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 intolerance of uncertainty, pandemic anxiety, and mental flexibility. Specifically, intolerance of uncertainty will be positively related to pandemic anxiety and negatively related to mental flexibility; and pandemic anxiety will be negatively related to mental flexibility.

4 Check Your 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':    284 obs. of  7 variables:
##  $ X        : int  7888 7365 8747 7357 8760 8654 8738 7911 8463 8834 ...
##  $ age      : chr  "1 under 18" "1 under 18" "1 under 18" "1 under 18" ...
##  $ mhealth  : chr  "none or NA" "none or NA" "none or NA" "none or NA" ...
##  $ iou      : num  3.48 1.59 1.59 1.26 1.93 ...
##  $ mfq_state: num  3.75 4 5.88 4.75 5.5 ...
##  $ pas_covid: num  4.44 3.11 3.22 1.78 2.78 ...
##  $ brs      : num  2 3.83 3.83 4 4.67 ...
# 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(iou, pas_covid, mfq_state))

# 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
## iou          1 284 3.01 0.91   3.09    3.02 1.07 1.11 4.78  3.67 -0.07    -0.94
## pas_covid    2 284 3.34 0.64   3.44    3.37 0.66 1.00 5.00  4.00 -0.40     0.65
## mfq_state    3 284 3.69 0.99   3.75    3.71 0.93 1.12 6.00  4.88 -0.22    -0.36
##             se
## iou       0.05
## pas_covid 0.04
## mfq_state 0.06
# 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$iou)

hist(d$pas_covid)

hist(d$mfq_state)

# 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$iou, d$pas_covid)

plot(d$iou, d$mfq_state)

plot(d$pas_covid, d$mfq_state)

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

sum(d2$iou < -3 | d2$iou > 3)
## [1] 0
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] 2
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] 0

5.2 Issues with My Data

Two of my variables meet all of the assumptions of Pearson’s correlation coefficient. One variable, pandemic anxiety, had two outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction. Any correlations with pandemic anxiety should be evaluated carefully due to this risk.

6 Run a Single Correlation

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

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$iou, y = d2$pas_covid)
## Correlation matrix 
##      [,1]
## [1,] 0.32
## Sample Size 
## [1] 284
## 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 
##             iou pas_covid mfq_state
## iou        1.00      0.32     -0.59
## pas_covid  0.32      1.00     -0.16
## mfq_state -0.59     -0.16      1.00
## Sample Size 
## [1] 284
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##           iou pas_covid mfq_state
## iou         0      0.00      0.00
## pas_covid   0      0.00      0.01
## mfq_state   0      0.01      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 my hypothesis that intolerance of uncertainty, pandemic anxiety, and mental flexibility would be correlated with one another, I calculated a series of Pearson’s correlation coefficients. Two of the variables (intolerance of uncertainty and mental flexibility) met the required assumptions of the test, with both meeting the standards of normality and containing no outliers. One variable, pandemic anxiety, had two outliers; so any significant results involving pandemic anxiety should be evaluated carefully.

As predicted, I found that all three variables were significantly correlated (all ps < .01). The effect size of the correlation between intolerance of uncertainty and pandemic anxiety was moderate (0.30 ≤ r ≥ 0.49; Cohen, 1988). The effect size of the correlation between intolerance of uncertainty and mental flexibility was strong (r > 0.50). The effect size of the correlation between pandemic anxiety and mental flexibility was weak (0.10 ≤ r ≥ 0.29). Additionally, all correlations were found to be in the same direction as predicted. Intolerance of uncertainty was found to be positively related to pandemic anxiety, and negatively related to mental flexibility. Pandemic anxiety was found to be negatively related to mental flexibility. 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
Intolerance of Uncertainty 3.01 0.91
Pandemic Anxiety 3.34 0.64 .32**
[.22, .42]
Mental Flexibility 3.69 0.99 -.59** -.16**
[-.66, -.51] [-.27, -.05]
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.