition do two random variables x and y have a covariance term cov(x,y) = 0?

c) How are the normal distribution, binomial distribution, and Poisson distribution related to each other?

SS 15

Population Dynamics

Consider a population of N individuals with non-overlapping generations. Each individual in the succeeding generation is equally likely to descend from any individual in the current generation. The population size N is constant over all generations.

a) What is the probability that two randomly chosen individuals from the last generation have their last common ancestor exactly t generations ago?

WS 15-16 Retest

Amino Acid Substitutions in Evolution

Problem 6: Amino Acid Substitutions in Evolution

Fibrinopeptides evolve with a rate of 9 substitutions per site per 10^9 years, while lysozymes evolve with 1 substitution per site per 10^9 years.

a) What is the probability that there has been no substitution at a given site after 2×10^9 years in a fibrinopeptide?

b) What is the probability that a given site in a lysozyme underwent two substitutions in 0.5×10^9 years?