Running a Correlation
Sylvie Morgan
2024-11-11
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
We predict that stress, the need to belong, self-efficacy, and social media use will all be correlated with each other. Additionally, we predict that self-efficacy will be negatively correlated with the need to belong, such that participants who report higher levels of self-efficacy will report lower need to belong.
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': 2146 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" ...
## $ belong : num 2.8 4.2 3.6 4 3.4 4.2 3.9 3.6 2.9 2.5 ...
## $ stress : num 3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
## $ efficacy : num 3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...
## $ socmeduse : int 47 23 34 35 37 13 37 43 37 29 ...# 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(belong, stress, efficacy, socmeduse))
# You can use the describe() command on an entire dataframe (d) or just on a single variable (d$pss)
describe(d2) ## vars n mean sd median trimmed mad min max range skew
## belong 1 2146 3.21 0.61 3.2 3.23 0.59 1.3 5.0 3.7 -0.27
## stress 2 2146 3.06 0.60 3.1 3.06 0.59 1.3 4.6 3.3 -0.02
## efficacy 3 2146 3.11 0.44 3.1 3.12 0.44 1.2 4.0 2.8 -0.19
## socmeduse 4 2146 34.27 8.60 35.0 34.54 7.41 11.0 55.0 44.0 -0.31
## kurtosis se
## belong -0.10 0.01
## stress -0.15 0.01
## efficacy 0.36 0.01
## socmeduse 0.20 0.19# NOTE: Our fake variable has high kurtosis, which we'll ignore for the lab. You don't need to discuss univariate normality in the results write-ups for the labs/homework, but you will need to discuss it in your final project manuscript.
# also use histograms to examine your continuous variables
hist(d$belong) 
hist(d$stress) 
hist(d$efficacy) 
hist(d$socmeduse) 
# last, use scatterplots to examine your continuous variables together, for each pairing
plot(d$belong, d$stress) 
plot(d$belong, d$efficacy) 
plot(d$belong, d$socmeduse) 
plot(d$stress, d$efficacy) 
plot(d$stress, d$socmeduse) 
plot(d$efficacy, d$socmeduse) 
5 Check Your Assumptions
5.1 Pearson’s Correlation Coefficient Assumptions
- Should have two measurements for each participant
- Variables should be continuous and normally distributed
- Outliers should be identified and removed
- Relationship between the variables should be linear
5.1.1 Checking for Outliers
Note: You are not required to screen out outliers or take any action based on what you see here. This is something you will check and then discuss in your write-up.
# We are going to standardize (z-score) all of our variables, and check them for outliers.
d2$belong <- scale(d2$belong, center=T, scale=T)
hist(d2$belong) 
sum(d2$belong < -3 | d2$belong > 3) ## [1] 2d2$stress <- scale(d2$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$socmeduse <- scale(d2$socmeduse, center=T, scale=T)
hist(d2$socmeduse) 
sum(d2$socmeduse < -3 | d2$socmeduse > 3) ## [1] 05.2 Issues with My Data
Two of my variables meet all of the assumptions of Pearson’s correlation coefficient. One variable, the need to belong, had a normal kurtosis of -0.10 but had 2 outliers. Additionally, a second variable, self-efficacy, had a normal kurtosis of 0.36 but had 10 outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction. These variables also appear to have non-linear relationships with the other two variables, stress and social media use. Pearson’s r may underestimate the strength of a non-linear relationship and distort the relationship direction. Any correlations with measures of the need to belong and self-efficacy should be evaluated carefully due to these risks.
[Make sure to revise the above paragraph for your HW.]
6 Run a Single Correlation
corr_output <- corr.test(d2$belong, d2$stress) 7 View Single Correlation
corr_output ## Call:corr.test(x = d2$belong, y = d2$stress)
## Correlation matrix
## [,1]
## [1,] 0.29
## Sample Size
## [1] 2146
## 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
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|
Remember, Pearson’s r is also an effect size!
corr_output_m <- corr.test(d2) 9 View Test Output
corr_output_m ## Call:corr.test(x = d2)
## Correlation matrix
## belong stress efficacy socmeduse
## belong 1.00 0.29 -0.26 0.27
## stress 0.29 1.00 -0.40 0.11
## efficacy -0.26 -0.40 1.00 0.03
## socmeduse 0.27 0.11 0.03 1.00
## Sample Size
## [1] 2146
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## belong stress efficacy socmeduse
## belong 0 0 0.00 0.00
## stress 0 0 0.00 0.00
## efficacy 0 0 0.00 0.21
## socmeduse 0 0 0.21 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 diagonal10 Write Up Results
To test our hypothesis that the need to belong, stress, self-efficacy, and social media use would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. Two of the variables (stress and social media use) met the required assumptions of the test, with both variables meeting the standards of normality and containing no outliers. Two variables, the need to belong and self-efficacy, had 2 outliers and 10 outliers respectively, as well as non-linear relationships with the other variables; so any significant results involving the need to belong or self-efficacy should be evaluated carefully.
After testing out hypothesis, we found that only two variables, need to belong and stress, were significantly correlated (all ps < .001). The variables of self-efficacy and social media use were found to not be significantly correlated (ps > .001). The effect sizes of all variables were medium.(rs > .30; Cohen, 1988). Our second hypothesis was also supported, that the need to belong would be lower in participants who reported higher levels of self-efficacy, as can be seen by the correlation coefficients reported in Table 1.
[In your HW, revise the above two paragraphs to fit your results. Make sure to discuss ALL predicted correlations and if sig or not.]
| Variable | M | SD | 1 | 2 | 3 |
|---|---|---|---|---|---|
| The Need to Belong | 3.21 | 0.61 | |||
| Stress | 3.06 | 0.60 | .29** | ||
| [.25, .33] | |||||
| Self-Efficacy | 3.11 | 0.44 | -.26** | -.40** | |
| [-.30, -.22] | [-.43, -.36] | ||||
| Social Media Use | 34.27 | 8.60 | .27** | .11** | .03 |
| [.23, .31] | [.06, .15] | [-.02, .07] | |||
| 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.