Running a T-test
Teagan Kennedy
2026-10-28
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(file="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 people with anxiety disorders will also report significantly higher levels of depression than people without any mental disorders.
Note: Depression was measured using the Patient Health Questionnaire (PHQ-9) in this dataset.
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': 694 obs. of 7 variables:
## $ X : int 520 2814 3146 3295 717 6056 4753 5365 2044 1965 ...
## $ mhealth : chr "none or NA" "none or NA" "none or NA" "none or NA" ...
## $ urban_rural: chr "town" "town" "town" "town" ...
## $ covid_pos : int 0 0 0 0 0 0 0 0 0 0 ...
## $ big5_ext : num 2 2.67 4.67 4.33 1.67 ...
## $ isolation_c: num 1 1 1 1 1 1 1 1 1 1 ...
## $ phq : num 1.56 1.44 1.11 1.33 1.44 ...# 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$mhealth <- as.factor(d$mhealth)
str(d)## 'data.frame': 694 obs. of 7 variables:
## $ X : int 520 2814 3146 3295 717 6056 4753 5365 2044 1965 ...
## $ mhealth : Factor w/ 8 levels "anxiety disorder",..: 5 5 5 5 5 5 5 5 5 5 ...
## $ urban_rural: chr "town" "town" "town" "town" ...
## $ covid_pos : int 0 0 0 0 0 0 0 0 0 0 ...
## $ big5_ext : num 2 2.67 4.67 4.33 1.67 ...
## $ isolation_c: num 1 1 1 1 1 1 1 1 1 1 ...
## $ phq : num 1.56 1.44 1.11 1.33 1.44 ...table(d$mhealth, useNA = "always")##
## anxiety disorder bipolar
## 79 3
## depression eating disorders
## 11 18
## none or NA obsessive compulsive disorder
## 538 15
## other ptsd
## 17 13
## <NA>
## 0## Checking the Continuous variable (DV)
# you can use the describe() command on an entire dataframe (d) or just on a single variable within your dataframe -- which we will do here
describe(d$phq)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 694 2.27 0.86 2.22 2.23 0.99 1 4 3 0.37 -0.89 0.03# also use a histogram to visualize your continuous variable
hist(d$phq)
# use the describeBy() command to view the means and standard deviations by group
# it's very similar to the describe() command but splits the dataframe according to the 'group' variable
describeBy(d$phq, group=d$mhealth)##
## Descriptive statistics by group
## group: anxiety disorder
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 79 2.77 0.82 2.78 2.79 0.82 1 4 3 -0.2 -0.93 0.09
## ------------------------------------------------------------
## group: bipolar
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3 3.59 0.17 3.56 3.59 0.16 3.44 3.78 0.33 0.21 -2.33 0.1
## ------------------------------------------------------------
## group: depression
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 11 2.7 0.77 2.78 2.69 1.15 1.56 3.89 2.33 -0.04 -1.6 0.23
## ------------------------------------------------------------
## group: eating disorders
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 18 2.8 0.74 2.72 2.8 1.07 1.67 4 2.33 -0.04 -1.43 0.17
## ------------------------------------------------------------
## group: none or NA
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 538 2.13 0.82 2 2.06 0.82 1 4 3 0.56 -0.6 0.04
## ------------------------------------------------------------
## group: obsessive compulsive disorder
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 15 2.78 0.72 2.78 2.79 0.82 1.56 3.78 2.22 0 -1.47 0.19
## ------------------------------------------------------------
## group: other
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 17 2.8 0.88 2.78 2.84 1.15 1 4 3 -0.17 -1 0.21
## ------------------------------------------------------------
## group: ptsd
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 13 2.72 0.88 2.78 2.73 0.99 1.33 4 2.67 0.08 -1.42 0.24# lastly, use a boxplot to examine your chosen continuous and categorical variables together
boxplot(d$phq~d$mhealth)
5 Check Your Assumptions
5.1 T-test Assumptions
- IV must have 2 levels
- Data values must be independent (independent t-test only)
- Data obtained via a random sample
- Dependent variable must be normally distributed
- Variances of the two groups are approximately equal
# If the IV has more than 2 levels, you must DROP any additional levels in order to meet the first assumption of a t-test.
## NOTE: This is a FOUR STEP process!
d <- subset(d, mhealth != "eating disorders") # use subset() to remove all participants from the additional level
table(d$mhealth, useNA = "always") # verify that now there are ZERO participants in the additional level##
## anxiety disorder bipolar
## 79 3
## depression eating disorders
## 11 0
## none or NA obsessive compulsive disorder
## 538 15
## other ptsd
## 17 13
## <NA>
## 0d$mhealth <- droplevels(d$mhealth) # use droplevels() to drop the empty factor
table(d$mhealth, useNA = "always") # verify that now the entire factor level is removed ##
## anxiety disorder bipolar
## 79 3
## depression none or NA
## 11 538
## obsessive compulsive disorder other
## 15 17
## ptsd <NA>
## 13 0######
d <- subset(d, mhealth != "other") # use subset() to remove all participants from the additional level
table(d$mhealth, useNA = "always") # verify that now there are ZERO participants in the additional level##
## anxiety disorder bipolar
## 79 3
## depression none or NA
## 11 538
## obsessive compulsive disorder other
## 15 0
## ptsd <NA>
## 13 0d$mhealth <- droplevels(d$mhealth) # use droplevels() to drop the empty factor
table(d$mhealth, useNA = "always") # verify that now the entire factor level is removed ##
## anxiety disorder bipolar
## 79 3
## depression none or NA
## 11 538
## obsessive compulsive disorder ptsd
## 15 13
## <NA>
## 0######
d <- subset(d, mhealth != "obsessive compulsive disorder") # use subset() to remove all participants from the additional level
table(d$mhealth, useNA = "always") # verify that now there are ZERO participants in the additional level##
## anxiety disorder bipolar
## 79 3
## depression none or NA
## 11 538
## obsessive compulsive disorder ptsd
## 0 13
## <NA>
## 0d$mhealth <- droplevels(d$mhealth) # use droplevels() to drop the empty factor
table(d$mhealth, useNA = "always") # verify that now the entire factor level is removed ##
## anxiety disorder bipolar depression none or NA
## 79 3 11 538
## ptsd <NA>
## 13 0######
d <- subset(d, mhealth != "ptsd") # use subset() to remove all participants from the additional level
table(d$mhealth, useNA = "always") # verify that now there are ZERO participants in the additional level##
## anxiety disorder bipolar depression none or NA
## 79 3 11 538
## ptsd <NA>
## 0 0d$mhealth <- droplevels(d$mhealth) # use droplevels() to drop the empty factor
table(d$mhealth, useNA = "always") # verify that now the entire factor level is removed ##
## anxiety disorder bipolar depression none or NA
## 79 3 11 538
## <NA>
## 0########
d <- subset(d, mhealth != "depression") # use subset() to remove all participants from the additional level
table(d$mhealth, useNA = "always") # verify that now there are ZERO participants in the additional level##
## anxiety disorder bipolar depression none or NA
## 79 3 0 538
## <NA>
## 0d$mhealth <- droplevels(d$mhealth) # use droplevels() to drop the empty factor
table(d$mhealth, useNA = "always") # verify that now the entire factor level is removed ##
## anxiety disorder bipolar none or NA <NA>
## 79 3 538 0##########
d <- subset(d, mhealth != "bipolar") # use subset() to remove all participants from the additional level
table(d$mhealth, useNA = "always") # verify that now there are ZERO participants in the additional level##
## anxiety disorder bipolar none or NA <NA>
## 79 0 538 0d$mhealth <- droplevels(d$mhealth) # use droplevels() to drop the empty factor
table(d$mhealth, useNA = "always") # verify that now the entire factor level is removed ##
## anxiety disorder none or NA <NA>
## 79 538 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.5.2 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(phq~mhealth, data =d)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 0.119 0.7302
## 615Levene’s test revealed that our data has non-significant variances between the two comparison groups, people with anxiety disorders and people with no mental disorders, on their levels of depression.
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 our data has no issues with homogeneity of variance, we’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 two levels . To proceed with this analysis, I will drop all the participants who have some mental disorder besides anxiety (depression, ptsd, bipolar, etc) from my sample. I will make a note to discuss this issue in my Methods section write-up and in my Discussion section as a limitation of my study.
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$phq~d$mhealth) # t_output will now show in your Global Environment7 View Test Output
t_output##
## Welch Two Sample t-test
##
## data: d$phq by d$mhealth
## t = 6.4439, df = 101.79, p-value = 3.927e-09
## alternative hypothesis: true difference in means between group anxiety disorder and group none or NA is not equal to 0
## 95 percent confidence interval:
## 0.4423746 0.8358240
## sample estimates:
## mean in group anxiety disorder mean in group none or NA
## 2.766526 2.1274278 Calculate Cohen’s d - Effect Size
# once again, we use the same formula, y~x, to calculate cohen's d
# We **only** calculate effect size if the test is SIG!
d_output <- cohen.d(d$phq~d$mhealth) # d_output will now show in your Global Environment9 View Effect Size
d_output##
## Cohen's d
##
## d estimate: 0.7818796 (medium)
## 95 percent confidence interval:
## lower upper
## 0.5412615 1.0224977## Remember to always take the ABSOLAUTE VALUE of the effect size value (i.e., it will never be negative)10 Write Up Results
To test our hypothesis that people with anxiety disorders in our sample would report significantly higher levels of depression than people without mental disorders, we used an independent samples t-test. This required us to drop all participants with a non-anxiety mental disorder from our sample, as we are limited to a two group comparison when using this test. We tested the homogeneity of variance with Levene’s test and did not find signs of heterogeneity (p = 0.73). Regardless, we chose to conduct our t-test with Welch’s t-test rather than Student’s t-test.
As predicted, we found that people with anxiety disorders (M = 2.77, SD = 0.82) did report significantly higher levels of depression than people without mental disorders (M = 2.13, SD = 0.74); t(102) = , p < 0.001 (see Figure 1). The effect size was calculated using Cohen’s d, with a value of 0.78 (medium) effect; Cohen, 1988).
References
Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.