Running a Correlation
Sarah Sammakieh
2025-11-05
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 table2 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 loneliness, resiliency, and disordered eating. Specifically, loneliness will be negatively related to resiliency and positively related to disordered eating, and resiliency will be negatively related to disordered eating.
4 Check Your Variables
str(d)## 'data.frame': 380 obs. of 7 variables:
## $ X : int 6350 6608 6612 6715 6726 6778 6859 6860 6929 6980 ...
## $ relationship_status: chr "Single, never married" "Single, never married" "Single, never married" "Single, never married" ...
## $ mhealth : chr "none or NA" "obsessive compulsive disorder" "none or NA" "none or NA" ...
## $ big5_neu : num 6 3.33 4.67 3 5 ...
## $ edeq12 : num 1.83 2.75 1.25 1.92 1.67 ...
## $ brs : num 2.17 3.17 3.17 3 2 ...
## $ isolation_c : num 2.5 3.25 2.75 3 3.5 3.25 1.75 2 3 3.5 ...# 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(edeq12, brs, isolation_c))
# You can use the describe() command on an entire dataframe (d) or just on a single variable (d$pss)
describe(d2)## vars n mean sd median trimmed mad min max range skew kurtosis
## edeq12 1 380 2.16 0.81 2.08 2.13 1.05 1 4.0 3.0 0.23 -1.09
## brs 2 380 2.63 0.87 2.67 2.62 0.99 1 5.0 4.0 0.15 -0.59
## isolation_c 3 380 2.63 0.74 2.75 2.69 0.74 1 3.5 2.5 -0.48 -0.94
## se
## edeq12 0.04
## brs 0.04
## isolation_c 0.04# NOTE: Our fake variable has high kurtosis, which we'll ignore for the lab because we created it to be problematic. If you have high skew or kurtosis for any of your project variables, you will need to discuss it below in the Issues with My Data and Write up Results sections, as well as in your final project manuscript if your data does not meet the normality assumption.
# also use histograms to examine your continuous variables
# Because we are looking at 3 variables, we will have 3 histograms.
hist(d$edeq12)
hist(d$brs)
hist(d$isolation_c)
# 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$edeq12, d$brs)
plot(d$edeq12, d$isolation_c)
plot(d$brs, d$isolation_c)
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$edeq12 <- scale(d2$edeq12, center=T, scale=T)
hist(d2$edeq12)
sum(d2$edeq12 < -3 | d2$edeq12 > 3)## [1] 0d2$brs <- scale(d2$brs, center=T, scale=T)
hist(d2$brs)
sum(d2$brs < -3 | d2$brs > 3)## [1] 0d2$isolation_c <- scale(d2$isolation_c, center=T, scale=T)
hist(d2$isolation_c)
sum(d2$isolation_c < -3 | d2$isolation_c > 3)## [1] 05.2 Issues with My Data
All of my variables met the assumptions of Pearson’s correlation coefficient. The skew and kurtosis were within the normal range, the relationships showed no signs of non-linearity, and there were no outliers that were identified.
6 Run a Single Correlation
corr_output <- corr.test(d2$edeq12, d2$brs)7 View Single Correlation
corr_output## Call:corr.test(x = d2$edeq12, y = d2$brs)
## Correlation matrix
## [,1]
## [1,] -0.37
## Sample Size
## [1] 380
## 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
## edeq12 brs isolation_c
## edeq12 1.00 -0.37 0.42
## brs -0.37 1.00 -0.49
## isolation_c 0.42 -0.49 1.00
## Sample Size
## [1] 380
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## edeq12 brs isolation_c
## edeq12 0 0 0
## brs 0 0 0
## isolation_c 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 disordered eating, resiliency, and loneliness would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. All three of the variables met the required assumptions of the test, with all meeting the standards of normality and containing no outliers.
As predicted, we found that all three variables were significantly correlated (all ps < .001). The effect sizes of all correlations were moderate (rs > .30; Cohen, 1988). Additionally, loneliness was found to be negatively related to resiliency, and positively related to disordered eating. Resiliency was also negatively related to disordered eating, as predicted. Please refer to the correlation coefficients reported in Table 1.
| Variable | M | SD | 1 | 2 |
|---|---|---|---|---|
| Disordered Eating | 2.16 | 0.81 | ||
| Resiliency | 2.63 | 0.87 | -.37** | |
| [-.46, -.28] | ||||
| Loneliness | 2.63 | 0.74 | .42** | -.49** |
| [.34, .50] | [-.57, -.41] | |||
| 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.