Running a Correlation
fatou mbengue
2026-06-18
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 stress, subjective well being, and self efficacy. Specifically, perceived stress will be negatively related to subjective well-being and negatively related to self efficacy.
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': 3096 obs. of 7 variables:
## $ ResponseID : chr "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
## $ gender : chr "f" "m" "m" "f" ...
## $ race_rc : chr "white" "white" "white" "other" ...
## $ stress : num 3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
## $ swb : num 4.33 4.17 1.83 5.17 3.67 ...
## $ moa_independence: num 3.67 3.67 3.5 3 3.83 ...
## $ support : num 6 6.75 5.17 5.58 6 ...# 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, moa_independence))
# You can use the describe() command on an entire dataframe (d) or just on a single variable (d$pss)
describe(d2)## vars n mean sd median trimmed mad min max range skew
## stress 1 3096 3.05 0.60 3.00 3.05 0.59 1.3 4.7 3.4 0.04
## swb 2 3096 4.47 1.32 4.67 4.53 1.48 1.0 7.0 6.0 -0.37
## moa_independence 3 3096 3.54 0.47 3.67 3.61 0.49 1.0 4.0 3.0 -1.44
## kurtosis se
## stress -0.17 0.01
## swb -0.45 0.02
## moa_independence 2.51 0.01# NOTE: Our fake variable has high kurtosis, which we'll ignore for the lab because we created it to be problematic. If you have high skew or kurtosis for any of your project variables, you will need to discuss it below in the Issues with My Data and Write up Results sections, as well as in your final project manuscript if your data does not meet the normality assumption.
# also use histograms to examine your continuous variables
# Because we are looking at 3 variables, we will have 3 histograms.
hist(d$stress)
hist(d$swb)
hist(d$moa_independence)
# 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$stress, d$moa_independence)
plot(d$swb, d$moa_independence)
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$stress<- scale(d$stress, center=T, scale=T)
hist(d$stress)
sum(d2$stress < -3 | d2$stress > 3)## [1] 0d2$swb<- scale(d$swb, center=T, scale=T)
hist(d$swb)
sum(d2$swb < -3 | d2$swb > 3)## [1] 0d2$moa_independence<- scale(d$moa_independence, center=T, scale=T)
hist(d$moa_independence)
sum(d2$moa_independence < -3 | d2$moa_independence > 3)## [1] 515.2 Issues with My Data
All three of my variables met the assumptions of Pearson’s correlation coefficient. The variables appeared reasonably normal, and any potential outliers should be interpreted with caution. Visual inspection of the scatterplots suggested that the relationships between the variables were approximately linear. Therefore, the assumptions of Pearson’s correlation were adequately met and we proceeded with the analysis.
[Make sure to revise the above paragraph for your HW. If you do not have any non-linear relationships (which hopefully you won’t), remove those sentences as they will no longer be relevant. Delete this reminder in your HW.]
6 Run a Single Correlation
corr_output <- corr.test(d$stress, d$swb)7 View Single Correlation
corr_output## Call:corr.test(x = d$stress, y = d$swb)
## Correlation matrix
## [1] -0.51
## Sample Size
## [1] 3096
## These are the unadjusted probability values.
## The probability values adjusted for multiple tests are in the p.adj object.
## [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 moa_independence
## stress 1.00 -0.51 -0.02
## swb -0.51 1.00 0.10
## moa_independence -0.02 0.10 1.00
## Sample Size
## [1] 3096
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## stress swb moa_independence
## stress 0.00 0 0.18
## swb 0.00 0 0.00
## moa_independence 0.18 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| x
10 Write Up Results
To test our hypothesis that perceived stress, subjective well-being, and self-efficacy would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. All three variables met the required assumptions of the test, meeting acceptable standards of normality and showing no serious issues with outliers or non-linear relationships.
As predicted, we found significant correlations among the variables. The effect sizes ranged from moderate to strong according to Cohen’s (1988) guidelines. Additionally, perceived stress was found to be negatively related to subjective well-being and negatively related to self-efficacy, 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. 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 |
|---|---|---|---|---|
| Perceived Stress | 3.05 | 0.60 | ||
| Subjective Well-Being | 4.47 | 1.32 | -.51** | |
| [-.53, -.48] | ||||
| Self-Efficacy | 3.54 | 0.47 | -.02 | .10** |
| [-.06, .01] | [.07, .14] | |||
| 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.