Correlation Lab

Loading Libraries

library(psych) # for the describe() command and the corr.test() command
library(apaTables) # to create our correlation table
library(kableExtra) # to create our correlation table

Importing Data

d <- read.csv(file="Data/mydata.csv", header=T)
# 
 # since we're focusing on our continuous variables, we're going to drop our categorical variables. this will make some stuff we're doing later easier.
 d <- subset(d, select=-c(gender, phq))

State Your Hypotheses - PART OF YOUR WRITEUP

Age, gender, and self-esteem (RSE) will significantly predict perceived stress (PSS), depressive symptoms (PHQ), and disordered eating behaviors (EDE-Q12), with lower self-esteem correlating with higher stress, depression, and disordered eating, and gender moderating these relationships.

Check Your Assumptions

Pearson’s Correlation Coefficient Assumptions

• Should have two measurements for each participant for each variable (confirmed by earlier procedures – we dropped any participants with missing data)
• Variables should be continuous and normally distributed, or assessments of the relationship may be inaccurate (confirmed above – if issues, make a note and continue)
• Outliers should be identified and removed, or results will be inaccurate (will do below)
• Relationship between the variables should be linear, or they will not be detected (will do below)

Checking for Outliers

Outliers can mask potential effects and cause Type II error (you assume there is no relationship when there really is one, e.g., false negative).

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.

 # using the scale() command to standardize our variable, viewing a histogram, and then counting statistical outliers
d$rse <- scale(d$rse, center=T, scale=T)
hist(d$rse)

sum(d$rse < -3 | d$rse > 3)

[1] 0

d$pss <- scale(d$pss, center=T, scale=T)
hist(d$pss)

sum(d$pss < -3 | d$pss > 3)

[1] 0

d$edeq12 <- scale(d$edeq12, center=T, scale=T)
hist(d$edeq12)

sum(d$edeq12 < -3 | d$edeq12 > 3)

[1] 0

Checking for Linear Relationships

Non-linear relationships cannot be detected by Pearson’s correlation (the type of correlation we’re doing here). This means that you may underestimate the relationship between a pair of variables if they have a non-linear relationship, and thus your understanding of what’s happening in your data will be inaccurate.

Visually check that relationships are linear and write a brief description of any potential nonlinearity. You will have to use your judgement. There are no penalties for answering ‘wrong’, so try not to stress out about it too much – just do your best.

 # use scatterplots to examine your continuous variables together
plot(d$rse, d$pss)

plot(d$rse, d$edeq12)

plot(d$pss, d$edeq12)

Check Your Variables

describe(d)

       vars   n mean   sd median trimmed  mad   min  max range  skew kurtosis
age*      1 939 2.09 1.64   1.00    1.86 0.00  1.00 5.00  4.00  1.00    -0.86
rse       2 939 0.00 1.00   0.07    0.02 1.04 -2.32 1.89  4.22 -0.20    -0.75
pss       3 939 0.00 1.00   0.08   -0.01 1.16 -2.01 2.17  4.18  0.11    -0.80
edeq12    4 939 0.00 1.00  -0.18   -0.10 1.02 -1.21 2.93  4.14  0.69    -0.50
         se
age*   0.05
rse    0.03
pss    0.03
edeq12 0.03

# Histograms for variable distributions
hist(d$rse)

hist(d$pss)

hist(d$edeq12)

Issues with My Data - PART OF YOUR WRITEUP

point out non linear groups as well as skew

Run Pearson’s Correlation

There are two ways to run Pearson’s correlation in R. You can calculate each correlation one-at-a-time using multiple commands, or you can calculate them all at once and report the scores in a matrix. The matrix output can be confusing at first, but it’s more efficient. We’ll do it both ways.

Run a Single Correlation

 corr_output <- corr.test(d$rse, d$pss)

View Single Correlation

Strong effect: Between |0.50| and |1| Moderate effect: Between |0.30| and |0.49| Weak effect: Between |0.10| and |0.29| Trivial effect: Less than |0.09|

 corr_output

Call:corr.test(x = d$rse, y = d$pss)
Correlation matrix 
      [,1]
[1,] -0.73
Sample Size 
[1] 939
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 option

Create a Correlation Matrix

# corr_output_m <- corr.test(d)

View Test Output

Strong effect: Between |0.50| and |1| Moderate effect: Between |0.30| and |0.49| Weak effect: Between |0.10| and |0.29| Trivial effect: Less than |0.09|

# corr_output_m

Write Up Results

A Pearson correlation was conducted to examine the relationships between self-esteem (RSE), perceived stress (PSS), and disordered eating behaviors (EDE-Q12).

table_out <- apa.cor.table(d, filename = “table1.doc”, table.number = 1) # table_out2 <- as.data.frame(table_out$table.body)

Update variable names for clarity

table_out2$Variable <- c( “Perceived stress (PSS-4)”, ““,”Depression symptoms (PHQ-9)“,”“,”“,”Self-esteem (RSE-10)“,”“,”“,”Eating Disorder Examination Questionnaire (EDE-Q12)“,”“,”” )

Create the formatted correlation table

as.data.frame(table_out2) %>% kbl(row.names = F, align = c(“l”, “c”, “c”, “c”, “c”, “c”), caption = paste(“Table”, table_out\(table.number,": ",table_out\)table.title, sep=““), format =”html”, table.attr = “style=‘width: 75%;’”) %>% kable_classic() %>% footnote( general = “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.”, symbol = c(“indicates p < .05”, “indicates p < .01.”), symbol_manual = c(“*“,”**“), threeparttable = T)

References

Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.