Running a T-test
Reuben Kruger
2026-06-02
1 Loading Libraries
# install any packages you have not previously used, then comment them back out.
#install.packages("car")
#install.packages("effsize")
library(psych) # for the describe() command
library(car) # for the leveneTest() command## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitlibrary(effsize) # for the cohen.d() command##
## Attaching package: 'effsize'## The following object is masked from 'package:psych':
##
## cohen.d2 Importing Data
d <- read.csv("Data/projectdata.csv", header=T)
# For the HW, you will import the project dataset you cleaned previously
# This will be the dataset you'll use for HWs throughout the rest of the semester3 State Your Hypothesis
We predict that there will be a significant difference in anxiety (GAD) symptoms by relationship status, between those who are single and those who are in a relationship.
4 Check Your Variables
# you **only** need to check the variables you're using in the current analysis
## Checking the Categorical variable (IV)
str(d)## 'data.frame': 612 obs. of 7 variables:
## $ X : int 520 2814 3146 3295 717 6056 4753 5365 2044 1965 ...
## $ education : chr "1 equivalent to not completing high school" "prefer not to say" "2 equivalent to high school completion" "prefer not to say" ...
## $ relationship_status: chr "Single, never married" "Single, never married" "Prefer not to say" "Single, never married" ...
## $ exercise : chr "1 less than 1 hour" "1 less than 1 hour" "1 less than 1 hour" "1 less than 1 hour" ...
## $ pss : num 2.75 2.25 3 2 1.75 2 1 1.25 3 1.25 ...
## $ support : num 2.83 3 4 4 3.67 ...
## $ gad : num 1.14 1.29 1 1 1.14 ...# if the categorical variable you're using is showing as a "chr" (character), you must change it to be a ** factor ** -- using the next line of code (as.factor)
d$relationship_status <- as.factor(d$relationship_status)
str(d)## 'data.frame': 612 obs. of 7 variables:
## $ X : int 520 2814 3146 3295 717 6056 4753 5365 2044 1965 ...
## $ education : chr "1 equivalent to not completing high school" "prefer not to say" "2 equivalent to high school completion" "prefer not to say" ...
## $ relationship_status: Factor w/ 4 levels "In a relationship/married but living apart",..: 4 4 2 4 4 2 4 4 4 1 ...
## $ exercise : chr "1 less than 1 hour" "1 less than 1 hour" "1 less than 1 hour" "1 less than 1 hour" ...
## $ pss : num 2.75 2.25 3 2 1.75 2 1 1.25 3 1.25 ...
## $ support : num 2.83 3 4 4 3.67 ...
## $ gad : num 1.14 1.29 1 1 1.14 ...table(d$relationship_status, useNA="always")##
## In a relationship/married but living apart
## 60
## Prefer not to say
## 63
## Single, divorced or widowed
## 2
## Single, never married
## 487
## <NA>
## 0## Checking the Continuous variable (DV)
# you can use the describe() command on an entire dataframe (d) or just on a single variable within your dataframe -- which we will do here
describe(d$gad)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 612 2.17 0.93 2 2.11 1.06 1 4 3 0.47 -1 0.04# also use a histogram to visualize your continuous variable
hist(d$gad)
# use the describeBy() command to view the means and standard deviations by group
# it's very similar to the describe() command but splits the dataframe according to the 'group' variable
describeBy(d$gad, group=d$relationship_status)##
## Descriptive statistics by group
## group: In a relationship/married but living apart
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 60 2.42 0.89 2.43 2.42 1.06 1 4 3 0.09 -1.21 0.12
## ------------------------------------------------------------
## group: Prefer not to say
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 63 2.17 0.98 2 2.1 1.06 1 4 3 0.55 -1.1 0.12
## ------------------------------------------------------------
## group: Single, divorced or widowed
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2 2.57 0.4 2.57 2.57 0.42 2.29 2.86 0.57 0 -2.75 0.29
## ------------------------------------------------------------
## group: Single, never married
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 487 2.14 0.92 2 2.07 1.06 1 4 3 0.51 -0.94 0.04# lastly, use a boxplot to examine your chosen continuous and categorical variables together
boxplot(d$gad ~ d$relationship_status)
5 Check Your Assumptions
5.1 T-test Assumptions
- IV must have 2 levels
- Data values must be independent (independent t-test only)
- Data obtained via a random sample
- Dependent variable must be normally distributed
- Variances of the two groups are equal
# If the IV has more than 2 levels, you must DROP any additional levels in order to meet the first assumption of a t-test.
## NOTE: This is a FOUR STEP process!
d <- subset(d, relationship_status != "Prefer not to say") # use subset() to remove all participants from the additional level
table(d$relationship_status, useNA="always") # verify that now there are ZERO participants in the additional level##
## In a relationship/married but living apart
## 60
## Prefer not to say
## 0
## Single, divorced or widowed
## 2
## Single, never married
## 487
## <NA>
## 0d$relationship_status <- droplevels(d$relationship_status) # use droplevels() to drop the empty factor
table(d$relationship_status, useNA="always") # verify that now the entire factor level is removed##
## In a relationship/married but living apart
## 60
## Single, divorced or widowed
## 2
## Single, never married
## 487
## <NA>
## 0## Repeat ALL THE STEPS ABOVE if your IV has more levels that need to be DROPPED. Copy the 4 lines of code, and replace the level name in the subset() command.
d <- subset(d, relationship_status != "Single, divorced or widowed")
table(d$relationship_status, useNA="always")##
## In a relationship/married but living apart
## 60
## Single, divorced or widowed
## 0
## Single, never married
## 487
## <NA>
## 0d$relationship_status <- droplevels(d$relationship_status)
table(d$relationship_status, useNA="always")##
## In a relationship/married but living apart
## 60
## Single, never married
## 487
## <NA>
## 05.2 Testing Homogeneity of Variance with Levene’s Test
We can test whether the variances of our two groups are equal using Levene’s test. The NULL hypothesis is that the variance between the two groups is equal, which is the result we WANT. So when running Levene’s test we’re hoping for a NON-SIGNIFICANT result!
# use the leveneTest() command from the car package to test homogeneity of variance
# it uses the same 'formula' setup that we'll use for our t-test: formula is y~x, where y is our DV and x is our IV
leveneTest(gad ~ relationship_status, data=d)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 0.0166 0.8976
## 545Levene’s test revealed that our data does not have significantly different variances between our two comparison groups of those in a relationship and those single, never married, on their levels of anxiety symptoms, indicating homogeneity of variance was met (p = .90).
When running a t-test, we can account for heterogeneity in our variance by using the Welch’s t-test, which does not have the same assumption about variance as the Student’s t-test (the general default type of t-test in statistics). R defaults to using Welch’s t-test so this doesn’t require any changes on our part! Even if your data has no issues with homogeneity of variance, you’ll still use Welch’s t-test – it handles the potential issues around variance well and there are no real downsides. We’re using Levene’s test here to get into the habit of checking the homogeneity of our variance, even if we already have the solution for any potential problems.
5.3 Issues with My Data
My independent variable has more than 2 levels. To proceed with this analysis, I will drop the “Prefer not to say” and “Single, divorced or widowed” participants from my sample as we are limited to a 2 group comparison when using this test. I will make a note to discuss this issue in my methods section of my write-up and in my discussion section as a limitation of this study.
My data does not have issues regarding homogeneity of variance, as Levene’s test was non-significant (p = .90). I will still use Welch’s T-test rather than Student’s T-test in my analysis.
6 Run a T-test
# Very simple! we use the same formula of y~x, where y is our DV and x is our IV
t_output <- t.test(d$gad ~ d$relationship_status) # t_output will now show in your Global Environment7 View Test Output
t_output##
## Welch Two Sample t-test
##
## data: d$gad by d$relationship_status
## t = 2.2918, df = 75.48, p-value = 0.0247
## alternative hypothesis: true difference in means between group In a relationship/married but living apart and group Single, never married is not equal to 0
## 95 percent confidence interval:
## 0.03672646 0.52452318
## sample estimates:
## mean in group In a relationship/married but living apart
## 2.421429
## mean in group Single, never married
## 2.1408048 Calculate Cohen’s d - Effect Size
# once again, we use the same formula, y~x, to calculate cohen's d
# We **only** calculate effect size if the test is SIG!
d_output <- cohen.d(d$gad ~ d$relationship_status) # d_output will now show in your Global Environment9 View Effect Size
d_output##
## Cohen's d
##
## d estimate: 0.3049822 (small)
## 95 percent confidence interval:
## lower upper
## 0.03561098 0.57435341## Remember to always take the ABSOLUTE VALUE of the effect size value (i.e., it will never be negative)10 Write Up Results
To test our hypothesis that there would be a significant difference in anxiety (GAD) symptoms by relationship status, we used an independent samples T-test. This required us to drop the “Prefer not to say” and “Single, divorced or widowed” participants from our sample as we are limited to a 2 group comparison when using this test.
We tested homogeneity of variance with Levene’s test and found no significant difference in variances between our two groups (p = .90). Our data met all assumptions of an independent samples T-test. We used Welch’s T-test for our analysis.
As predicted, we found that those in a relationship (M = 2.42, SD = 0.89) reported significantly higher anxiety symptoms than those who were single (M = 2.14, SD = 0.92), t(75.48) = 2.29, p = .025. The effect size was calculated using Cohen’s d with a value of 0.30 (small).
References
Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.