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 perceived social support, self efficacy, and perceived stress. Specifically, perceived social support will be positively related to self efficacy, but negatively related to perceived stress.

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':    3143 obs. of  7 variables:
##  $ ResponseID: chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ income    : chr  "1 low" "1 low" "rather not say" "rather not say" ...
##  $ marriage5 : chr  "are currently divorced from one another" "are currently married to one another" "are currently married to one another" "are currently married to one another" ...
##  $ belong    : num  2.8 4.2 3.6 4 3.4 4.2 3.9 3.6 2.9 2.5 ...
##  $ efficacy  : num  3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...
##  $ support   : num  6 6.75 5.17 5.58 6 ...
##  $ stress    : num  3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
# 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(support, efficacy, 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 kurtosis
## support     1 3143 5.54 1.13   5.75    5.66 0.99 0.0 7.0   7.0 -1.10     1.44
## efficacy    2 3143 3.13 0.45   3.10    3.13 0.44 1.1 4.0   2.9 -0.23     0.44
## stress      3 3143 3.05 0.60   3.00    3.05 0.59 1.3 4.7   3.4  0.03    -0.16
##            se
## support  0.02
## efficacy 0.01
## stress   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$support)

hist(d$efficacy)

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$support, d$efficacy)

plot(d$support, d$stress)

plot(d$efficacy, d$stress)

5 Check Your Assumptions

5.1 Pearson’s Correlation Coefficient Assumptions

  • Should have two 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$support<- scale(d2$support, center=T, scale=T)
hist(d2$support)

sum(d2$support < -3 | d2$support > 3)
## [1] 43
d2$efficacy<- scale(d2$efficacy, center=T, scale=T)
hist(d2$efficacy)

sum(d2$efficacy < -3 | d2$efficacy > 3)
## [1] 14
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 meet all of the assumptions of Pearson’s correlation coefficient. The variable support had kurtosis of 1.44 and 43 outliers. The variable efficacy had kurtosis of 0.44 and 14 outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction. The variables support and efficacy also appear to have nonlinear relationships with the other variable. Pearson’s r may underestimate the strength of a non-linear relationship and distort the relationship direction. Any correlations with support and efficacy should be evaluated carefully due to these risks.

6 Run a Single Correlation

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

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$support, y = d2$efficacy)
## Correlation matrix 
##      [,1]
## [1,] 0.21
## Sample Size 
## [1] 3143
## 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 
##          support efficacy stress
## support     1.00     0.21  -0.21
## efficacy    0.21     1.00  -0.40
## stress     -0.21    -0.40   1.00
## Sample Size 
## [1] 3143
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##          support efficacy stress
## support        0        0      0
## efficacy       0        0      0
## stress         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 perceived social support, self efficacy, and perceived stress 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, meeting the standards of normality and containing no outliers. The variable support had kurtosis of 1.44 and 43 outliers. The variable efficacy had kurtosis of 0.44 and 14 outliers.These variables also had non-linear relationships with the other variables; so any significant results involving support and efficacy should be evaluated carefully.

As predicted, we found that all three variables were significantly correlated (all ps < .001). The effect size of the correlation between support and efficacy and the effect size of the correlation between support and stress were weak(rs between .10 and .29; Cohen, 1988).The effect size of the correlation between efficacy and stress was moderate(rs between .30 and .49; Cohen, 1988). Additionally, support was found to be negatively related to stress, and positively related to efficacy, 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
Perceived Social Support 5.54 1.13
Self Efficacy 3.13 0.45 .21**
[.18, .24]
Percieved Stress 3.05 0.60 -.21** -.40**
[-.25, -.18] [-.43, -.37]
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.