Running a T-test
Drew David
2024-03-21
1 Loading Libraries
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':
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## logitlibrary(effsize) # for the cohen.d() command##
## Attaching package: 'effsize'## The following object is masked from 'package:psych':
##
## cohen.d2 Importing Data
# for the homework: import the dataset you cleaned previously
# this will be the dataset you'll use throughout the rest of the semester
d <- read.csv(file="Data/rc_cleaned_data.csv", header=T)3 State Your Hypothesis
We predict that people who report less income will report significantly more stress than people that report a higher income, as measured by the generalized anxiety scale (gad).
(Note: The above hypothesis is for the lab. You will need to come up with your own hypothesis, specific to your chosen variables, for the homework.)
4 Check Your Variables
# you only need to check the variables you're using in the current analysis
# although you checked them previously, it's always a good idea to look them over again and be sure that everything is correct
str(d)## 'data.frame': 370 obs. of 8 variables:
## $ income : chr "3 high" "2 middle" "2 middle" "2 middle" ...
## $ mhealth : chr "none or NA" "none or NA" "none or NA" "anxiety disorder" ...
## $ big5_neu : num 6 4 2.67 5.33 3.67 ...
## $ pas_covid: num 3.22 4.22 3.22 4.56 3.67 ...
## $ gad : num 1.86 2 1.43 2.86 1.57 ...
## $ phq : num 1.33 2.33 1.11 2.33 1.56 ...
## $ variable2: chr "3 high" "2 middle" "2 middle" "2 middle" ...
## $ variable3: chr "none or NA" "none or NA" "none or NA" "anxiety disorder" ...d$income <- as.factor(d$income)
table(d$income, useNA = "always")##
## 1 low 2 middle 3 high prefer not to say
## 42 176 99 53
## <NA>
## 0# you can use the describe() command on an entire datafrom (d) or just on a single variable (d$gad)
describe(d$gad)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 370 1.54 0.61 1.43 1.43 0.42 1 4 3 1.6 2.49 0.03# also use a histogram to examine your continuous variable
hist(d$gad)
# can 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$gad, group=d$income)##
## Descriptive statistics by group
## group: 1 low
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 42 1.86 0.7 1.71 1.79 0.74 1 3.29 2.29 0.66 -0.7 0.11
## ------------------------------------------------------------
## group: 2 middle
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 176 1.53 0.63 1.29 1.41 0.42 1 4 3 1.81 3.46 0.05
## ------------------------------------------------------------
## group: 3 high
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 99 1.47 0.53 1.29 1.38 0.42 1 3.29 2.29 1.44 1.55 0.05
## ------------------------------------------------------------
## group: prefer not to say
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 53 1.46 0.5 1.43 1.38 0.42 1 3.43 2.43 1.78 3.83 0.07# last, use a boxplot to examine your continuous and categorical variables together
boxplot(d$gad~d$income)
#Depndent variable goes first 5 Check Your Assumptions
5.1 T-test Assumptions
- IV must be a categorical variable with two levels
- Data values must be independent (in this case, that the collection of one variable isn’t based on the response to another variable)
- Data obtained via a random sample
- Dependent variable must be normally distributed
- Variances of the two groups are approximately equal
Some of these we can check in R, while others are down to our research design. These assumptions are confirmed by our research design, so we don’t have to do anything now:
- Data values must be independent (in this case, that the collection of one variable isn’t based on the response to another variable) – confirmed by the data report that details how the data was collected
- Data obtained via a random sample – confirmed by the data report that details how the data was collected
This assumption is not met:
- IV must be a categorical variable with two levels – participants could answer M, F, or NB for their gender, so there are three levels, not two
This assumption was confirmed in the section above:
- Dependent variable must be normally distributed – we checked skew and kurtosis above. For our class, even if your variables don’t meet the assumption we’ll proceed anyway, just make a note of it.
So we only have one assumption to test:
- Variances of the two groups are approximately equal – AKA homogeneity of variance. Tested below!
# subetting to drop the nb group so that our IV only has two levels
d <- subset(d, income == c("1 low", "3 high"))
d$income <- droplevels(d$income) # using droplevels() to drop the empty factor5.2 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
# 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
# for levens test on the HW you want the P value to be above 0.05
leveneTest(gad~income, data = d)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 0.2567 0.6141
## 64As you can see, our data is very close to significant. 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 assumptions as Student’s t-test (the default type of t-test) about variance. 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 a 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 medium income and not answered 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.
6 Run a T-test
# very simple! we specify the dataframe alongside the variables instead of having a separate argument for the dataframe like we did for leveneTest()
t_output <- t.test(d$gad~d$income)7 View Test Output
t_output##
## Welch Two Sample t-test
##
## data: d$gad by d$income
## t = 2.0695, df = 35.02, p-value = 0.04594
## alternative hypothesis: true difference in means between group 1 low and group 3 high is not equal to 0
## 95 percent confidence interval:
## 0.007085409 0.735771734
## sample estimates:
## mean in group 1 low mean in group 3 high
## 1.904762 1.533333# if P value is below 0.05 its signficant 8 Calculate Cohen’s d
# once again, we use our formula to calculate cohen's d
d_output <- cohen.d(d$gad~d$income)9 View Effect Size
d_output##
## Cohen's d
##
## d estimate: 0.5730513 (medium)
## 95 percent confidence interval:
## lower upper
## 0.03578067 1.1103219710 Write Up Results
To test our hypothesis that people who report less income will report significantly more stress than people that report a higher income, as measured by the generalized anxiety scale (gad).t. This required us to drop our low and not answered 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 no of heterogeneity (p = .694). This suggests that there is an increased chance of Type I error. Our data met all of our assumption.
As predicted, we found that low income (M = 1.86, SD = .7) reported significantly higher generalized anxiety than high income (M = 1.47, SD = .53); t(18.683) = 0.34675, p < .001 (see Figure 1). The effect size was calculated using Cohen’s d, with a value of .128 (negligible effect; Cohen, 1988).
References
Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.