Running a Correlation
Radhika Saxena
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
We predict there will be a significant relationship between Stress, Satisfaction with life, and Exploitativeness . Specifically, Stress will be negatively related to Satisfaction with Life and positively related to Exploitativeness; and Satisfaction with Life will be negatively related to Exploitativeness.
In your HW, paste in your correlation hypothesis from your Hypothesis Activity assignment – make any necessary revisions based on grader feedback. Delete this reminder in your HW.]
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': 2092 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" ...
## $ swb : num 4.33 4.17 1.83 5.17 3.67 ...
## $ stress : num 3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
## $ exploit : num 2 3.67 4.33 1.67 4 ...
## $ moa_independence: num 3.67 3.67 3.5 3 3.83 ...# 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, swb, exploit))
# You can use the describe() command on an entire dataframe (d) or just on a single variable (d$pss)
describe(d2)## vars n mean sd median trimmed mad min max range skew kurtosis
## stress 1 2092 3.07 0.60 3.1 3.07 0.59 1.3 4.6 3.3 -0.02 -0.15
## swb 2 2092 4.43 1.33 4.5 4.49 1.48 1.0 7.0 6.0 -0.36 -0.49
## exploit 3 2092 2.37 1.38 2.0 2.18 1.48 1.0 7.0 6.0 0.96 0.36
## se
## stress 0.01
## swb 0.03
## exploit 0.03# NOTE: Our fake variable has high kurtosis, which we'll ignore for the lab because we created it to be problematic. If you have high skew or kurtosis for any of your project variables, you will need to discuss it below in the Issues with My Data and Write up Results sections, as well as in your final project manuscript if your data does not meet the normality assumption.
# also use histograms to examine your continuous variables
# Because we are looking at 3 variables, we will have 3 histograms.
hist(d$stress)
hist(d$swb)
hist(d$exploit)
# 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$stress, d$swb)
plot(d$stress, d$exploit)
plot(d$swb, d$exploit)
5 Check Your Assumptions
5.1 Pearson’s Correlation Coefficient Assumptions
- Should have all measurement 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$stress > 3)## [1] 0d2$swb <- scale(d2$swb, center=T, scale=T)
hist(d2$swb)
sum(d2$swb < -3 | d2$swb > 3)## [1] 0d2$exploit <- scale(d2$exploit, center=T, scale=T)
hist(d2$exploit)
sum(d2$exploit < -3 | d2$exploit > 3)## [1] 225.2 Issues with My Data
Two of my variables meet all of the assumptions of Pearson’s correlation coefficient. One variable, Exploitativeness had 22 outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction. This variable, exploitativeness, also appears to have non-linear relationships with the other two variables. Pearson’s r may underestimate the strength of a non-linear relationship and distort the relationship direction. Any correlations with exploitativeness should be evaluated carefully due to these risks.
6 Run a Single Correlation
corr_output <- corr.test(d2$stress, d2$swb)7 View Single Correlation
corr_output## Call:corr.test(x = d2$stress, y = d2$swb)
## Correlation matrix
## [,1]
## [1,] -0.5
## Sample Size
## [1] 2092
## 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 swb exploit
## stress 1.00 -0.50 0.04
## swb -0.50 1.00 -0.08
## exploit 0.04 -0.08 1.00
## Sample Size
## [1] 2092
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## stress swb exploit
## stress 0.00 0 0.09
## swb 0.00 0 0.00
## exploit 0.09 0 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 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, satisfaction with life, and exploitativeness would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. Two of the variables (stress and satisfaction with life) met the required assumptions of the test, with both meeting the standards of normality and containing no outliers. One variable, exploitativeness, had 22 outliers as well as non-linear relationships with the other variables; so any significant results involving exploitativeness should be evaluated carefully.
Our hypothesis was partially supported, we found that variables stress and satisfaction with life were significantly and negatively correlated in the direction we predicted (ps < .001) the effect size was strong (r = 0.50, Cohen, 1988). Variables satisfaction with life was significantly and negatively correlated with exploitativeness in the direction we predicted (ps < .001) and the effect size was found to be trivial (r = 0.08, Cohen, 1988). However, variables stress and exploitativeness are not found to be significantly correlated (p = 0.09). Please refer to 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 whether supported or not. Always report the Pearson’s r and p-value for every prediction. If your p-values vary (some are < .05 while others are <.001), then you can say that they are all less than the largest of the major sig division: .05, .01, .001. Similarly, if your effect sizes vary, make sure to update the wording above and specify which were trivial/small/medium/large based on what you have (i.e., do not state any size you did not find). Delete this reminder in your HW.]
| Variable | M | SD | 1 | 2 |
|---|---|---|---|---|
| Stress | 3.07 | 0.60 | ||
| Satisfaction with Life | 4.43 | 1.33 | -.50** | |
| [-.53, -.46] | ||||
| Exploitativeness | 2.37 | 1.38 | .04 | -.08** |
| [-.01, .08] | [-.12, -.04] | |||
| 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.