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, Mental Flexibility (State), and Perceived Stress. Specifically, (Mental Flexibility (State) will be negatively related to Intolerance of Uncertainty and Perceived Stress, however Perceived Stress will be positively related to Intolerance of Uncertainty.

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(iou, mfq_26, pss))

# 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       1 666 2.68 0.92   2.56    2.65 1.04 1.0 4.78  3.78  0.29    -0.85
## mfq_26    2 666 4.25 0.65   4.30    4.26 0.59 1.8 6.00  4.20 -0.26     0.13
## pss       3 666 3.13 0.95   3.25    3.15 1.11 1.0 5.00  4.00 -0.12    -0.76
##          se
## iou    0.04
## mfq_26 0.03
## pss    0.04
# NOTE: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$mfq_26)

hist(d$pss)

# 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$iou, d$mfq_26)

plot(d$iou, d$pss)

plot(d$mfq_26, d$pss)

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$mfq_26 <- scale(d2$mfq_26, center=T, scale=T)
hist(d2$mfq_26)

sum(d2$mfq_26 < -3 | d2$mfq_26 > 3)
## [1] 2
d2$pss <- scale(d2$pss, center=T, scale=T)
hist(d2$pss)

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

5.2 Issues with My Data

All of my variables met all of the assumptions of Pearson’s correlation coefficient. None of my variables had high kurtosis or outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction. All of my variables also represented linear relationships with one another. Although the following concerns do not appear to apply to my data, it should be noted that Pearson’s r may underestimate the strength of a non-linear relationship and distort the relationship direction. Any correlations with fakeness should be evaluated carefully due to these risks.

6 Run a Single Correlation

corr_output <- corr.test(d2$iou, d2$mfq_26)

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$iou, y = d2$mfq_26)
## Correlation matrix 
##       [,1]
## [1,] -0.57
## Sample Size 
## [1] 666
## 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 mfq_26   pss
## iou     1.00  -0.57  0.64
## mfq_26 -0.57   1.00 -0.47
## pss     0.64  -0.47  1.00
## Sample Size 
## [1] 666
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##        iou mfq_26 pss
## iou      0      0   0
## mfq_26   0      0   0
## pss      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 Intolerance of Uncertainty, Mental Flexibility (State), and Percieved Stress Scale would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. All three of the variables met the required assumptions of the test, all meeting the standards of normality and containing no outliers.

As predicted, we found that all 3 variables were significantly correlated (all ps <.001). The effect sizes between Intolerance of Uncertainty and both Mental Flexibility (State) and Percieved Stress Scale were large. The effect size between Mental Flexibility (State) and Perceived Stress Scale was medium (rs > #; Cohen, 1988). 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 2.68 0.92
Mental Flexibility (State) 4.25 0.65 -.57**
[-.62, -.51]
Percieved Stress Scale 3.13 0.95 .64** -.47**
[.59, .68] [-.53, -.41]
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.