1 Loading Libraries

#install.packages("apaTables")
#install.packages("kableExtra")

library(psych) # for the describe() command and the corr.test() command
## Warning: package 'psych' was built under R version 4.4.3
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 stress, support, and mindfulness. Specifically, all three variables will be negatively related to mindfulness; and support will be positively related to mindfulness.

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(stress, support, mindful))

# 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
## stress     1 3126 3.05 0.60   3.00    3.05 0.59 1.30 4.7  3.40  0.04    -0.16
## support    2 3126 5.53 1.13   5.75    5.66 0.99 0.00 7.0  7.00 -1.12     1.50
## mindful    3 3126 3.71 0.84   3.73    3.71 0.79 1.13 6.0  4.87 -0.06    -0.13
##           se
## stress  0.01
## support 0.02
## mindful 0.02
# 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$stress)

hist(d$support)

hist(d$mindful)

# 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$stress, d$support)

plot(d$stress, d$mindful)

plot(d$support, d$mindful)

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

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

sum(d2$support < -3 | d2$support > 3)
## [1] 45
d2$mindful <- scale(d2$mindful, center= T, scale= T)
hist(d2$mindful)

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

5.2 Issues with My Data

One of my variables meet all of the assumptions of Pearson’s correlation coefficient. Two variable, had outliers, support and mindful. Mindful has 2 outliers and support has 45. Outliers can distort the relationship between two variables and sway the correlation in their direction. The variable, stress, also appears to have non-linear relationships with the support variable. Pearson’s r may underestimate the strength of a non-linear relationship and distort the relationship direction. Any correlations with stress should be evaluated carefully due to these risks.

6 Run a Single Correlation

corr_output <- corr.test(d2$stress, d2$support)

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$stress, y = d2$support)
## Correlation matrix 
##       [,1]
## [1,] -0.21
## Sample Size 
## [1] 3126
## 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 
##         stress support mindful
## stress    1.00   -0.21   -0.40
## support  -0.21    1.00    0.18
## mindful  -0.40    0.18    1.00
## Sample Size 
## [1] 3126
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##         stress support mindful
## stress       0       0       0
## support      0       0       0
## mindful      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 stress, support, and mindfulness would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. One of the variables (stress) met the required assumptions of the test, with both meeting the standards of normality and containing no outliers . Two variables, support and mindful, had 45 and 2 outliers respectfully, as well as the stress variable having a non-linear relationship with the support variable; so any significant results involving stress should be evaluated carefully .

As predicted, we found that all three variables were significantly correlated (all ps < .001). The effect sizes of all correlations were large (rs > .50; Cohen, 1988). Additionally, stress was found to be negatively related to mindfulness and support, and support is positively related to mindfulness, as predicted. 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
Stress 3.05 0.60
Support 5.53 1.13 -.21**
[-.24, -.18]
Mindfulness 3.71 0.84 -.40** .18**
[-.43, -.37] [.15, .22]
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.