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 will report significantly higher levels of Stress than high income .

Note: Conscientiousness was measured using the International Personality Item Pool (IPIP) in this dataset.

[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':    2146 obs. of  7 variables:
##  $ ResponseID: chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ age       : chr  "1 between 18 and 25" "1 between 18 and 25" "1 between 18 and 25" "1 between 18 and 25" ...
##  $ income    : chr  "1 low" "1 low" "rather not say" "rather not say" ...
##  $ stress    : num  3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
##  $ support   : num  6 6.75 5.17 5.58 6 ...
##  $ socmeduse : int  47 23 34 35 37 13 37 43 37 29 ...
##  $ belong    : num  2.8 4.2 3.6 4 3.4 4.2 3.9 3.6 2.9 2.5 ...

# 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)

str(d)

## 'data.frame':    2146 obs. of  7 variables:
##  $ ResponseID: chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ age       : chr  "1 between 18 and 25" "1 between 18 and 25" "1 between 18 and 25" "1 between 18 and 25" ...
##  $ income    : Factor w/ 4 levels "1 low","2 middle",..: 1 1 4 4 2 4 1 1 3 4 ...
##  $ stress    : num  3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
##  $ support   : num  6 6.75 5.17 5.58 6 ...
##  $ socmeduse : int  47 23 34 35 37 13 37 43 37 29 ...
##  $ belong    : num  2.8 4.2 3.6 4 3.4 4.2 3.9 3.6 2.9 2.5 ...

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

## 
##          1 low       2 middle         3 high rather not say           <NA> 
##            598            615            350            583              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 2146 3.06 0.6    3.1    3.06 0.59 1.3 4.6   3.3 -0.02    -0.15 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    1 598 3.05 0.59    3.1    3.05 0.59 1.5 4.6   3.1 -0.01    -0.15 0.02
## ------------------------------------------------------------ 
## group: 2 middle
##    vars   n mean  sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 615 3.04 0.6    3.1    3.04 0.59 1.3 4.6   3.3 -0.02    -0.19 0.02
## ------------------------------------------------------------ 
## group: 3 high
##    vars   n mean   sd median trimmed  mad min max range skew kurtosis   se
## X1    1 350 3.03 0.63      3    3.02 0.59 1.3 4.6   3.3 0.02    -0.29 0.03
## ------------------------------------------------------------ 
## group: rather not say
##    vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
## X1    1 583 3.13 0.57    3.1    3.13 0.59 1.4 4.6   3.2 -0.01    -0.04 0.02

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

boxplot(d$stress~d$income)

5 Check Your Assumptions

5.1 T-test Assumptions

IV must have 2 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, income  != "rather not say") # use subset() to remove all participants from the additional level

table(d$income, useNA = "always") # verify that now there are ZERO participants in the additional level

## 
##          1 low       2 middle         3 high rather not say           <NA> 
##            598            615            350              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 2 middle   3 high     <NA> 
##      598      615      350        0

d <- subset(d, income != "2 middle") # use subset() to remove all participants from the additional level

table(d$income, useNA = "always") # verify that now there are ZERO participants in the additional level

## 
##    1 low 2 middle   3 high     <NA> 
##      598        0      350        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> 
##    598    350      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(stress~income, data =d)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   1  1.7133 0.1909
##       946

Levene’s test revealed that our data has appoximately equal variances between the two comparison groups, low and high income, on their levels of stress

[Revise the above statement for you HW assignment.]

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 the middle income participants and “rather not say” participants 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.

[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)  # t_output will now show in your Global Environment

7 View Test Output

t_output

## 
##  Welch Two Sample t-test
## 
## data:  d$stress by d$income
## t = 0.66174, df = 690.29, p-value = 0.5084
## alternative hypothesis: true difference in means between group 1 low and group 3 high is not equal to 0
## 95 percent confidence interval:
##  -0.0537464  0.1083933
## sample estimates:
##  mean in group 1 low mean in group 3 high 
##             3.054181             3.026857

8 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_output will now show in your Global Environment

9 View Effect Size

## 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 higher income level in our sample would report significantly higher levels of conscientiousness than men, we used an independant sample t-test . This required us to drop our middle income and “rather not 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 no signs of heterogeneity (p < .001). This suggests that there is no increased chance of Type 1 error.

Unexpectedly, we found there was no significant difference in Stress reported among Low and High income.