Running a Correlation
Riley Mentzer
2026-11-06
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 there will be a significant relationship between independence, interpersonal exploitativeness, 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.
# 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': 2087 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 ...
## $ npi : num 0.6923 0.1538 0.0769 0.0769 0.7692 ...
## $ swb : num 4.33 4.17 1.83 5.17 3.67 ...
## $ exploit : num 2 3.67 4.33 1.67 4 ...# 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(moa_independence, exploit, swb))
# You can use the describe() command on an entire dataframe (d) or just on a single variable (d$pss)
describe(d2)## vars n mean sd median trimmed mad min max range skew
## moa_independence 1 2087 3.54 0.47 3.67 3.61 0.49 1 4 3 -1.49
## exploit 2 2087 2.36 1.38 2.00 2.18 1.48 1 7 6 0.96
## swb 3 2087 4.43 1.33 4.50 4.49 1.48 1 7 6 -0.36
## kurtosis se
## moa_independence 2.75 0.01
## exploit 0.37 0.03
## swb -0.50 0.03# NOTE: Our fake variable has high kurtosis, which we'll ignore for the lab because we created it to be problematic. If you have high skew or kurtosis for any of your project variables, you will need to discuss it below in the Issues with My Data and Write up Results sections, as well as in your final project manuscript if your data does not meet the normality assumption.
# also use histograms to examine your continuous variables
# Because we are looking at 3 variables, we will have 3 histograms.
hist(d$moa_independence)
hist(d$exploit)
hist(d$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$moa_independence, d$exploit)
plot(d$moa_independence, d$swb)
plot(d$swb, d$exploit)
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$moa_independence<- scale(d2$moa_independence, center=T, scale=T)
hist(d2$moa_independence)
sum(d2$moa_independence < -3 | d2$moa_independence > 3)## [1] 36 d2$exploit<- scale(d2$exploit, center=T, scale=T)
hist(d2$exploit)
sum(d2$exploit < -3 | d2$exploit > 3)## [1] 22 d2$swb<- scale(d2$swb, center=T, scale=T)
hist(d2$swb)
sum(d2$swb < -3 | d2$swb > 3)## [1] 05.2 Issues with My Data
Two of my variables meet all of the assumptions of Pearson’s correlation coefficient. One variable, independence, had high kurtosis (2.75) and 36 outliers. The variable, explotativeness, had 22 outliers as well. Outliers can distort the relationship between two variables and sway the correlation in their direction.
[Make sure to revise the above paragraph for your HW. If you do not have any non-linear relationships (which hopefully you won’t), remove those sentences as they will no longer be relevant. Delete this reminder in your HW.]
6 Run a Single Correlation
corr_output <- corr.test(d2$moa_independence, d2$swb)7 View Single Correlation
corr_output## Call:corr.test(x = d2$moa_independence, y = d2$swb)
## Correlation matrix
## [,1]
## [1,] 0.08
## Sample Size
## [1] 2087
## 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
## moa_independence exploit swb
## moa_independence 1.00 -0.01 0.08
## exploit -0.01 1.00 -0.08
## swb 0.08 -0.08 1.00
## Sample Size
## [1] 2087
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## moa_independence exploit swb
## moa_independence 0.00 0.51 0
## exploit 0.51 0.00 0
## swb 0.00 0.00 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 V1, V2, and V3 would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. One of the variables (satisfaction with life) met the required assumptions of the test, meeting the standards of normality and containing no outliers . However, one variable, independence, had high kurtosis (2.75), and 36 outliers and, one variable, exploitativness, had 22 outliers. So any significant results involving independence or exploitativness should be evaluated carefully .
As predicted, we found that two of the three variables were significantly correlated (all ps < .001). The effect sizes of all correlations were small (rs < 0.10; Cohen, 1988). Additionally, independence was found to be positively related to satisfaction with life, exploitiveness was negatively related to satisfaction with life, as predicted. 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.
| Variable | M | SD | 1 | 2 |
|---|---|---|---|---|
| Independence | 3.54 | 0.47 | ||
| Exploitativeness | 2.36 | 1.38 | -.01 | |
| [-.06, .03] | ||||
| Satisfaction with Life | 4.43 | 1.33 | .08** | -.08** |
| [.04, .13] | [-.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.