Running a Correlation HW
Molly Barber
2026-11-08
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 4.3.3library(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 satisfaction with life, independence, and the need to belong. Specifically, all three variables will be positively correlated.
4 Check Your Variables
str(d)## 'data.frame': 3085 obs. of 7 variables:
## $ ResponseID : chr "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
## $ edu : chr "2 Currently in college" "5 Completed Bachelors Degree" "2 Currently in college" "2 Currently in college" ...
## $ usdream : chr "american dream is important and achievable for me" "american dream is important and achievable for me" "american dream is not important and maybe not achievable for me" "american dream is not important and maybe not achievable for me" ...
## $ swb : num 4.33 4.17 1.83 5.17 3.67 ...
## $ moa_independence: num 3.67 3.67 3.5 3 3.83 ...
## $ belong : num 2.8 4.2 3.6 4 3.4 4.2 3.9 3.6 2.9 2.5 ...
## $ efficacy : num 3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...# 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(swb, moa_independence, belong))
# You can use the describe() command on an entire dataframe (d) or just on a single variable (d$pss)
describe(d2)## vars n mean sd median trimmed mad min max range skew
## swb 1 3085 4.47 1.32 4.67 4.53 1.48 1.0 7 6.0 -0.37
## moa_independence 2 3085 3.54 0.46 3.67 3.61 0.49 1.0 4 3.0 -1.45
## belong 3 3085 3.24 0.61 3.30 3.25 0.59 1.3 5 3.7 -0.26
## kurtosis se
## swb -0.45 0.02
## moa_independence 2.54 0.01
## belong -0.14 0.01# NOTE: Our fake variable has high kurtosis, which we'll ignore for the lab because we created it to be problematic. If you have high skew or kurtosis for any of your project variables, you will need to discuss it below in the Issues with My Data and Write up Results sections, as well as in your final project manuscript if your data does not meet the normality assumption.
# also use histograms to examine your continuous variables
# Because we are looking at 3 variables, we will have 3 histograms.
hist(d$swb)
hist(d$moa_independence)
hist(d$belong)
# 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$swb, d$moa_independence)
plot(d$swb, d$belong)
plot(d$moa_independence, d$belong)
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$swb <- scale(d2$swb, center=T, scale=T)
hist(d2$swb)
sum(d2$swb < -3 | d2$swb > 3)## [1] 0d2$moa_independence <- scale(d2$moa_independence, center=T, scale=T)
hist(d2$moa_independence)
sum(d2$moa_independence < -3 | d2$moa_independence > 3)## [1] 51d2$belong <- scale(d2$belong, center=T, scale=T)
hist(d2$belong)
sum(d2$belong < -3 | d2$belong > 3)## [1] 75.2 Issues with My Data
One of my variables meet all of the assumptions of Pearson’s correlation coefficient. One variable, independence, had high kurtosis (2.54) and 51 outliers. Another variable, belong, had 7 outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction. This variable, independence, also appears to have non-linear relationships with the other two variables. Pearson’s r may underestimate the strength of a non-linear relationship and distort the relationship direction. Any correlations with independence should be evaluated carefully due to these risks.
6 Run a Single Correlation
corr_output <- corr.test(d2$swb, d2$moa_independence)7 View Single Correlation
corr_output## Call:corr.test(x = d2$swb, y = d2$moa_independence)
## Correlation matrix
## [,1]
## [1,] 0.1
## Sample Size
## [1] 3085
## 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
## swb moa_independence belong
## swb 1.00 0.10 -0.15
## moa_independence 0.10 1.00 0.02
## belong -0.15 0.02 1.00
## Sample Size
## [1] 3085
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## swb moa_independence belong
## swb 0 0.00 0.00
## moa_independence 0 0.00 0.32
## belong 0 0.32 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 life satisfaction, independence, and need to belong would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. One of the variables (life satisfaction) met the required assumptions of the test, with both meeting the standards of noramlity and containing no outliers. One variable, independence, had high kurtosis (2.54), 51 outliers as well as non-linear relationships with the other variables, and need to belong had 7 outliers; so any significant results involving independence and need to belong should be evaluated carefully.
Unlike what we predicted, we found that two of the three variables were not significantly correlated (p = .10, p = -.15, p = .02). The effect sizes of the one significant correlation was small (rs > 0.10, < 0.29; Cohen, 1988). Additionally, satisfaction with life and need to belong was found to be negatively related. 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 |
|---|---|---|---|---|
| Satisfaction with Life | 4.47 | 1.32 | ||
| Independence | 3.54 | 0.46 | .10** | |
| [.07, .14] | ||||
| Need to Belong | 3.24 | 0.61 | -.15** | .02 |
| [-.18, -.11] | [-.02, .05] | |||
| 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.