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)

# 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 there will be a significant relationship between perceived stress, subjective well-being, and self-efficacy. Specifically, perceived stress will be negatively related to subjective well-being and negatively related to self-efficacy, while subjective well-being will be positively related to self-efficacy.

4 Check Your Variables

# 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! DELETE LINES 48-52!

# 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':    3165 obs. of  7 variables:
##  $ ResponseID: chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ gender    : chr  "f" "m" "m" "f" ...
##  $ race_rc   : chr  "white" "white" "white" "other" ...
##  $ swb       : num  4.33 4.17 1.83 5.17 3.67 ...
##  $ efficacy  : num  3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...
##  $ support   : num  6 6.75 5.17 5.58 6 ...
##  $ stress    : num  3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
# 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, efficacy))

# 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 kurtosis
## stress      1 3165 3.05 0.60   3.00    3.05 0.59 1.3 4.7   3.4  0.03    -0.17
## swb         2 3165 4.47 1.32   4.67    4.53 1.48 1.0 7.0   6.0 -0.36    -0.45
## efficacy    3 3165 3.13 0.45   3.10    3.13 0.44 1.1 4.0   2.9 -0.24     0.46
##            se
## stress   0.01
## swb      0.02
## efficacy 0.01
# NOTE: Our fake variable has high kurtosis, which we'll ignore for the lab because we created it to be problematic. If you have high skew or kurtosis for any of your project variables, you will need to discuss it below in the Issues with My Data and Write up Results sections, as well as in your final project manuscript if your data does not meet the normality assumption.


# also use histograms to examine your continuous variables
# Because we are looking at 3 variables, we will have 3 histograms.

hist(d$stress)

hist(d$swb)

hist(d$efficacy)

# last, use scatterplots to examine your continuous variables together, for each pairing
# because we are looking at 3 variables, we will have 3 pairings/plots. 

plot(d$stress, d$swb)

plot(d$stress, d$efficacy)

plot(d$swb, d$efficacy)

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 removed outliers in later analyses.

# We are going to standardize (z-score) all of our 3 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$efficacy <- scale(d2$efficacy, center=T, scale=T)
hist(d2$efficacy)

sum(d2$efficacy < -3 | d2$efficacy > 3)
## [1] 16

5.2 Issues with My Data

All three variables met the assumptions of Pearson’s correlation coefficient. The variables were continuous, approximately normally distributed, and demonstrated linear relationships with one another. Although outliers were examined, no action was taken because outlier removal was not part of this analysis. Therefore, the results can be interpreted with confidence.

6 Run a Single Correlation

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

7 View Single Correlation

corr_output
## Call:corr.test(x = d$stress, y = d2$swb)
## Correlation matrix 
##      [,1]
## [1,] -0.5
## Sample Size 
## [1] 3165
## 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 efficacy
## stress      1.0 -0.5     -0.4
## swb        -0.5  1.0      0.4
## efficacy   -0.4  0.4      1.0
## Sample Size 
## [1] 3165
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##          stress swb efficacy
## stress        0   0        0
## swb           0   0        0
## efficacy      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 well-being, and self-efficacy would be significantly related to one another, we calculated a series of Pearson’s correlation coefficients. All three variables met the assumptions required for Pearson’s correlation coefficient, including normality and linearity.

As predicted, all three variables were significantly correlated with one another (all ps < .001). Perceived stress was strongly and negatively related to subjective well-being, r = -.50, p < .001, indicating that participants who reported higher stress tended to report lower subjective well-being. Perceived stress was also moderately and negatively related to self-efficacy, r = -.40, p < .001, suggesting that participants with higher stress reported lower confidence in their ability to handle challenges. Finally, subjective well-being was moderately and positively related to self-efficacy, r = .40, p < .001, indicating that participants with higher self-efficacy tended to report greater subjective well-being. These findings support all of our predictions. 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 Well-Being 4.47 1.32 -.50**
[-.53, -.48]
Self-Efficacy 3.13 0.45 -.40** .40**
[-.43, -.37] [.37, .43]
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.