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Exercise 1

A t-test is suitable for comparing a single mean to an hypothesized mean or two means to each other. If using two means these may be collected from paired observation (the same individuals) or from independent samples (two different groups).

In these examples we will work with the data set from Haun et al. 2019. To download and load the data set:

library(tidyverse)
download.file("https://ndownloader.figstatic.com/files/14702420", destfile = "./data/hypertrophy.csv")

hypertrophy <- read_csv("./data/hypertrophy.csv")

We will start by looking at the variables SUB_ID, CLUSTER and T3T1_PERCENT_CHANGE_RNA. These variables can be selected by using the code below.

hyp1 <- hypertrophy %>%
  select(SUB_ID, CLUSTER, T3T1_PERCENT_CHANGE_RNA) %>%
  print()

The T3T1_PERCENT_CHANGE_RNA variable is the percentage change in total RNA content per muscle weight from the beginning to the end of the training period.

Using all participants, let’s say that we want to assess if training increases RNA content. What kind of test would you use and how can we formulate a null hypothesis using this limited data?

Try to write ?t.test in the console to read the help pages for the t.test if you are not sure.

Here is a possible solution

A one sample t-test can be used to test is a mean differs from a nulll hypothesis. Above we state a directional question “if training increases RNA content”. If we want to keep this direction in the statistical hypothesis we want to use a one sample, one-tailed t-test with a directional alternative hypothesis alternative = "greater".

We could also be open to the hypothesis that RNA content can be lower or higher than 0. This would imply a two-tailed test, only testing difference (alternative = "two.sided").

Since the variable of interest is calculated as a change (in percentage) the null hypothesis of no change equals 0 in percentage change.

# To acces the specific variable 
t.test(hyp1$T3T1_PERCENT_CHANGE_RNA, mu = 0, alternative = "two.sided")

The confidence interval together with the p-value suggests that this result, or an even more extreme results is improbable if the null hypothesis is true.

Exercise 2

The same test can be perfomed using the raw data. We will use the raw variables to test in RNA changes with training. The variables of interest are:

hyp2 <- hypertrophy %>%
  select(SUB_ID, CLUSTER, T1_RNA, T3_RNA) %>%
  print()

Using this new data set, how would you test if RNA changes wit training. What kind of test do you choose?

Here is a possible solution

The data are paired, meaning that we now have two data points from each participant. In the t-test function we need to specify paired = TRUE in this case. The null hypothesis can still be directional or “two.sided”.

t.test(hyp2$T3_RNA, hyp2$T1_RNA, paired = TRUE, alternative = "two.sided")

How does this correspond to the test of percentage change above?

Exercise 3

An independent, two sample t-test compares means from two groups that are not in any meaningful way related.

Calculate any difference of RNA increases between T1 and T3 between the HIGH and LOW cluster group. Are the groups different (at the population level)?

Here is a possible solution

We could use the change score, not converted to percentages to compare the groups. We have to remove participants not belonging to any group.

hyp3 <- hypertrophy %>%
  select(SUB_ID, CLUSTER, T3T1__RNA) %>%
  filter(!is.na(CLUSTER)) %>%
  print()

The t-test can now be used with a formula. We want to explain the variable T3T1__RNA with the grouping variable (CLUSTER). In R we can write this as a formula T3T1__RNA ~ CLUSTER. In the help-pages of t.testwe can see that a method exists for class formula. This means that the function can be used differently than what we have previously done. Notice also that the data argument is needed since we do not enter the data directly.

t.test(T3T1__RNA  ~ CLUSTER, data = hyp3)

What conclusions do you draw from the results?

Here is a possible solution

The mean increase in the LOW group is slightly higher than in the HIGH group, however the results are not so different than what would be expected in the null hypothesis was true. We do not have strong evidence against the null

It is a good idea to plot the data to see what is going on. A simple boxplot will tell the story

hyp3 %>%
  ggplot(aes(CLUSTER, T3T1__RNA)) + geom_b

Exercise 4

When writing up results it is good practice to include the test statistic together with a mean difference, a confidence interval and a p-value.

How can you use R to get all these values from a single test? Use the t-test performed in exercise 2 to get all values from the test function.

Here is a possible solution

# First, save the test in an object

ttest <- t.test(hyp2$T3_RNA, hyp2$T1_RNA, paired = TRUE, alternative = "two.sided")


# the test statistic
ttest$statistic

# Mean difference 
ttest$estimate

# Confidence interval
ttest$conf.int

# The confidence interval is two numbers the upper and the lower value
# to get only the lower
ttest$conf.int[1]

# And the upper
ttest$conf.int[2]

# And finally the p-value
ttest$p.value

Exercise 5

When writing results in R markdown we can add results from a test automatically in the test. Try to write Rmarkdown combined with R code to create the following output:

Total RNA content increased from T1 to T3 with 90.5 units (95% CI: [51.5, 129.5], t(29) = 4.74, p = 0).

Here is a possible solution

I first saves the t-test in an oject from where I save all values that I’m interested in.

hypertrophy <- read_csv("./data/hypertrophy.csv")

hyp2 <- hypertrophy %>%
  select(SUB_ID, CLUSTER, T1_RNA, T3_RNA) 

# First, save the test in an object
ttest <- t.test(hyp2$T3_RNA, hyp2$T1_RNA, paired = TRUE, alternative = "two.sided")


# degress of freedom
df <- ttest$parameter
# the test statistic
statistic <- ttest$statistic
# Mean difference 
estimate <- ttest$estimate
# Confidence interval
ci <- ttest$conf.int
# And finally the p-value
pval <- ttest$p.value

I then write up a section combining text and R code

Total RNA content increased from T1 to T3 with `r round(estimate, 1)` units (95% CI: [`r round(ci[1], 1)`, `r round(ci[2], 1)`], t(`r df`) = `r round(statistic,2)`, p = `r round(pval, 3)`).