Running a Correlation
Rose Deol
2026-11-08
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 perceived social support, social media use, and satisfaction with life. Specifically, all three variables will be positively related.
4 Check Your Variables
# We're going to create a fake variable for this lab, so that we have four variables.
# NOTE: YOU WILL SKIP THIS STEP FOR THE HOMEWORK! DELETE LINES 48-52!
str(d)## 'data.frame': 2148 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" ...
## $ party_rc : chr "democrat" "independent" "apolitical" "apolitical" ...
## $ swb : num 4.33 4.17 1.83 5.17 3.67 ...
## $ support : num 6 6.75 5.17 5.58 6 ...
## $ socmeduse : int 47 23 34 35 37 13 37 43 37 29 ...
## $ 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, socmeduse, swb))
# You can use the describe() command on an entire dataframe (d) or just on a single variable (d$pss)
describe(d2)## vars n mean sd median trimmed mad min max range skew kurtosis
## support 1 2148 5.53 1.13 5.75 5.66 0.99 0 7 7 -1.09 1.33
## socmeduse 2 2148 34.25 8.60 35.00 34.52 7.41 11 55 44 -0.31 0.20
## swb 3 2148 4.44 1.33 4.50 4.50 1.48 1 7 6 -0.36 -0.49
## se
## support 0.02
## socmeduse 0.19
## swb 0.03# NOTE: Our fake variable has high kurtosis, which we'll ignore for the lab because we created it to be problematic. If you have high skew or kurtosis for any of your project variables, you will need to discuss it below in the Issues with My Data and Write up Results sections, as well as in your final project manuscript if your data does not meet the normality assumption.
# also use histograms to examine your continuous variables
# Because we are looking at 3 variables, we will have 3 histograms.
hist(d$support)
hist(d$socmeduse)
hist(d$swb)
# 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$support, d$socmeduse)
plot(d$support, d$swb)
plot(d$socmeduse, d$swb)
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$support > 3)## [1] 27d2$socmeduse <- scale(d2$socmeduse, center=T, scale=T)
hist(d2$socmeduse)
sum(d2$socmeduse < -3 | d2$socmeduse > 3)## [1] 0d2$swb <- scale(d2$swb, center=T, scale=T)
hist(d2$swb)
sum(d2$swb < -3 | d2$swb > 3)## [1] 05.2 Issues with My Data
None of my variables meet all of the assumptions of Pearson’s correlation coefficient. One variable, support, did not have a normal distribution and was skewed right and had 27 outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction. This variable, support, also appears to have a nonlinear relationship with the social media use. Pearson’s r may underestimate the strength of a non-linear relationship and distort the relationship direction. Any correlations with support should be evaluated carefully due to these risks. Social media use and satisfaction with life variables also had a nonlinear relationship, however, besides this they meet all other assumptions.
6 Run a Single Correlation
corr_output <- corr.test(d2$support, d2$socmeduse)7 View Single Correlation
corr_output## Call:corr.test(x = d2$support, y = d2$socmeduse)
## Correlation matrix
## [,1]
## [1,] 0.2
## Sample Size
## [1] 2148
## 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
## support socmeduse swb
## support 1.00 0.20 0.46
## socmeduse 0.20 1.00 0.09
## swb 0.46 0.09 1.00
## Sample Size
## [1] 2148
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## support socmeduse swb
## support 0 0 0
## socmeduse 0 0 0
## swb 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 my hypothesis that percieved soical support, social media use, and satisfaction with life would be correlated with one another, I calculated a series of Pearson’s correlation coefficients. None of the variables met the required assumptions of the test. Two variables, social media use and satisfaction with life, met most of the standards of normality and containing no outliers. They however did not have a linear relationship with one another, and social media use also had no linear relationship with the satisfaction of life variable. One variable, perceived social support, had 27 outliers as well a as non-linear relationship with social media use; so any significant results involving perceived social support should be evaluated carefully.
As predicted, I found that all three variables were significantly correlated (all ps < .001). The effect sizes of all correlations ranged from trivial (rs = 0.09; Cohen, 1988) to moderate (rs < 0.5; Cohen, 1988). The effect size between support and social media use was weak (r= 0.2), the effect size between support and satisfaction with life was moderate, (r = 0.46), adn the effect size between social media use and satisfaction with life was trivial (r = 0.09). As predicted, perceived social support and satisfaction with life were positively realted, however all other correlations seem to be non-linear according to their scatter plots. Please refer to the correlation coefficients reported in Table 1.
| Variable | M | SD | 1 | 2 |
|---|---|---|---|---|
| Percieved Social Support | 5.53 | 1.13 | ||
| Social Media Use | 34.25 | 8.60 | .20** | |
| [.15, .24] | ||||
| Satisfaction with Life | 4.44 | 1.33 | .46** | .09** |
| [.43, .50] | [.05, .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.