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="Data/projectdata.csv", header=T)

3 State Your Hypothesis

There will be a significant relationship between perceived stress, subjective wellbeing, and perceived social support. Specifically, perceived stress will be negatively related to subjective wellbeing and perceived social support, while subjective wellbeing will be positively related to perceived social support.

4 Check Your Variables

# check the variables being used in the current analysis
str(d)
## 'data.frame':    3162 obs. of  7 variables:
##  $ ResponseID: chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ gender    : chr  "f" "m" "m" "f" ...
##  $ 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 ...
##  $ swb       : num  4.33 4.17 1.83 5.17 3.67 ...
##  $ belong    : num  2.8 4.2 3.6 4 3.4 4.2 3.9 3.6 2.9 2.5 ...
##  $ support   : num  6 6.75 5.17 5.58 6 ...
# subset only the continuous variables used in this analysis
d2 <- subset(d, select=c(stress, swb, support))

# descriptive statistics for the analysis variables
describe(d2)
##         vars    n mean   sd median trimmed  mad min max
## stress     1 3162 3.05 0.60   3.00    3.05 0.59 1.3 4.7
## swb        2 3162 4.48 1.32   4.67    4.53 1.48 1.0 7.0
## support    3 3162 5.53 1.13   5.75    5.66 0.99 0.0 7.0
##         range  skew kurtosis   se
## stress    3.4  0.03    -0.17 0.01
## swb       6.0 -0.36    -0.45 0.02
## support   7.0 -1.10     1.43 0.02
# histograms to examine the distribution of each variable
hist(d$stress)

hist(d$swb)

hist(d$support)

# scatterplots for each pairing of variables
plot(d$stress, d$swb)

plot(d$stress, d$support)

plot(d$swb, d$support)

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: For correlations, you will NOT screen out outliers or take any action based on what you see here. This is something you will simply check and then discuss in your write-up. We will learn how to remove outliers in later analyses.

# Standardize (z-score) all 3 variables and check 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$support <- scale(d2$support, center=T, scale=T)
hist(d2$support)

sum(d2$support < -3 | d2$support > 3)
## [1] 44

5.2 Issues with My Data

Two of my variables (perceived stress and subjective wellbeing) meet all of the assumptions of Pearson’s correlation coefficient, with both meeting the standards of normality and containing no outliers. One variable, perceived social support, had 44 outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction. Any correlations involving perceived social support should be interpreted with some caution.

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,] -0.5
## Sample Size 
## [1] 3162
## 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

corr_output_m <- corr.test(d2)

9 View Test Output

corr_output_m
## Call:corr.test(x = d2)
## Correlation matrix 
##         stress   swb support
## stress    1.00 -0.50   -0.21
## swb      -0.50  1.00    0.47
## support  -0.21  0.47    1.00
## Sample Size 
## [1] 3162
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##         stress swb support
## stress       0   0       0
## swb          0   0       0
## support      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!

Remember, Pearson’s r is also an effect size! We don’t report effect sizes for non-sig correlations.

  • 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|

10 Write Up Results

To test our hypothesis that perceived stress, subjective wellbeing, and perceived social support would be significantly related to one another, we calculated a series of Pearson’s correlation coefficients. Two of the variables (perceived stress and subjective wellbeing) met the required assumptions of the test, with both meeting the standards of normality and containing no outliers. One variable, perceived social support, had 44 outliers; so any significant results involving perceived social support should be interpreted with some caution.

As predicted, we found that all three variables were significantly correlated (all ps < .001). Effect sizes varied across the three relationships (Cohen, 1988). The relationship between perceived stress and subjective wellbeing was strong (r = −.50, 95% CI [−.53, −.47]), the relationship between subjective wellbeing and perceived social support was moderate (r = .47, 95% CI [.44, .50]), and the relationship between perceived stress and perceived social support was weak (r = −.21, 95% CI [−.24, −.18]). Perceived stress was negatively related to both subjective wellbeing and perceived social support, while subjective wellbeing was positively related to perceived social support, all as predicted. Please refer to the correlation coefficients reported in Table 1.

Table 1: Means, standard deviations, and correlations with confidence intervals
Variable M SD 1 2
Perceived Stress 3.05 0.60
Subjective Wellbeing 4.48 1.32 -.50**
[-.53, -.48]
Perceived Social Support 5.53 1.13 -.21** .47**
[-.24, -.18] [.44, .50]
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.