Running a T-test
Philippe Pitts
2026-11-04
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## Warning: package 'psych' was built under R version 4.4.3library(car) # for the leveneTest() command## Warning: package 'car' was built under R version 4.4.3## 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
There will be significant difference in maturity scores between married and divorced individuals.
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': 3126 obs. of 7 variables:
## $ ResponseID : chr "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
## $ marriage5 : chr "are currently divorced from one another" "are currently married to one another" "are currently married to one another" "are currently married to one another" ...
## $ edu : chr "2 Currently in college" "5 Completed Bachelors Degree" "2 Currently in college" "2 Currently in college" ...
## $ mindful : num 2.4 1.8 2.2 2.2 3.2 ...
## $ support : num 6 6.75 5.17 5.58 6 ...
## $ stress : num 3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
## $ moa_maturity: num 3.67 3.33 3.67 3 3.67 ...# 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$marriage5 <- as.factor(d$marriage5)
str(d)## 'data.frame': 3126 obs. of 7 variables:
## $ ResponseID : chr "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
## $ marriage5 : Factor w/ 4 levels "are currently divorced from one another",..: 1 2 2 2 2 2 2 2 2 3 ...
## $ edu : chr "2 Currently in college" "5 Completed Bachelors Degree" "2 Currently in college" "2 Currently in college" ...
## $ mindful : num 2.4 1.8 2.2 2.2 3.2 ...
## $ support : num 6 6.75 5.17 5.58 6 ...
## $ stress : num 3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
## $ moa_maturity: num 3.67 3.33 3.67 3 3.67 ...table(d$marriage5, useNA = "always")##
## are currently divorced from one another
## 730
## are currently married to one another
## 2107
## never married each other and are not together
## 242
## never married each other but are currently together
## 47
## <NA>
## 0## Checking the Continuous variable (DV)
# you can use the describe() command on an entire dataframe (d) or just on a single variable within your dataframe -- which we will do here
describe(d$moa_maturity)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3126 3.59 0.43 3.67 3.65 0.49 1 4 3 -1.2 1.88 0.01# also use a histogram to visualize your continuous variable
hist(d$moa_maturity)
# use the describeBy() command to view the means and standard deviations by group
# it's very similar to the describe() command but splits the dataframe according to the 'group' variable
describeBy(d$moa_maturity, group=d$marriage5)##
## Descriptive statistics by group
## group: are currently divorced from one another
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 730 3.58 0.45 3.67 3.64 0.49 1.33 4 2.67 -1.35 2.54 0.02
## ------------------------------------------------------------
## group: are currently married to one another
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2107 3.6 0.42 3.67 3.65 0.49 1 4 3 -1.12 1.57 0.01
## ------------------------------------------------------------
## group: never married each other and are not together
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 242 3.6 0.46 3.67 3.66 0.49 1.67 4 2.33 -1.31 1.86 0.03
## ------------------------------------------------------------
## group: never married each other but are currently together
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 47 3.55 0.49 3.67 3.62 0.49 2 4 2 -1.07 0.69 0.07# lastly, use a boxplot to examine your chosen continuous and categorical variables together
boxplot(d$moa_maturity~d$marriage5)
5 Check Your Assumptions
5.1 T-test Assumptions
- IV must have two levels
- Data values must be independent (independent t-test only)
- Data obtained via a random sample
- Dependent variable must be normally distributed
- Variances of the two groups are approx equal.
# If the IV has more than 2 levels, you must DROP any additional levels in order to meet the first assumption of a t-test.
## NOTE: This is a FOUR STEP process!
d <- subset(d, marriage5 != "nb") # use subset() to remove all participants from the additional level
table(d$marriage5, useNA = "always") # verify that now there are ZERO participants in the additional level##
## are currently divorced from one another
## 730
## are currently married to one another
## 2107
## never married each other and are not together
## 242
## never married each other but are currently together
## 47
## <NA>
## 0d$marriage5 <- droplevels(d$marriage5) # use droplevels() to drop the empty factor
table(d$marriage5, useNA = "always") # verify that now the entire factor level is removed ##
## are currently divorced from one another
## 730
## are currently married to one another
## 2107
## never married each other and are not together
## 242
## never married each other but are currently together
## 47
## <NA>
## 0## Repeat ALL THE STEPS ABOVE if your IV has more levels that need to be DROPPED. Copy the 4 lines of code, and replace the level name in the subset() command.
d <- subset(d, marriage5 != "never married each other and are not together") # use subset() to remove all participants from the additional level
table(d$marriage5, useNA = "always") # verify that now there are ZERO participants in the additional level##
## are currently divorced from one another
## 730
## are currently married to one another
## 2107
## never married each other and are not together
## 0
## never married each other but are currently together
## 47
## <NA>
## 0d$marriage5 <- droplevels(d$marriage5) # use droplevels() to drop the empty factor
table(d$marriage5, useNA = "always") # verify that now the entire factor level is removed ##
## are currently divorced from one another
## 730
## are currently married to one another
## 2107
## never married each other but are currently together
## 47
## <NA>
## 0## Repeat ALL THE STEPS ABOVE if your IV has more levels that need to be DROPPED. Copy the 4 lines of code, and replace the level name in the subset() command.
d <- subset(d, marriage5 != "never married each other but are currently together") # use subset() to remove all participants from the additional level
table(d$marriage5, useNA = "always") # verify that now there are ZERO participants in the additional level##
## are currently divorced from one another
## 730
## are currently married to one another
## 2107
## never married each other but are currently together
## 0
## <NA>
## 0d$marriage5 <- droplevels(d$marriage5) # use droplevels() to drop the empty factor
table(d$marriage5, useNA = "always") # verify that now the entire factor level is removed ##
## are currently divorced from one another are currently married to one another
## 730 2107
## <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(moa_maturity~marriage5, data =d)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 0.3829 0.5361
## 2835Levene’s test revealed that there was no significant difference in the variances between the two marriage comparison groups, married and unmarried individuals, and their levels of maturity.
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 originally had more than two levels. To fix this, removed two levels, them being, “never married each other but currently together” and “never married each other and currently not together”. After doing this, I can proceed with my analysis. I will make note of any issues that arose in my methods section write-up and in my discussion section.
My data does not have any issues regarding homogeneity of variance, as Levene’s test was not significant. Either way, to ensure accuracy, I will use Welch’s t-test instead of 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$moa_maturity~d$marriage5) # t_output will now show in your Global Environment7 View Test Output
t_output##
## Welch Two Sample t-test
##
## data: d$moa_maturity by d$marriage5
## t = -0.90893, df = 1207.8, p-value = 0.3636
## alternative hypothesis: true difference in means between group are currently divorced from one another and group are currently married to one another is not equal to 0
## 95 percent confidence interval:
## -0.05443703 0.01996702
## sample estimates:
## mean in group are currently divorced from one another
## 3.578082
## mean in group are currently married to one another
## 3.5953178 Calculate Cohen’s d - Effect Size
# once again, we use the same formula, y~x, to calculate cohen's d
# We **only** calculate effect size if the test is SIG!
d_output <- cohen.d(d$moa_maturity~d$marriage5) # d_output will now show in your Global Environment9 View Effect Size
d_output##
## Cohen's d
##
## d estimate: -0.04016157 (negligible)
## 95 percent confidence interval:
## lower upper
## -0.12437920 0.04405605## 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 there would be a significant difference in maturity levels between married and divorced individuals, we used an independent sample t-test. This required us to group participants into two categories, 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 = .364). This suggests that the assumption of equal variances was met. To ensure accurate results, we used Welch’s t-test, which does not assume homogeneity of variance. Our data met all other assumptions of an independent samples t-test.
Contrary to my hypothesis, we found that married people (M = 3.60, SD = 0.42) reported slightly higher levels of maturity than divorced individuals (M = 3.58, SD = 0.45); t(1207.8) = -0.91, p = .364 (see Figure 1). The effect size was calculated using Cohen’s d, with a value of -0.04. (negligible; Cohen, 1988).
References
Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.