1 Loading Libraries

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

library(psych) # for the describe() command and the corr.test() command
## Warning: package 'psych' was built under R version 4.4.3
library(apaTables) # to create our correlation table
## Warning: package 'apaTables' was built under R version 4.4.3
library(kableExtra) # to create our correlation table
## Warning: package 'kableExtra' was built under R version 4.4.3

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 that life satisfaction will be negatively correlated with perceived stress, such that participants who report higher levels of life satisfaction will report lower levels of perceived stress.

4 Check Your Variables

# We're going to create a fake variable for this lab, so that we have four 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':    2163 obs. of  7 variables:
##  $ ResponseID: chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ gender    : chr  "f" "m" "m" "f" ...
##  $ age       : chr  "1 between 18 and 25" "1 between 18 and 25" "1 between 18 and 25" "1 between 18 and 25" ...
##  $ 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 ...
##  $ support   : num  6 6.75 5.17 5.58 6 ...
##  $ swb       : num  4.33 4.17 1.83 5.17 3.67 ...
# 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(swb, stress))

# 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
## swb       1 2163 4.43 1.33    4.5    4.49 1.48 1.0 7.0   6.0 -0.35    -0.49
## stress    2 2163 3.07 0.60    3.1    3.07 0.59 1.3 4.6   3.3 -0.01    -0.15
##          se
## swb    0.03
## stress 0.01
# 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

# because we are looking at 4 variables, we will have 4 histograms. You may not have this many for your HW. Make as many as you need to reflect your hypothesis.

hist(d2$swb)

hist(d2$stress)

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

# because we are looking at 4 variables, we will have 6 pairings/plots. You may not have this many for your HW. Make as many as you need to reflect your hypothesis.

plot(d2$swb, d2$stress)

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 always check and then discuss in your write-up.

# We are going to standardize (z-score) all of our 4 variables, and check them for outliers.

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

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

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

5.2 Issues with My Data

All of my variables meet all of the assumptions of Pearson’s correlation coefficient and present no outliers. Pearson’s r may underestimate the strength of a non-linear relationship and distort the relationship direction.

[Make sure to revise the above paragraph for your HW.]

6 Run a Single Correlation

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

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$swb, y = d2$stress)
## Correlation matrix 
##       [,1]
## [1,] -0.49
## Sample Size 
## [1] 2163
## 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!

9 Write Up Results

To test our hypothesis that life satisfaction and perceived stress would be correlated, we calculated a Pearson’s correlation coefficient. Both variables met the required assumptions for the test, demonstrating normality and containing no outliers.

As predicted, life satisfaction and perceived stress were negatively correlated (p < .001), such that participants who reported higher levels of life satisfaction reported lower levels of perceived stress. The effect sizes of the correlation was moderate (r < .5; Cohen, 1988). The correlation coefficient and confidence interval are reported in Table 1.

[In your HW, revise the above two paragraphs to fit your results. Make sure to discuss ALL predicted correlations and whether supported or not. Always report the Pearson’s r and p-value for any prediction.]

Table 1: Means, standard deviations, and correlations with confidence intervals
Variable M SD 1
Life Satisfaction 4.43 1.33
Perceived Stress 3.07 0.60 -.49**
[-.52, -.46]
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.