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)

3 State Your Hypothesis

There will be a significant relationship between mental flexibility, intolerance of uncertainty, and perceived stress. Specifically, mental flexibility will be negatively related to intolerance of uncertainty and perceived stress, while intolerance of uncertainty will be positively related to perceived stress.

4 Check Your Variables

str(d)
## 'data.frame':    685 obs. of  7 variables:
##  $ X        : int  520 2814 3146 3295 717 6056 4753 2044 1965 1246 ...
##  $ education: chr  "1 equivalent to not completing high school" "prefer not to say" "2 equivalent to high school completion" "prefer not to say" ...
##  $ mhealth  : chr  "none or NA" "none or NA" "none or NA" "none or NA" ...
##  $ iou      : num  2.22 1.52 1.78 1.85 2.22 ...
##  $ mfq_26   : num  2.7 4.55 4.8 3.8 4.5 4 5.8 4.5 5.25 5.15 ...
##  $ 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 ...
# 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(mfq_26, iou, 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
## mfq_26    1 685 4.24 0.65   4.25    4.25 0.67 1.8 6.00  4.20 -0.23     0.09
## iou       2 685 2.69 0.92   2.56    2.65 1.04 1.0 4.89  3.89  0.30    -0.82
## pss       3 685 3.14 0.94   3.25    3.15 1.11 1.0 5.00  4.00 -0.13    -0.73
##          se
## mfq_26 0.02
## iou    0.04
## pss    0.04
# 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$mfq_26)

hist(d$iou)

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$mfq_26, d$iou)

plot(d$mfq_26, d$pss)

plot(d$iou, d$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$mfq_26<- scale(d2$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
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

Two of my variables meet all of the assumptions of Pearson’s correlation coefficient. One variable, mental flexibility, had two outliers, although it did not have high skew (−0.23) or kurtosis (0.09). Intolerance of uncertainty had a skew of 0.30, kurtosis of −0.82, and zero outliers. Perceived stress had a skew of −0.13, kurtosis of −0.73, and zero outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction. Mental flexibility appeared to have linear relationships with the other two variables. Correlations involving mental flexibility should be evaluated carefully because its two outliers could affect the strength or direction of the relationships.

6 Run a Single Correlation

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

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$mfq_26, y = d2$pss)
## Correlation matrix 
##       [,1]
## [1,] -0.47
## Sample Size 
## [1] 685
## 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 
##        mfq_26   iou   pss
## mfq_26   1.00 -0.58 -0.47
## iou     -0.58  1.00  0.62
## pss     -0.47  0.62  1.00
## Sample Size 
## [1] 685
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##        mfq_26 iou pss
## mfq_26      0   0   0
## iou         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 mental flexibility, intolerance of uncertainty, and perceived stress would be related to one another, we calculated a series of Pearson’s correlation coefficients. Intolerance of uncertainty and perceived stress met all the assumptions of the test. Mental flexibility had two outliers, although it had acceptable skew (−0.23) and kurtosis (0.09) and appeared to have linear relationships with the other variables. Therefore, correlations involving mental flexibility should be evaluated carefully.

As predicted, all three variables were significantly correlated (all ps < .001). Mental flexibility was negatively related to intolerance of uncertainty, r = −.58, and this relationship had a large effect size. Mental flexibility was also negatively related to perceived stress, r = −.47, and this relationship had a moderate effect size. Intolerance of uncertainty was positively related to perceived stress, r = .62, and this relationship had a large effect size. All three results supported our hypothesis. 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
Mental Flexibility 4.24 0.65
Intolerance of Uncertainty 2.69 0.92 -.58**
[-.62, -.52]
Perceived Stress 3.14 0.94 -.47** .62**
[-.53, -.41] [.58, .67]
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.