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PS2010 Workshop Code Book

3 Workshop 3: t-Tests

Aims:

  • Practice running and interpreting a two-sample t-test in RStudio.

  • Practice running and interpreting a paired t-test in RStudio.

3.1 Part One

Part one of today’s workshop will involved running a two-sample t-test, which is appropriate for an independent measures design with two groups.

You should use the same data file from last week, as you will be aiming to answer “What impact does energy drink consumption (if any) have on sleep quality?”

You must have completed the week 2 workshop before starting this one.

3.2 Exercise 1: Import the Data

Import the Data File: sleep.csv

Before you begin, you will need the tidyverse package loaded.

install.packages("tidyverse") #install if needed.
install.packages("rstatix")   #install if needed.
install.packages("car")       #install if needed.
library(tidyverse)            #load package.
library(rstatix)              #load package.
library(car)                  #load package.

Then import the data file. Make sure it has the total_sleep score that you calculated last week.

mydata <- read_csv("sleep.csv")

3.3 Exercise 2: Inspect and Check Your Data

Take a look at your newly imported data file

Check the top right panel (the environment) and also use the code below to inspect your data set.

view(mydata) # this will open the data in a new tab.
names(mydata) # this will show the variable names.

It is really important to look at the variable names as you’ll be using them in code later on.

3.4 Exercise 3: Check Assumptions

3.4.1 Check Heteroscedasticity with Levene’s Test

Use Levene’s test to check for homogeneity of variance.

leveneTest(DV ~ IV, data = DATA)
  • Change DV to the name of your dependent variable.
  • Change IV to the name of your independent (grouping) variable.
  • Change DATA to the name of your data.

Run the code and interpret the output:

If the p-value is significant (<.05) then the variances differ across the two groups and the assumption has been violated, which could be an issue. If the p-value is not significant (>.05) then the variances are roughly equal.

Write up as follows:

F(df) = XX.XX, p = .XXX

Enter the degrees of freedom in place of df, the F value, and the p-value. Remember use p <.001 if the p-value is smaller than 0.001.

Here is an example where degrees of freedom is 36, F is 3.25, and p is .065:

F(36) = 3.25, p = .065

3.4.2 Check Normality with Shapiro-Wilk Test and Histograms

We need to check normality for both groups separately. We can filter the groups:

#first create a data set that contains energy drink consumers only.
yes <- mydata %>%
  filter(energy_drink == "yes")

#then run the test
shapiro.test(yes$total_sleep)

#then create a data set that contains non-consumers only.
no <- mydata %>%
  filter(energy_drink == "no")

#then run the test
shapiro.test(no$total_sleep)

We use a dollar sign $ to point R to a particular column. For example, when using shapiro.test(yes$total_sleep) you are saying to run the Shapiro Test on the yes data set column called total_score

Again, we want the p-values to be not significant. A non-significant p-value means the data are roughly normally distributed. If the p-value is significant, this could be an issue as it indicates the data are not normally distributed.

When reporting the Shapiro-Wilk test, you just need to report the test statistics (w = XX) and the p-value. Here is an example what it could look like:

W = 0.98, p = .875

You can also visually check the data with a quick histogram:

hist(yes$total_sleep)
hist(no$total_sleep)

Check the plots panel, and use the blue arrow to switch between the two plots.

3.4.3 A Note on Assumptions

Assessing assumptions can be a little tricky. For a two-sample t-test we will run something called Welch’s t-test which can cope with violations of assumptions.

You might ask what is the point of checking them. One reason is because it is helpful to report the characteristics (heteroscedasticity and normality) of your data.

3.5 Exercise 4: Run the Two-Sample t-Test and ask for Cohen’s d

Run the t-test.

t.test(total_sleep ~ energy_drink, data = mydata, var.equal = FALSE, alternative = "two.sided")

Ask for Cohen’s d:

cohens_d(data = mydata, total_sleep ~ energy_drink, var.equal = FALSE)

Interpret your t-test. - Is it significant? - What is the effect size? - If significant, how do the groups differ?

For the final question, you will need descriptive statistics. Hint: use the code from last week to find the mean and standard deviation for the two groups.

3.6 Part Two

Part two of today’s workshop will involved running a paired t-test, which is appropriate for a repeated measures design with two conditions.

Here we have a sleep intervention study. A group of participants completed the sleep quality questionnaire before completing an intervention which aimed to improve sleep. Afterwards, participants completed the sleep questionnaire again.

The independent variable is time point: before, after. The dependent variable is sleep quality score (0-100).

3.7 Exercise 5: Import the Data

We will calle the object int (short for intervention data)

int <- read_csv("sleep_intervention.csv")

3.8 Exercise 6: Inspect and Check Your Data

Take a look at your newly imported data file

Check the top right panel (the environment) and also use the code below to inspect your data set.

view(int) # this will open the data in a new tab.
names(int) # this will show the variable names.

3.9 Exercise 7: Check Assumptions

This time we only have to check normality, as heteroscedasiticty does not apply to repeated measures designs. However, we need to ensure the difference score is normally distributed.

diff <- int$after - int$before  #this will calculate the difference score.
shapiro.test(diff)              # run the Shapiro test
hist(diff)                      # also visually inspect data

You should interpret and report this in the same way as earlier (exercise 3).

3.10 Exercise 8: Run the Paired t-Test and ask for Cohen’s d

A paired t-test is a little different compared to the two-sample t-test.

t.test(NULL1, NULL2, paired = TRUE)

  • Change NULL1 to the column with the first condition.

  • Change NULL2 to the column with the second condition.

(Hint: you will need to use the dollar sign $ to specify which column)

👀 Click for a hint 
t.test(int$before, int$after, paired = TRUE)

Annoyingly, we need to use a different package for Cohen’s d for a paired t-test.

install.packages("effectsize") #install if needed.
library(effectsize)
effectsize::cohens_d(int$before, int$after, paired = TRUE)

3.11 Exercise 9: Calculate Descriptive Statistics

The final thing to do is to convert the data from wide format to long format. Often with repeated measures when asking for descriptive statistics or plots, we need the data in long format.

longd <- int %>%
  gather(time, score, before:after)

Code explanation:

  • Create a new object called longd where we will store the long data.

  • Base it on the original data set called int and then %>%

  • gather()

  • The first argument is the name of your independent variable. I have called it time The second argument is the name of your dependent variable. I have called it sleep.

  • before:after will then take all and any columns from before through to after and re-arrange them into long data format.

Once you have created the new long data set called long we can use it to calculate descriptive statistics. But first check it to see the difference.

view(longd)
names(longd)

Now adapt the code below to ask for the mean and standard deviation.

desc <- longd %>%
  group_by(NULL) %>%
  summarise(mean_sleep = mean(NULL)
            sd_sleep = sd(NULL))

Change NULL1 to the name of the independent variable in the long data file, and NULL2 to the dependent variable. Use names(long) if you need a reminder.

Make note of the mean and standard deviation for the before and after conditions.

Well Done. You have reached the end of the workshop.