Running a Correlation
Sydney Miller
2026-11-04
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 4.5.2library(apaTables) # to create our correlation table
library(kableExtra) # to create our correlation table## Warning: package 'kableExtra' was built under R version 4.5.22 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 semester3 State Your Hypothesis
There will be a significant relationship between stress, self-efficiency, and independence. Specifically, stress will be negatively related to self-efficiency and negatively related to independence; and self-efficiency will be positively related to independence.
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': 2065 obs. of 7 variables:
## $ ResponseID : chr "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
## $ age : chr "1 between 18 and 25" "1 between 18 and 25" "1 between 18 and 25" "1 between 18 and 25" ...
## $ income : chr "1 low" "1 low" "rather not say" "rather not say" ...
## $ moa_independence: num 3.67 3.67 3.5 3 3.83 ...
## $ moa_safety : num 2.75 3.25 3 1.25 2.25 2.5 4 3.25 2.75 3.5 ...
## $ efficacy : num 3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...
## $ 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(stress, efficacy, moa_independence))
# You can use the describe() command on an entire dataframe (d) or just on a single variable (d$pss)
describe(d2)## vars n mean sd median trimmed mad min max range skew
## stress 1 2065 3.07 0.60 3.10 3.07 0.59 1.3 4.6 3.3 -0.02
## efficacy 2 2065 3.11 0.44 3.10 3.12 0.44 1.2 4.0 2.8 -0.21
## moa_independence 3 2065 3.54 0.47 3.67 3.61 0.49 1.0 4.0 3.0 -1.50
## kurtosis se
## stress -0.14 0.01
## efficacy 0.40 0.01
## moa_independence 2.78 0.01# NOTE: Our fake variable has high kurtosis, which we'll ignore for the lab because we created it to be problematic. If you have high skew or kurtosis for any of your project variables, you will need to discuss it below in the Issues with My Data and Write up Results sections, as well as in your final project manuscript if your data does not meet the normality assumption.
# also use histograms to examine your continuous variables
# Because we are looking at 3 variables, we will have 3 histograms.
hist(d$stress)
hist(d$efficacy)
hist(d$moa_independence)
# 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$stress,d$efficacy)
plot(d$stress, d$moa_independence)
plot(d$efficacy, d$moa_independence)
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$stress > 3)## [1] 0d2$efficacy<- scale(d2$efficacy, center=T, scale=T)
hist(d2$efficacy)
sum(d2$efficacy < -3 | d2$efficacy > 3)## [1] 10d2$moa_independence<- scale(d2$moa_independence, center=T, scale=T)
hist(d2$moa_independence)
sum(d2$moa_independence < -3 | d2$moa_independence > 3)## [1] 355.2 Issues with My Data
One of my variables met all of the assumptions of Pearson’s correlation coefficient. One variable, independence had high kurtosis (2.78) and had 35 outliers. Additionally, one variable, self-efficiency, had 10 outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction.Any correlations with independence and self-efficiency should be evaluated carefully due to these risks.
6 Run a Single Correlation
corr_output <- corr.test(d2$stress, d2$efficacy)7 View Single Correlation
corr_output## Call:corr.test(x = d2$stress, y = d2$efficacy)
## Correlation matrix
## [,1]
## [1,] -0.4
## Sample Size
## [1] 2065
## 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 option8 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 efficacy moa_independence
## stress 1.00 -0.40 -0.01
## efficacy -0.40 1.00 0.09
## moa_independence -0.01 0.09 1.00
## Sample Size
## [1] 2065
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## stress efficacy moa_independence
## stress 0.0 0 0.6
## efficacy 0.0 0 0.0
## moa_independence 0.6 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, self-efficacy, and independence 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 meeting the standards of normality and containing no outliers. One variable, independence, had high kurtosis (2.78) and had 35 outliers. Additionally, one variable, self-efficacy, had 10 outliers; so any significant results involving independence and self-efficacy should be evaluated carefully .
Our hypothesis was partially supported as there was a significant relationship with self-efficacy with stress and independence (both ps < .001). There was not a significant relationship between stress and independence (p = 0.6). The effect size for stress and self-efficacy is moderate (0.30 >r > 0.49; Cohen, 1988) and the effect size for self-efficacy and independence was Trivial (0.09 > r; Cohen, 1988). Additionally, self-efficacy was found to be negatively related to stress, and positively related to independence, as predicted. Please refer to the correlation coefficients reported in Table 1.
| Variable | M | SD | 1 | 2 |
|---|---|---|---|---|
| Stress | 3.07 | 0.60 | ||
| Self-efficacy | 3.11 | 0.44 | -.40** | |
| [-.43, -.36] | ||||
| Independence | 3.54 | 0.47 | -.01 | .09** |
| [-.05, .03] | [.04, .13] | |||
| 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.