1 Loading Libraries

#install.packages("apaTables")
#install.packages("kableExtra")

library(psych) # for the describe() command and the corr.test() command
library(apaTables) # to create our correlation table
library(kableExtra) # to create our correlation table

2 Importing Data

d <- read.csv(file="Project Folder Data/projectdata.csv", header=T)

# For HW, import the your project dataset you cleaned previously; this will be the dataset you'll use throughout the rest of the semester

3 State Your Hypothesis

We predict that there will be a significant relationship between percieved stress and satisfaction with life. We also predict that percieved stress and social media use will be correlated with each other.

4 Check Your Variables

# you only need to check the variables you're using in the current analysis
# it's always a good idea to look them to be sure that everything is correct
str(d)
## 'data.frame':    2159 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" ...
##  $ edu       : chr  "2 Currently in college" "5 Completed Bachelors Degree" "2 Currently in college" "2 Currently in college" ...
##  $ 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 ...
##  $ stress    : num  3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
##  $ swb       : num  4.33 4.17 1.83 5.17 3.67 ...
# We're going to create a fake variable for this lab, so that we have four variables. 
# NOTE: YOU WILL SKIP THIS STEP FOR THE HOMEWORK!

#d$fake <- (d$unhappy*d$worry)/d$life_satis

# Since we're focusing only on our continuous variables, we're going to subset them into their own dataframe. This will make some stuff we're doing later on easier.

d2 <- subset(d, select=c(stress,swb,socmeduse))

# You can use the describe() command on an entire dataframe (d) or just on a single variable (d$pss)

describe(d2)
##           vars    n  mean   sd median trimmed  mad  min  max range  skew
## stress       1 2159  3.07 0.60    3.1    3.07 0.59  1.3  4.6   3.3 -0.02
## swb          2 2159  4.44 1.33    4.5    4.49 1.48  1.0  7.0   6.0 -0.35
## socmeduse    3 2159 34.25 8.59   35.0   34.52 7.41 11.0 55.0  44.0 -0.31
##           kurtosis   se
## stress       -0.15 0.01
## swb          -0.49 0.03
## socmeduse     0.20 0.18
# NOTE: Our fake variable has high kurtosis, which we'll ignore for the lab. You don't need to discuss univariate normality in the results write-ups for the labs/homework, but you will need to discuss it in your final project manuscript.

# also use histograms to examine your continuous variables

hist(d$stress)

hist(d$swb)

hist(d$socmeduse)

# last, use scatterplots to examine your continuous variables together, for each pairing

plot(d$stress, d$swb)

plot(d$stress, d$socmeduse)

5 Check Your Assumptions

5.1 Pearson’s Correlation Coefficient Assumptions

  • Should have two measurements for each participant
  • Variables should be continuous and normally distributed
  • Outliers should be identified and removed
  • Relationship between the variables should be linear

5.1.1 Checking for Outliers

Note: You are not required to screen out outliers or take any action based on what you see here. This is something you will check and then discuss in your write-up.

# We are going to standardize (z-score) all of our variables, and check them for outliers.

d2$stress <- scale(d2$stress, center=T, scale=T)
hist(d2$stress)

sum(d2$stress < -3 | d2$stress > 3)
## [1] 0
d2$swb <- scale(d2$swb, center=T, scale=T)
hist(d2$swb)

sum(d2$swb < -3 | d2$swb > 3)
## [1] 0
d2$socmeduse <- scale(d2$socmeduse, center=T, scale=T)
hist(d2$socmeduse)

sum(d2$socmeduse < -3 | d2$socmeduse > 3)
## [1] 0

5.2 Issues with My Data

Three of my variables meet all of the assumptions of Pearson’s correlation coefficient. All variables have univariate normality and no outliers within any of the data. Outliers can distort the relationship between two variables and sway the correlation in their direction. Pearson’s r may underestimate the strength of a non-linear relationship and distort the relationship direction.

6 Run a Single Correlation

corr_output <- corr.test(d2$stress, d2$swb)

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$stress, y = d2$swb)
## Correlation matrix 
##       [,1]
## [1,] -0.49
## Sample Size 
## [1] 2159
## These are the unadjusted probability values.
##   The probability values  adjusted for multiple tests are in the p.adj object. 
##      [,1]
## [1,]    0
## 
##  To see confidence intervals of the correlations, print with the short=FALSE option

8 Create a Correlation Matrix

Strong: Between |0.50| and |1| Moderate: Between |0.30| and |0.49| Weak: Between |0.10| and |0.29| Trivial: Less than |0.09|

Remember, Pearson’s r is also an effect size!

corr_output_m <- corr.test(d2)

9 View Test Output

corr_output_m
## Call:corr.test(x = d2)
## Correlation matrix 
##           stress   swb socmeduse
## stress      1.00 -0.49      0.11
## swb        -0.49  1.00      0.09
## socmeduse   0.11  0.09      1.00
## Sample Size 
## [1] 2159
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##           stress swb socmeduse
## stress         0   0         0
## swb            0   0         0
## socmeduse      0   0         0
## 
##  To see confidence intervals of the correlations, print with the short=FALSE option
# Remember to report the p-values from the matrix that are ABOVE the diagonal

10 Write Up Results

To test our hypothesis that perceived stress, satisfaction with life, and social media use were correlated one another, we calculated a series of Pearson’s correlation coefficients. Three of the variables (perceived stress,satisfaction with life, and social media use) met the required assumptions of the test, with all three meeting the standards of normality and containing no outliers.

As predicted, we found that all three variables were significantly correlated (all ps < .001). The effect sizes of all correlations were large (rs < .5; Cohen, 1988). Our second hypothesis was also supported, that stress would be correlated with social media use, as can be seen by the correlation coefficients reported in Table 1.

Table 1: Means, standard deviations, and correlations with confidence intervals
Variable M SD 1 2 3
Perceived Stress 3.07 0.60
Satisfaction With Life 4.44 1.33 -.49**
[-.52, -.46]
Social Media Use 34.25 8.59 .11** .09**
[.07, .15] [.05, .13]
Need to Belong 3.21 0.61 .29** -.15** .27**
[.25, .33] [-.19, -.11] [.23, .31]
Note:
M and SD are used to represent mean and standard deviation, respectively. Values in square brackets indicate the 95% confidence interval. The confidence interval is a plausible range of population correlations that could have caused the sample correlation.
* indicates p < .05
** indicates p < .01.

References

Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.