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

There will be a significant relationship between loneliness, depression, and extroversion. Specifically, loneliness will be positively related to depression and negatively related to extroversion; and depression will be negatively related to extroversion.

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':    694 obs. of  7 variables:
##  $ X          : int  520 2814 3146 3295 717 6056 4753 5365 2044 1965 ...
##  $ mhealth    : chr  "none or NA" "none or NA" "none or NA" "none or NA" ...
##  $ urban_rural: chr  "town" "town" "town" "town" ...
##  $ covid_pos  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ big5_ext   : num  2 2.67 4.67 4.33 1.67 ...
##  $ isolation_c: num  1 1 1 1 1 1 1 1 1 1 ...
##  $ phq        : num  1.56 1.44 1.11 1.33 1.44 ...
# 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(isolation_c, phq, big5_ext))

# 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
## isolation_c    1 694 2.28 0.81   2.25    2.28 1.11   1 3.5   2.5 -0.01    -1.22
## phq            2 694 2.27 0.86   2.22    2.23 0.99   1 4.0   3.0  0.37    -0.89
## big5_ext       3 694 4.26 1.44   4.33    4.29 1.48   1 7.0   6.0 -0.17    -0.80
##               se
## isolation_c 0.03
## phq         0.03
## big5_ext    0.05
# also use histograms to examine your continuous variables
# Because we are looking at 3 variables, we will have 3 histograms.

hist(d$isolation_c)

hist(d$phq)

hist(d$big5_ext)

# 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$isolation_c, d$phq)

plot(d$phq, d$big5_ext)

plot(d$big5_ext, d$isolation_c)

5 Check Your Assumptions

5.1 Pearson’s Correlation Coefficient Assumptions

  • Should have all 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$isolation_c <- scale(d2$isolation_c, center=TRUE, scale=TRUE)
hist(d2$isolation_c)

sum(d2$isolation_c < -3 | d2$isolation_c > 3)
## [1] 0
d2$phq <- scale(d2$phq, center=TRUE, scale=TRUE)
hist(d2$phq)

sum(d2$phq < -3 | d2$phq > 3)
## [1] 0
d2$big5_ext <- scale(d2$big5_ext, center=TRUE, scale=TRUE)
hist(d2$big5_ext)

sum(d2$big5_ext < -3 | d2$fake > 3)
## [1] 0

5.2 Issues with My Data

All of my variables meet all of the assumptions of Pearson’s correlation coefficient,so we can move forward with using Pearson’s r without any major risks.

6 Run a Single Correlation

corr_output <- corr.test(d2$isolation_c, d2$phq)

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$isolation_c, y = d2$phq)
## Correlation matrix 
##      [,1]
## [1,] 0.71
## Sample Size 
## [1] 694
## 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 
##             isolation_c   phq big5_ext
## isolation_c        1.00  0.71    -0.30
## phq                0.71  1.00    -0.27
## big5_ext          -0.30 -0.27     1.00
## Sample Size 
## [1] 694
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##             isolation_c phq big5_ext
## isolation_c           0   0        0
## phq                   0   0        0
## big5_ext              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 depression, loneliness, and extroversion would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. All of the variables met the required assumptions of the test, with all meeting the standards of normality and containing no outliers.

As predicted, we found that all three variables were significantly correlated (all ps < 0.001). The effect size of the correlation between depression and isolation was strong (r > 0.5; Cohen, 1988), the effect size of the correlation between extroversion and isolation was moderate ( 0.49 > r > 0.30), and the effect size of the correlation between extroversion and depression was weak (0.29 > r > 0.10). Additionally, isolation was found to be positively related to depression, and extroversion was found to be negatively related to both depression and isolation, 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
Loneliness 2.28 0.81
Depression 2.27 0.86 .71**
[.67, .74]
Extroversion 4.26 1.44 -.30** -.27**
[-.37, -.23] [-.34, -.20]
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.