1 Loading Libraries

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

library(psych) # for the describe() command and the corr.test() command
## Warning: package 'psych' was built under R version 4.5.2
library(apaTables) # to create our correlation table
## Warning: package 'apaTables' was built under R version 4.5.2
library(kableExtra) # to create our correlation table
## Warning: package 'kableExtra' was built under R version 4.5.2

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 Negative Effects of COVID-19, Anxiety Disorder,Eating Disorder.Specifically, all three variables will be positively related.

4 Check Your Variables

# 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(covid_neg, gad, edeq12))

# 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
## covid_neg    1 366 0.20 0.81   0.00    0.00 0.00   0 6.00  6.00 4.41    20.18
## gad          2 366 1.55 0.61   1.43    1.44 0.42   1 4.00  3.00 1.64     2.77
## edeq12       3 366 1.67 0.54   1.58    1.62 0.49   1 3.75  2.75 1.00     0.80
##             se
## covid_neg 0.04
## gad       0.03
## edeq12    0.03
# 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$covid_neg)

hist(d$gad)

hist(d$edeq12)

# 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$covid_neg, d$gad)

plot(d$covid_neg, d$edeq12) 

plot(d$gad, d$edeq12)

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

sum(d2$covid_neg < -3 | d2$covid_neg > 3)
## [1] 15
d2$gad <- scale(d2$gad, center=T, scale=T)
hist(d2$gad)

sum(d2$gad< -3 | d2$gad > 3)
## [1] 6
d2$edeq12 <- scale(d2$edeq12, center=T, scale=T)
hist(d2$edeq12)

sum(d2$edeq12< -3 | d2$edeq12 > 3)
## [1] 4

5.2 Issues with My Data

One of my variables meet all of the assumptions of Pearson’s correlation coefficient. Two variables, negative effects of COVID had high kurtosis (20.18) and 15 outliers, anxiety disorder had high kurtosis (2.77) and 6 outliers. Eating disorder had 4 outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction.

6 Run a Single Correlation

corr_output <- corr.test(d2$gad, d2$edeq12)

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$gad, y = d2$edeq12)
## Correlation matrix 
##      [,1]
## [1,] 0.37
## Sample Size 
## [1] 366
## 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 
##           covid_neg  gad edeq12
## covid_neg      1.00 0.08  -0.01
## gad            0.08 1.00   0.37
## edeq12        -0.01 0.37   1.00
## Sample Size 
## [1] 366
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##           covid_neg  gad edeq12
## covid_neg      0.00 0.26   0.89
## gad            0.13 0.00   0.00
## edeq12         0.89 0.00   0.00
## 
##  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 negative effects of covid, anxiety, and eating disorder would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. One of the variables (eating disorder) has outliers (4) . Two variables, negative effects of covid and anxiety, had high kurtosis and outliers. Negative effects of covid had a kurtosis of 20.18 and 15 outliers. Anxiety had a kurtosis of 2.77 and 6 outliers.

Not as predicted, we found that no variables were significantly correlated (all ps > .05).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
Negative effects of COVID 0.20 0.81
Anxiety 1.55 0.61 .08
[-.02, .18]
Eating Disorder 1.67 0.54 -.01 .37**
[-.11, .10] [.28, .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.