Running a T-test
Annelise Osmundson
2024-10-31
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 those who have a graduate degree or higher will report significantly higher levels of disordered eating than those whi have not completed high school, as measured by the Eating Disorder Questionnaire (edeq12).
[Remember to revise the above hypothesis in you HW assignment.]
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': 390 obs. of 7 variables:
## $ X : int 6291 6294 6298 6312 6326 6330 6331 6335 6348 6350 ...
## $ urban_rural: chr "town" "city" "town" "town" ...
## $ education : chr "4 equivalent to AP/IB completion" "prefer not to say" "4 equivalent to AP/IB completion" "4 equivalent to AP/IB completion" ...
## $ edeq12 : num 2.5 2.17 2.08 1.17 2.17 ...
## $ mfq_state : num 4 4 2.75 3.12 3.12 ...
## $ swemws : num 3.14 2.57 2.14 2.29 1.86 ...
## $ brs : num 4 2.5 1.17 2.33 2 ...# 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$education <- as.factor(d$education)
table(d$education, useNA = "always")##
## 1 equivalent to not completing high school
## 94
## 2 equivalent to high school completion
## 178
## 3 equivalent to vocational/technical program completion
## 3
## 4 equivalent to AP/IB completion
## 66
## 5 undergraduate degree
## 15
## 6 graduate degree or higher
## 8
## prefer not to say
## 26
## <NA>
## 0## Checking the Continuous variable (DV)
# you can use the describe() command on an entire dataframe (d) or just on a single variable within your dataframe -- which we will do here
describe(d$edeq12)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 390 2.11 0.8 2 2.07 0.99 1 4 3 0.34 -1 0.04# also use a histogram to visualize your continuous variable
hist(d$edeq12)
# use the describeBy() command to view the means and standard deviations by group
# it's very similar to the describe() command but splits the dataframe according to the 'group' variable
describeBy(d$edeq12, group=d$education)##
## Descriptive statistics by group
## group: 1 equivalent to not completing high school
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 94 2.26 0.87 2.21 2.23 1.17 1 4 3 0.16 -1.28 0.09
## ------------------------------------------------------------
## group: 2 equivalent to high school completion
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 178 2.08 0.79 2 2.03 0.99 1 4 3 0.34 -1 0.06
## ------------------------------------------------------------
## group: 3 equivalent to vocational/technical program completion
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 3 2.64 0.59 2.75 2.64 0.62 2 3.17 1.17 -0.18 -2.33 0.34
## ------------------------------------------------------------
## group: 4 equivalent to AP/IB completion
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 66 2.22 0.75 2.17 2.21 0.74 1 3.83 2.83 0.17 -0.87 0.09
## ------------------------------------------------------------
## group: 5 undergraduate degree
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 15 1.58 0.29 1.58 1.58 0.37 1 2.17 1.17 -0.01 -0.49 0.07
## ------------------------------------------------------------
## group: 6 graduate degree or higher
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 8 1.22 0.23 1.12 1.22 0.19 1 1.58 0.58 0.49 -1.61 0.08
## ------------------------------------------------------------
## group: prefer not to say
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 26 2.05 0.8 2 2.01 0.99 1 3.83 2.83 0.37 -1.08 0.16# last, use a boxplot to examine your continuous and categorical variables together
boxplot(d$edeq12~d$education)
5 Check Your Assumptions
5.1 T-test Assumptions
- IV must have two levels
- Data values must be independent (independent t-test only)
- Data obtained via a random sample
- Dependent variable must be normally distributed
- Variances of the two groups are approximately equal
# If the IV has more than 2 levels, you must drop the additional levels so that you meet the first assumption of a t-test.
d <- subset(d, education != "2 equivalent to high school completion")
table(d$education, useNA = "always") #verify that now there are no participants in the removed level##
## 1 equivalent to not completing high school
## 94
## 2 equivalent to high school completion
## 0
## 3 equivalent to vocational/technical program completion
## 3
## 4 equivalent to AP/IB completion
## 66
## 5 undergraduate degree
## 15
## 6 graduate degree or higher
## 8
## prefer not to say
## 26
## <NA>
## 0d$education <- droplevels(d$education) # use droplevels() to drop the empty factor
table(d$education, useNA = "always") #verify that now the entire factor level is removed ##
## 1 equivalent to not completing high school
## 94
## 3 equivalent to vocational/technical program completion
## 3
## 4 equivalent to AP/IB completion
## 66
## 5 undergraduate degree
## 15
## 6 graduate degree or higher
## 8
## prefer not to say
## 26
## <NA>
## 0d <- subset(d, education != "3 equivalent to vocational/technical program completion")
table(d$education, useNA = "always") #verify that now there are no participants in the removed level##
## 1 equivalent to not completing high school
## 94
## 3 equivalent to vocational/technical program completion
## 0
## 4 equivalent to AP/IB completion
## 66
## 5 undergraduate degree
## 15
## 6 graduate degree or higher
## 8
## prefer not to say
## 26
## <NA>
## 0d$education <- droplevels(d$education) # use droplevels() to drop the empty factor
table(d$education, useNA = "always") #verify that now the entire factor level is removed ##
## 1 equivalent to not completing high school
## 94
## 4 equivalent to AP/IB completion
## 66
## 5 undergraduate degree
## 15
## 6 graduate degree or higher
## 8
## prefer not to say
## 26
## <NA>
## 0d <- subset(d, education != "4 equivalent to AP/IB completion")
table(d$education, useNA = "always") #verify that now there are no participants in the removed level##
## 1 equivalent to not completing high school
## 94
## 4 equivalent to AP/IB completion
## 0
## 5 undergraduate degree
## 15
## 6 graduate degree or higher
## 8
## prefer not to say
## 26
## <NA>
## 0d$education <- droplevels(d$education) # use droplevels() to drop the empty factor
table(d$education, useNA = "always") #verify that now the entire factor level is removed ##
## 1 equivalent to not completing high school
## 94
## 5 undergraduate degree
## 15
## 6 graduate degree or higher
## 8
## prefer not to say
## 26
## <NA>
## 0d <- subset(d, education != "5 undergraduate degree")
table(d$education, useNA = "always") #verify that now there are no participants in the removed level##
## 1 equivalent to not completing high school
## 94
## 5 undergraduate degree
## 0
## 6 graduate degree or higher
## 8
## prefer not to say
## 26
## <NA>
## 0d$education <- droplevels(d$education) # use droplevels() to drop the empty factor
table(d$education, useNA = "always") #verify that now the entire factor level is removed ##
## 1 equivalent to not completing high school
## 94
## 6 graduate degree or higher
## 8
## prefer not to say
## 26
## <NA>
## 0d <- subset(d, education != "prefer not to say")
table(d$education, useNA = "always") #verify that now there are no participants in the removed level##
## 1 equivalent to not completing high school
## 94
## 6 graduate degree or higher
## 8
## prefer not to say
## 0
## <NA>
## 0d$education <- droplevels(d$education) # use droplevels() to drop the empty factor
table(d$education, useNA = "always") #verify that now the entire factor level is removed ##
## 1 equivalent to not completing high school
## 94
## 6 graduate degree or higher
## 8
## <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(edeq12~education, data = d)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 14.639 0.0002268 ***
## 100
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1As you can see, the data has significantly different variances between the two comparison groups.
[Revise the above statement for you HW assignment.]
When running a t-test, we can account for heterogeneity in our variance by using Welch’s t-test, which does not have the same assumption about variance as Student’s t-test (the general default type of t-test). 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 just 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 the non-binary participants from my sample. I will make a note to discuss this issue in my Method write-up and in my Discussion as a limitation of my study.
My data also has some 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.
[Revise the above statements for you HW assignment.]
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$edeq12~d$education)7 View Test Output
t_output##
## Welch Two Sample t-test
##
## data: d$edeq12 by d$education
## t = 8.616, df = 31.972, p-value = 7.651e-10
## alternative hypothesis: true difference in means between group 1 equivalent to not completing high school and group 6 graduate degree or higher is not equal to 0
## 95 percent confidence interval:
## 0.7935323 1.2849251
## sample estimates:
## mean in group 1 equivalent to not completing high school
## 2.257979
## mean in group 6 graduate degree or higher
## 1.2187508 Calculate Cohen’s d
# once again, we use the same formula, y~x, to calculate cohen's d
d_output <- cohen.d(d$edeq12~d$education)9 View Effect Size
d_output##
## Cohen's d
##
## d estimate: 1.230691 (large)
## 95 percent confidence interval:
## lower upper
## 0.4802811 1.981101810 Write Up Results
To test our hypothesis that those with a graduate degree or higher in our sample would report significantly higher symptoms of disordered eating than those who have not completed high school, we used an independent samples t-test. This required us to drop our equivalent to high school completion, equivalent to vocation/technical program completion, equivalent to AP/IB completion, undergraduate degree, and prefer not to say 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 < .001). 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 a t-test.
As predicted, we found that those with a graduate degree or higher (M = 1.22, SD = 0.23) reported significantly higher symptoms of disordered eating than those who have not completed high school (M = 2.26, SD = 0.87); t(8.616) = 31.972, p < 7.651e-10 (see Figure 1). The effect size was calculated using Cohen’s d, with a value of 1.23 (large effect; Cohen, 1988).
[Revise the above statements for you HW assignment.]
References
Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.