library(psych) # for the describe() command
library(car) # for the leveneTest() command
library(effsize) # for the cohen.d() commandt-Test HW
Loading Libraries
Importing Data
# UPDATE THIS FOR HOMEWORK!
d <- read.csv(file="Data/mydata.csv", header=T)State Your Hypothesis - PART OF YOUR WRITEUP
Men will report increased levels of narcissism compared to women.
State your t-test hypothesis. Remember, a t-test has one continuous variable as the dependent variable, and one categorical variable with two levels as the independent variable. If your IV of choice has more than one level, you will need to pick two levels to compare and drop the rest, or combine levels until you only have two left.
Check Your Assumptions
T-test Assumptions
- Data values must be independent (independent t-test only) (confirmed by data report)
- Data obtained via a random sample (confirmed by data report)
- IV must have two levels (will check below)
- Dependent variable must be normally distributed (will check below. if issues, note and proceed)
- Variances of the two groups must be approximately equal, aka ‘homogeneity of variance’. Lacking this makes our results inaccurate (will check below - this really only applies to Student’s t-test, but we’ll check it anyway)
Checking IV levels
# preview the levels and counts for your IV
table(d$gender, useNA = "always")
f m nb <NA>
2313 785 54 0 # # rerun this code to see the table without all the other variables
# # note that the table() output shows you exactly how the levels of your variable are written. when recoding, make sure you are spelling them exactly as they appear
#
# # to drop levels from your variable
# # this subsets the data and says that any participant who is coded as 'LEVEL BAD' should be removed
# # if you don't need this for the homework, comment it out (add a # at the beginning of the line)
d <- subset(d, gender != "nb")
# # this helps drop the bird owners
# d <- subset(d, pet != "cat and dog")
# d <- subset(d, pet != "fish")
# d <- subset(d, pet != "multiple types of pet")
# d <- subset(d, pet != "no pets")
# d <- subset(d, pet != "other")
# table(d$, useNA = "always")
# table(d$mhealth_rc, useNA = "always")
# table(d$mhealth, d$mhealth_rc, useNA = "always")
# # to combine levels
# # this says that where any participant is coded as 'LEVEL BAD' it should be replaced by 'LEVEL GOOD'
# # you can repeat this as needed, changing 'LEVEL BAD' if you have multiple levels that you want to combine into a single level
# # if you don't need this for the homework, comment it out (add a # at the beginning of the line)
# d$mhealth_rc[d$mhealth == "anxiety disorder"] <- "mental health diagnosis"
# # might not need to do this for the homework make sure to check
# d$mhealth_rc[d$mhealth == "bipolar"] <- "mental health diagnosis"
# d$mhealth_rc[d$mhealth == "depression"] <- "mental health diagnosis"
# d$mhealth_rc[d$mhealth == "eating disorders"] <- "mental health diagnosis"
# d$mhealth_rc[d$mhealth == "obsessive compulsive disorder"] <- "mental health diagnosis"
# d$mhealth_rc[d$mhealth == "other"] <- "mental health diagnosis"
# d$mhealth_rc[d$mhealth == "ptsd"] <- "mental health diagnosis"
# d$mhealth_rc[d$mhealth == "none or NA"] <- "none or NA"
# # preview your changes and make sure everything is correct
table(d$gender, useNA = "always")
f m <NA>
2313 785 0 # table(d$mhealth_rc, useNA = "always")
# # check your variable types
str(d)'data.frame': 3098 obs. of 6 variables:
$ gender : chr "f" "m" "m" "f" ...
$ sibling : chr "at least one sibling" "at least one sibling" "at least one sibling" "at least one sibling" ...
$ npi : num 0.6923 0.1538 0.0769 0.0769 0.7692 ...
$ belong : num 2.8 4.2 3.6 4 3.4 4.2 3.9 3.6 2.9 2.5 ...
$ socmeduse: int 47 23 34 35 37 13 37 43 37 29 ...
$ stress : num 3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...# # make sure that your IV is recognized as a factor by R
d$gender <- as.factor(d$gender)
# d$mhealth_rc <- as.factor(d$mhealth_rc)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
leveneTest(npi~gender, data = d)Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 1 41.315 1.495e-10 ***
3096
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1^^^ remember that you DON’T want statistical significance with the levene test because non-significance signifies homogeneity
This is more of a formality in our case, because we are 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 extra effort on our part!
Check Normality
# 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
# you can use the describe() command on an entire datafrom (d) or just on a single variable (d$pss)
# use it to check the skew and kurtosis of your DV
# remember that you want to make sure skew and kurtosis is between -2 and 2
describe(d$npi) vars n mean sd median trimmed mad min max range skew kurtosis se
X1 1 3098 0.28 0.31 0.15 0.24 0.23 0 1 1 0.93 -0.71 0.01# 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$npi, group=d$gender)
Descriptive statistics by group
group: f
vars n mean sd median trimmed mad min max range skew kurtosis se
X1 1 2313 0.26 0.3 0.15 0.22 0.23 0 1 1 1.08 -0.39 0.01
------------------------------------------------------------
group: m
vars n mean sd median trimmed mad min max range skew kurtosis se
X1 1 785 0.34 0.33 0.15 0.32 0.23 0 1 1 0.56 -1.32 0.01# also use a histogram to examine your continuous variable
hist(d$npi)
# last, use a boxplot to examine your continuous and categorical variables together
# categorical/IV goes on the right, and continous/DV goes on the left
boxplot(d$npi~d$gender)
Issues with My Data - PART OF YOUR WRITEUP
Briefly describe any issues with your data and how you’ve resolved them. For instance, if you are using a gender variable that has three levels, you should say that you dropped or combined two of the levels for your analysis. This should be written in an appropriate scientific tone.
A note that might be helpful: the opposite of ‘homogeneity of variance’ (the thing we want) is ‘heterogeneity of variance’ (the thing we don’t want). So, you could say something like this, if needed:
We dropped participants who were another gender other than male or female (e.g. non-binary). Before proceeding with analysis, we confirmed that all t-test assumptions were met. Levene’s test found significant heterogeneity of variance (p < .001). As a result, Welch’s t-test will be used. Our dependent variable is normally distributed (skew and kurtosis between -2 and +2).
Run a T-test
# # very simple! we specify the dataframe alongside the variables instead of having a separate argument for the dataframe like we did for leveneTest()
t_output <- t.test(d$npi~d$gender)View Test Output
t_output
Welch Two Sample t-test
data: d$npi by d$gender
t = -6.2791, df = 1237.1, p-value = 4.706e-10
alternative hypothesis: true difference in means between group f and group m is not equal to 0
95 percent confidence interval:
-0.11011927 -0.05768807
sample estimates:
mean in group f mean in group m
0.2587715 0.3426752 Calculate Cohen’s d
# # once again, we use our formula to calculate cohen's d
d_output <- cohen.d(d$npi~d$gender)View Effect Size
- Trivial: < .2
- Small: between .2 and .5
- Medium: between .5 and .8
- Large: > .8
d_output
Cohen's d
d estimate: -0.2739281 (small)
95 percent confidence interval:
lower upper
-0.3552058 -0.1926503 Write Up Results
We tested our hypothesis that men would report increased levels of narcissism than women using an independent samples t-test. We dropped participants who were another gender other than male or female (e.g. non-binary). Before proceeding with analysis, we confirmed that all t-test assumptions were met. Our dependent variable is normally distributed (skew and kurtosis between -2 and +2). Levene’s test found significant heterogeneity of variance (p < .001). As a result, Welch’s t-test will be used. During the t-test, we did find a significant difference, t(1237.1) = -6.28, p < .001, d = -.27, 95% [-0.11, -.06]. (refer to Figure 1). Our effect size was small according to Cohen (1988)
References
Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.