Running a T-test HW
Molly Barber
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## Warning: package 'psych' was built under R version 4.3.3library(car) # for the leveneTest() command## Warning: package 'car' was built under R version 4.3.3## Loading required package: carData## Warning: package 'carData' was built under R version 4.3.3##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitlibrary(effsize) # for the cohen.d() command## Warning: package 'effsize' was built under R version 4.3.3##
## 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 there will be a significant difference in Satisfaction with Life by people’s level of education, with people having completed some graduate degree having a higher satisfaction with life.
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': 3085 obs. of 7 variables:
## $ ResponseID : chr "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
## $ edu : chr "2 Currently in college" "5 Completed Bachelors Degree" "2 Currently in college" "2 Currently in college" ...
## $ usdream : chr "american dream is important and achievable for me" "american dream is important and achievable for me" "american dream is not important and maybe not achievable for me" "american dream is not important and maybe not achievable for me" ...
## $ swb : num 4.33 4.17 1.83 5.17 3.67 ...
## $ moa_independence: num 3.67 3.67 3.5 3 3.83 ...
## $ belong : num 2.8 4.2 3.6 4 3.4 4.2 3.9 3.6 2.9 2.5 ...
## $ efficacy : num 3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...# 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$edu <- as.factor(d$edu)
str(d)## 'data.frame': 3085 obs. of 7 variables:
## $ ResponseID : chr "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
## $ edu : Factor w/ 7 levels "1 High school diploma or less, and NO COLLEGE",..: 2 5 2 2 2 2 5 2 2 2 ...
## $ usdream : chr "american dream is important and achievable for me" "american dream is important and achievable for me" "american dream is not important and maybe not achievable for me" "american dream is not important and maybe not achievable for me" ...
## $ swb : num 4.33 4.17 1.83 5.17 3.67 ...
## $ moa_independence: num 3.67 3.67 3.5 3 3.83 ...
## $ belong : num 2.8 4.2 3.6 4 3.4 4.2 3.9 3.6 2.9 2.5 ...
## $ efficacy : num 3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...table(d$edu, useNA = "always")##
## 1 High school diploma or less, and NO COLLEGE
## 53
## 2 Currently in college
## 2496
## 3 Completed some college, but no longer in college
## 35
## 4 Complete 2 year College degree
## 178
## 5 Completed Bachelors Degree
## 136
## 6 Currently in graduate education
## 131
## 7 Completed some graduate degree
## 56
## <NA>
## 0## Checking the Continuous variable (DV)
# you can use the describe() command on an entire dataframe (d) or just on a single variable within your dataframe -- which we will do here
describe(d$swb)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3085 4.47 1.32 4.67 4.53 1.48 1 7 6 -0.37 -0.45 0.02# also use a histogram to visualize your continuous variable
hist(d$swb)
# use the describeBy() command to view the means and standard deviations by group
# it's very similar to the describe() command but splits the dataframe according to the 'group' variable
describeBy(d$swb, group=d$edu)##
## Descriptive statistics by group
## group: 1 High school diploma or less, and NO COLLEGE
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 53 4.12 1.54 4.33 4.22 1.48 1 6.67 5.67 -0.43 -0.78 0.21
## ------------------------------------------------------------
## group: 2 Currently in college
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 2496 4.47 1.33 4.67 4.53 1.48 1 7 6 -0.37 -0.48 0.03
## ------------------------------------------------------------
## group: 3 Completed some college, but no longer in college
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 35 3.99 1.51 4.17 4.02 1.48 1 7 6 -0.31 -0.62 0.26
## ------------------------------------------------------------
## group: 4 Complete 2 year College degree
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 178 4.54 1.33 4.67 4.58 1.48 1.17 7 5.83 -0.27 -0.69 0.1
## ------------------------------------------------------------
## group: 5 Completed Bachelors Degree
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 136 4.51 1.34 4.5 4.54 1.48 1.5 7 5.5 -0.09 -0.78 0.11
## ------------------------------------------------------------
## group: 6 Currently in graduate education
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 131 4.63 1.14 4.83 4.69 0.99 1 7 6 -0.49 0.11 0.1
## ------------------------------------------------------------
## group: 7 Completed some graduate degree
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 56 4.78 1.17 5 4.78 0.99 2.33 7 4.67 -0.1 -0.72 0.16# lastly, use a boxplot to examine your chosen continuous and categorical variables together
boxplot(d$swb~d$edu)
5 Check Your Assumptions
5.1 T-test Assumptions
- IV must have two levels
- Data values must be independent (independent t-test only)
- Data obtained via a random sample
- Dependent variable must be normally distributed
- Variances of the two groups are approximately equal
# If the IV has more than 2 levels, you must DROP any additional levels in order to meet the first assumption of a t-test.
## NOTE: This is a FOUR STEP process!
d <- subset(d, edu != "2 Currently in college") # use subset() to remove all participants from the additional level
table(d$edu, useNA = "always") # verify that now there are ZERO participants in the additional level##
## 1 High school diploma or less, and NO COLLEGE
## 53
## 2 Currently in college
## 0
## 3 Completed some college, but no longer in college
## 35
## 4 Complete 2 year College degree
## 178
## 5 Completed Bachelors Degree
## 136
## 6 Currently in graduate education
## 131
## 7 Completed some graduate degree
## 56
## <NA>
## 0 d$edu <- droplevels(d$edu) # use droplevels() to drop the empty factor
table(d$edu, useNA = "always") # verify that now the entire factor level is removed ##
## 1 High school diploma or less, and NO COLLEGE
## 53
## 3 Completed some college, but no longer in college
## 35
## 4 Complete 2 year College degree
## 178
## 5 Completed Bachelors Degree
## 136
## 6 Currently in graduate education
## 131
## 7 Completed some graduate degree
## 56
## <NA>
## 0## Repeat ALL THE STEPS ABOVE if your IV has more levels that need to be DROPPED. Copy the 4 lines of code, and replace the level name in the subset() command.# If the IV has more than 2 levels, you must DROP any additional levels in order to meet the first assumption of a t-test.
## NOTE: This is a FOUR STEP process!
d <- subset(d, edu != "5 Completed Bachelors Degree") # use subset() to remove all participants from the additional level
table(d$edu, useNA = "always") # verify that now there are ZERO participants in the additional level##
## 1 High school diploma or less, and NO COLLEGE
## 53
## 3 Completed some college, but no longer in college
## 35
## 4 Complete 2 year College degree
## 178
## 5 Completed Bachelors Degree
## 0
## 6 Currently in graduate education
## 131
## 7 Completed some graduate degree
## 56
## <NA>
## 0 d$edu <- droplevels(d$edu) # use droplevels() to drop the empty factor
table(d$edu, useNA = "always") # verify that now the entire factor level is removed ##
## 1 High school diploma or less, and NO COLLEGE
## 53
## 3 Completed some college, but no longer in college
## 35
## 4 Complete 2 year College degree
## 178
## 6 Currently in graduate education
## 131
## 7 Completed some graduate degree
## 56
## <NA>
## 0## Repeat ALL THE STEPS ABOVE if your IV has more levels that need to be DROPPED. Copy the 4 lines of code, and replace the level name in the subset() command.# If the IV has more than 2 levels, you must DROP any additional levels in order to meet the first assumption of a t-test.
## NOTE: This is a FOUR STEP process!
d <- subset(d, edu != "3 Completed some college, but no longer in college") # use subset() to remove all participants from the additional level
table(d$edu, useNA = "always") # verify that now there are ZERO participants in the additional level##
## 1 High school diploma or less, and NO COLLEGE
## 53
## 3 Completed some college, but no longer in college
## 0
## 4 Complete 2 year College degree
## 178
## 6 Currently in graduate education
## 131
## 7 Completed some graduate degree
## 56
## <NA>
## 0 d$edu <- droplevels(d$edu) # use droplevels() to drop the empty factor
table(d$edu, useNA = "always") # verify that now the entire factor level is removed ##
## 1 High school diploma or less, and NO COLLEGE
## 53
## 4 Complete 2 year College degree
## 178
## 6 Currently in graduate education
## 131
## 7 Completed some graduate degree
## 56
## <NA>
## 0## Repeat ALL THE STEPS ABOVE if your IV has more levels that need to be DROPPED. Copy the 4 lines of code, and replace the level name in the subset() command.# If the IV has more than 2 levels, you must DROP any additional levels in order to meet the first assumption of a t-test.
## NOTE: This is a FOUR STEP process!
d <- subset(d, edu != "4 Complete 2 year College degree") # use subset() to remove all participants from the additional level
table(d$edu, useNA = "always") # verify that now there are ZERO participants in the additional level##
## 1 High school diploma or less, and NO COLLEGE
## 53
## 4 Complete 2 year College degree
## 0
## 6 Currently in graduate education
## 131
## 7 Completed some graduate degree
## 56
## <NA>
## 0 d$edu <- droplevels(d$edu) # use droplevels() to drop the empty factor
table(d$edu, useNA = "always") # verify that now the entire factor level is removed ##
## 1 High school diploma or less, and NO COLLEGE
## 53
## 6 Currently in graduate education
## 131
## 7 Completed some graduate degree
## 56
## <NA>
## 0## Repeat ALL THE STEPS ABOVE if your IV has more levels that need to be DROPPED. Copy the 4 lines of code, and replace the level name in the subset() command.# If the IV has more than 2 levels, you must DROP any additional levels in order to meet the first assumption of a t-test.
## NOTE: This is a FOUR STEP process!
d <- subset(d, edu != "6 Currently in graduate education") # use subset() to remove all participants from the additional level
table(d$edu, useNA = "always") # verify that now there are ZERO participants in the additional level##
## 1 High school diploma or less, and NO COLLEGE
## 53
## 6 Currently in graduate education
## 0
## 7 Completed some graduate degree
## 56
## <NA>
## 0 d$edu <- droplevels(d$edu) # use droplevels() to drop the empty factor
table(d$edu, useNA = "always") # verify that now the entire factor level is removed ##
## 1 High school diploma or less, and NO COLLEGE
## 53
## 7 Completed some graduate degree
## 56
## <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.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(swb~edu, data =d)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 3.9855 0.04843 *
## 107
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Levene’s test revealed that our data has significant variances between the two comparison groups,level of education, on their levels of life satisfaction.
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 two levels. To proceed with this analysis, I will drop all the levels between high school completion and no college and having completed graduate school 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.
My data also has an issue regarding homogeneity of variance, as Levene’s test was significant. To accommodate for this heterogeneity of variance, 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$swb~d$edu) # t_output will now show in your Global Environment7 View Test Output
t_output##
## Welch Two Sample t-test
##
## data: d$swb by d$edu
## t = -2.4849, df = 97.235, p-value = 0.01467
## alternative hypothesis: true difference in means between group 1 High school diploma or less, and NO COLLEGE and group 7 Completed some graduate degree is not equal to 0
## 95 percent confidence interval:
## -1.1765945 -0.1316939
## sample estimates:
## mean in group 1 High school diploma or less, and NO COLLEGE
## 4.122642
## mean in group 7 Completed some graduate degree
## 4.7767868 Calculate Cohen’s d - Effect Size
# once again, we use the same formula, y~x, to calculate cohen's d
# We **only** calculate effect size if the test is SIG!
d_output <- cohen.d(d$swb~d$edu) # d_output will now show in your Global Environment9 View Effect Size
d_output##
## Cohen's d
##
## d estimate: -0.4797042 (small)
## 95 percent confidence interval:
## lower upper
## -0.86502492 -0.09438353## 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 that have completed some graduate degree will have a higher level of life satisfaction, we used an independent samples t-test. This required us to drop our currently in college, some college, 2-year degree, 4-year degree, and currently in graduate education participants 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 found signs of heterogeneity (p = 0.048). This suggests that there is an increased chance of type I error. To correct for this issue, 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.
As predicted, we found that people that have completed some graduate education (M = 4.78 , SD = 1.17) reported significantly higher levels of life satisfaction than people with a high school diploma and no college (M = 4.12, SD = 1.54); t(97.24) = -2.48, p = 0.01 (see Figure 1). The effect size was calculated using Cohen’s d, with a value of 0.48 (small effect; Cohen, 1988).
References
Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.