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 generalized anxiety, disordered eating, and intolerance of uncertainty. Specifically, all three variables will be positively correlated.

4 Check Your Variables

# We're going to create a fake variable for this lab, so that we have four variables. 

str(d)
## 'data.frame':    669 obs. of  7 variables:
##  $ X     : int  520 2814 3146 3295 717 6056 4753 2044 1965 1246 ...
##  $ gender: chr  "female" "male" "female" "male" ...
##  $ age   : chr  "1 under 18" "1 under 18" "1 under 18" "1 under 18" ...
##  $ iou   : num  2.22 1.52 1.78 1.85 2.22 ...
##  $ pss   : num  2.75 2.25 3 2 1.75 2 1 3 1.25 1.25 ...
##  $ gad   : num  1.14 1.29 1 1 1.14 ...
##  $ edeq12: num  1.33 1.08 1 1 1.17 ...
# 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(gad, iou, 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   se
## gad       1 669 2.21 0.93   2.00    2.15 1.06   1 4.00  3.00 0.41    -1.06 0.04
## iou       2 669 2.71 0.93   2.59    2.67 1.04   1 4.89  3.89 0.28    -0.87 0.04
## edeq12    3 669 1.96 0.77   1.83    1.90 0.86   1 4.00  3.00 0.53    -0.84 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$gad)

hist(d$iou)

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$gad, d$iou)

plot(d$gad, d$edeq12)

plot(d$edeq12, d$iou)

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

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

sum(d2$iou < -3 | d2$iou > 3)
## [1] 0
d2$edeq12 <- scale(d2$edeq12, center=T, scale=T)
hist(d2$edeq12)

sum(d2$edeq12 < -3 | d2$edeq12 > 3)
## [1] 0

5.2 Issues with My Data

All three variables meet all of the assumptions of Pearson’s Correlation Coefficient.

6 Run a Single Correlation

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

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$gad, y = d2$iou)
## Correlation matrix 
##      [,1]
## [1,]  0.7
## Sample Size 
## [1] 669
## 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 
##         gad  iou edeq12
## gad    1.00 0.70   0.52
## iou    0.70 1.00   0.46
## edeq12 0.52 0.46   1.00
## Sample Size 
## [1] 669
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##        gad iou edeq12
## gad      0   0      0
## iou      0   0      0
## edeq12   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 generalized anxiety, intolerance of uncertainty, and disordered eating would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. All three variables met the required assumptions of the test, all meeting the standards of normality and containing no outliers.

As predicted, we found that all three variables were significantly correlated (all ps <.001). The effect sizes of the correlations between generalized anxiety with intolerance of uncertainty and disordered eating were large (rs > .50; Cohen, 1988), and effect size of the correlation between intolerance of uncertainty and disordered eating was medium (r = .46).

Table 1: Means, standard deviations, and correlations with confidence intervals
Variable M SD 1 2
Generalized Anxiety 2.21 0.93
Intolerance of Uncertainty 2.71 0.93 .70**
[.66, .74]
Disordered Eating 1.96 0.77 .52** .46**
[.46, .58] [.39, .51]
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.