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 independence, perceived social support, and perceived stress. Specifically, independence will be positively related to perceived social support but negatively related to perceived stress; and perceived social support will be negatively related to perceived stress.

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(moa_independence, support, stress))

# 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
## moa_independence    1 3095 3.54 0.46   3.67    3.61 0.49 1.0 4.0   3.0 -1.44
## support             2 3095 5.53 1.13   5.75    5.65 0.99 0.0 7.0   7.0 -1.12
## stress              3 3095 3.05 0.60   3.00    3.05 0.59 1.3 4.7   3.4  0.04
##                  kurtosis   se
## moa_independence     2.52 0.01
## support              1.50 0.02
## stress              -0.17 0.01
# 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$moa_independence)

hist(d$support)

hist(d$stress)

# 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$moa_independence, d$support)

plot(d$moa_independence, d$stress)

plot(d$support, d$stress)

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

sum(d2$moa_independence < -3 | d2$moa_independence > 3)
## [1] 51
d2$support <- scale(d2$support, center=T, scale=T)
hist(d2$support)

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

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

5.2 Issues with My Data

One of my variables met all of the assumptions of Pearson’s correlation coefficient. One variable, independence had high kurtosis (2.52) and 51 outliers. Another variable, perceived social support, had 45 outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction.

6 Run a Single Correlation

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

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$moa_independence, y = d2$support)
## Correlation matrix 
##      [,1]
## [1,]  0.1
## Sample Size 
## [1] 3095
## 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 
##                  moa_independence support stress
## moa_independence             1.00    0.10  -0.02
## support                      0.10    1.00  -0.21
## stress                      -0.02   -0.21   1.00
## Sample Size 
## [1] 3095
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##                  moa_independence support stress
## moa_independence             0.00       0   0.18
## support                      0.00       0   0.00
## stress                       0.18       0   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 our hypothesis that independence, perceived social support, and perceived stress would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. One of the variables (perceived stress) met the required assumptions of the test, meeting the standards of normality and containing no outliers. One variable, independence, had high kurtosis (2.52) and 51 outliers. Another variable, perceived social support, had 45 outliers; so any significant results involving independence and perceived social support should be evaluated carefully.

Our results found partial support for our hypothesis. We found that independence and perceived stress did not have a significant relationship (p = 0.18). However, independence and social support, and stress and social support both had significant relationships (p < 0.05). Independence was found to be positively related to perceived social support, and perceived social support was found to be negatively related to perceived stress. Please refer to the correlation coefficients reported in Table 1. The effect sizes for both significant correlations were small (0.10 < rs < 0.29; Cohen, 1988).

Table 1: Means, standard deviations, and correlations with confidence intervals
Variable M SD 1 2
Indepencen 3.54 0.46
Perceived Social Support 5.53 1.13 .10**
[.06, .13]
Perceived Stress 3.05 0.60 -.02 -.21**
[-.06, .01] [-.25, -.18]
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.