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':
## 
##     logit

library(effsize) # for the cohen.d() command

## 
## Attaching package: 'effsize'

## The following object is masked from 'package:psych':
## 
##     cohen.d

2 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 semester

3 State Your Hypothesis

We predict that low income individuals will report significantly higher levels of stress than high income individuals.

[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':    3112 obs. of  7 variables:
##  $ ResponseId  : chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ income      : chr  "1 low" "1 low" "rather not say" "rather not say" ...
##  $ 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" ...
##  $ efficacy    : num  3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...
##  $ 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 ...
##  $ support     : num  6 6.75 5.17 5.58 6 ...

# 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$income <- as.factor(d$income)

table(d$income, useNA = "always")

## 
##          1 low       2 middle         3 high rather not say           <NA> 
##            866            873            529            844              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$stress)

##    vars    n mean  sd median trimmed  mad min max range skew kurtosis   se
## X1    1 3112 3.05 0.6      3    3.05 0.59 1.3 4.7   3.4 0.03    -0.16 0.01

# also use a histogram to visualize your continuous variable

hist(d$stress)

# 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$stress, group=d$income)

## 
##  Descriptive statistics by group 
## group: 1 low
##    vars   n mean  sd median trimmed  mad min max range skew kurtosis   se
## X1    1 866 3.04 0.6      3    3.04 0.59 1.4 4.6   3.2 0.04    -0.21 0.02
## ------------------------------------------------------------ 
## group: 2 middle
##    vars   n mean  sd median trimmed  mad min max range skew kurtosis   se
## X1    1 873    3 0.6      3       3 0.59 1.3 4.6   3.3 0.01    -0.16 0.02
## ------------------------------------------------------------ 
## group: 3 high
##    vars   n mean   sd median trimmed  mad min max range skew kurtosis   se
## X1    1 529 3.03 0.63      3    3.02 0.59 1.3 4.7   3.4 0.06    -0.28 0.03
## ------------------------------------------------------------ 
## group: rather not say
##    vars   n mean   sd median trimmed  mad min max range skew kurtosis   se
## X1    1 844 3.13 0.57    3.1    3.12 0.59 1.4 4.7   3.3 0.06    -0.08 0.02

# last, use a boxplot to examine your continuous and categorical variables together

boxplot(d$stress~d$income)

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,income != "rather not say")
d <- subset(d,income != "2 middle")
table(d$income, useNA = "always") #verify that now there are no participants in the removed level

## 
##          1 low       2 middle         3 high rather not say           <NA> 
##            866              0            529              0              0

d$income<- droplevels(d$income) # use droplevels() to drop the empty factor

table(d$income, useNA = "always") #verify that now the entire factor level is removed

## 
##  1 low 3 high   <NA> 
##    866    529      0

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(stress~income, data = d)

## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value Pr(>F)
## group    1  2.0177 0.1557
##       1393

As you can see, the data has not significantly different variances between the two comparison groups.

Even though we do have homogeneity that we are still going to be using the Welch’s t-test

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 middle income and would rather not say 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 did not have an issue regarding homogeneity of variance as Levene’s test was not significant. To make sure, 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$stress~d$income)

7 View Test Output

t_output

## 
##  Welch Two Sample t-test
## 
## data:  d$stress by d$income
## t = 0.46193, df = 1071.1, p-value = 0.6442
## alternative hypothesis: true difference in means between group 1 low and group 3 high is not equal to 0
## 95 percent confidence interval:
##  -0.05134047  0.08295575
## sample estimates:
##  mean in group 1 low mean in group 3 high 
##             3.044919             3.029112

8 Calculate Cohen’s d

# once again, we use the same formula, y~x, to calculate cohen's d
d_output <- cohen.d(d$stress~d$income)

9 View Effect Size

d_output

## 
## Cohen's d
## 
## d estimate: 0.02581279 (negligible)
## 95 percent confidence interval:
##       lower       upper 
## -0.08244096  0.13406654

10 Write Up Results

To test our hypothesis that low income individuals in our sample would report significantly higher levels of stress than high income individuals, we used an independent samples t-test. This required us to drop our middle and rather not say groups 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 homogeneity (p> .001) and that the results were not significant, meaning that null hypothesis is true that variance between the two groups is equal. This suggests there is not an increased chance of a Type I error, but just to be sure we used a Welch’s t-test which does not assume homogeneity of variance. Our data met all other assumptions of a t-test.

We found that low income individuals (M = 3.04, SD = 0.6) reported similar levels of stress as than high income individuals (M = 3.03, SD = 0.63); t(1071.1) = 0.46193, p > .001 (see Figure 1). The effect size was calculated using Cohen’s d, with a value of .0258 (negligible; Cohen, 1988).