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 that pandemic anxiety will be significantly negatively correlated with mental flexibility, such that participants who report higher levels of pandemic anxiety will report lower levels of mental flexibility. Additionally, we predict that intolerance of uncertainty will be positively correlated with pandemic anxiety, such that participants who report higher levels of intolerance of uncertainty will report higher levels of pandemic anxiety.

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!

# 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':    931 obs. of  7 variables:
##  $ X        : int  321 401 520 1390 1422 2247 2526 2609 2689 2752 ...
##  $ age      : chr  "1 under 18" "4 between 36 and 45" "1 under 18" "5 over 45" ...
##  $ mhealth  : chr  "none or NA" "obsessive compulsive disorder" "none or NA" "none or NA" ...
##  $ big5_open: num  4 6 3.67 3 2 ...
##  $ iou      : num  2.48 2.81 2.22 1.48 1.74 ...
##  $ mfq_state: num  6 5 3 3.5 3.25 ...
##  $ pas_covid: num  2.33 4 3 2.89 2.67 ...
# 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(pas_covid, mfq_state, iou))

# 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
## pas_covid    1 931 3.22 0.68   3.22    3.24 0.66   1 5.00  4.00 -0.24     0.09
## mfq_state    2 931 4.14 0.96   4.25    4.19 0.93   1 6.00  5.00 -0.50     0.12
## iou          3 931 2.53 0.89   2.41    2.47 0.99   1 4.78  3.78  0.49    -0.63
##             se
## pas_covid 0.02
## mfq_state 0.03
## iou       0.03
# 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$pas_covid)

hist(d2$mfq_state)

hist(d2$iou)

# 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$pas_covid, d2$mfq_state)

plot(d2$iou, d2$pas_covid)

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

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

sum(d2$mfq_state < -3 | d2$mfq_state > 3)
## [1] 4
d2$iou <- scale(d2$iou, center=T, scale=T)
hist(d2$iou)

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

5.2 Issues with My Data

All of my variables fit into the assumption of normality (skew and kurtosis). Two of my variables had outliers, pandemic anxiety had one and mental flexibility had four. One of my variables, intolerance of uncertainty didn’t have outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction.

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

6 Run a Single Correlation

corr_output <- corr.test(d2$pas_covid, d2$mfq_state)

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$pas_covid, y = d2$mfq_state)
## Correlation matrix 
##       [,1]
## [1,] -0.26
## Sample Size 
## [1] 931
## 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 Run a Single Correlation

corr_output2 <- corr.test(d2$pas_covid, d2$iou)

9 View Single Correlation

corr_output2
## Call:corr.test(x = d2$pas_covid, y = d2$iou)
## Correlation matrix 
##      [,1]
## [1,] 0.38
## Sample Size 
## [1] 931
## 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

10 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!

11 Write Up Results

To test our first hypothesis that pandemic anxiety and mental flexibility would be negatively correlated, we calculated a Pearson’s correlation coefficients. Both variables did not meet the required assumptions of the test with pandemic anxiety having one outlier and mental flexibility having four outliers. To test our second hypothesis that pandemic anxiety and intolerance of uncertainty would be positively correlated, we calculated a Pearson’s correlation coefficients. One variable, pandemic anxiety, did not meet the required assumption of the test with pandemic anxiety having one outlier. The other variable, intolerance of uncertainty did meet the require assumptions of the test with no outliers. Any significant results involving pandemic anxiety and mental flexibility should be evaluated carefully.

As predicted, our first hypothesis was supported because we see a negative correlation between pandemic anxiety and mental flexibility (p < 0.001). The effect size of the correlations was weak (r > 0.26; Cohen, 1988). Our second hypothesis was supported, we see that pandemic anxiety would be higher in participants who reported higher levels of intolerance of uncertainty (p < 0.001). The effect size of the correlations was moderate (r > 0.38; Cohen, 1988). All results can be seen 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 2
Pandemic Anxiety 3.22 0.68
Mental Flexibility 4.14 0.96 -.26**
[-.32, -.20]
Intolerance of Uncertainty 2.53 0.89 .38** -.62**
[.33, .44] [-.66, -.58]
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.