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 table

2 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 semester

3 State Your Hypothesis

There will be a significant relationship between perceived stress, social media use, and need to belong. Specifically, perceived stress will be positively related to social media use and positively related to need to belong, and social media use will also be positively related to need to belong.

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':    3141 obs. of  7 variables:
##  $ ResponseID: chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ marriage5 : chr  "are currently divorced from one another" "are currently married to one another" "are currently married to one another" "are currently married to one another" ...
##  $ income    : chr  "1 low" "1 low" "rather not say" "rather not say" ...
##  $ stress    : num  3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
##  $ socmeduse : int  47 23 34 35 37 13 37 43 37 29 ...
##  $ belong    : num  2.8 4.2 3.6 4 3.4 4.2 3.9 3.6 2.9 2.5 ...
##  $ swb       : num  4.33 4.17 1.83 5.17 3.67 ...
# 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, socmeduse, 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
## stress       1 3141  3.05 0.60    3.0    3.05 0.59  1.3  4.7   3.4  0.03
## socmeduse    2 3141 34.45 8.55   35.0   34.73 7.41 11.0 55.0  44.0 -0.32
## belong       3 3141  3.23 0.60    3.3    3.25 0.59  1.3  5.0   3.7 -0.26
##           kurtosis   se
## stress       -0.16 0.01
## socmeduse     0.27 0.15
## belong       -0.13 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$socmeduse)

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$stress, d$socmeduse)

plot(d$stress, d$belong)

plot(d$socmeduse, d$belong)

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$stress <- scale(d2$stress, center=T, scale=T)
hist(d2$stress)

sum(d2$stress < -3 | d2$stress > 3)
## [1] 0
d2$socmeduse <- scale(d2$socmeduse, center=T, scale=T)
hist(d2$socmeduse)

sum(d2$socmeduse < -3 | d2$socmeduse > 3)
## [1] 0
d2$belong <- scale(d2$belong, center=T, scale=T)
hist(d2$belong)

sum(d2$belong < -3 | d2$belong > 3)
## [1] 6

5.2 Issues with My Data

All of my variables meet the assumptions of Pearson’s correlation coefficient. None of the variables exhibited high skewness or kurtosis, and all relationships appeared linear based on visual inspection of the scatterplots. Additionally, stress and social media use had no outliers, and need to belong had only 6 outliers. Given the large sample size and small number of outlying cases, these observations were retained for analysis. Therefore, the correlations can be interpreted without substantial concern regarding violations of the assumptions of Pearson’s correlation coefficient.

6 Run a Single Correlation

corr_output <- corr.test(d2$stress, d2$socmeduse)

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$stress, y = d2$socmeduse)
## Correlation matrix 
##      [,1]
## [1,] 0.09
## Sample Size 
## [1] 3141
## 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

8 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 socmeduse belong
## stress      1.00      0.09   0.30
## socmeduse   0.09      1.00   0.28
## belong      0.30      0.28   1.00
## Sample Size 
## [1] 3141
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##           stress socmeduse belong
## stress         0         0      0
## socmeduse      0         0      0
## belong         0         0      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 perceived stress, social media use, and need to belong would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. All of the variables met the required assumptions of the test, with all meeting the standards of normality and linearity and containing no major outliers. One variable, need to belong, had a small number of outliers (n = 6); however, given the large sample size, these cases were retained for analysis.

As predicted, we found that all three variables were significantly correlated (all ps < .001). The effect size of the correlation between perceived stress and social media use was trivial (r = .09), the effect size of the correlation between perceived stress and need to belong was moderate (r = .30), and the effect size of the correlation between social media use and need to belong was weak (r = .28). Additionally, perceived stress was positively related to social media use and need to belong, and social media use was also positively related to need to belong, as predicted. Please refer to the correlation coefficients reported in Table 1.

Table 1: Means, standard deviations, and correlations with confidence intervals
Variable M SD 1 2
Perceived Stress 3.05 0.60
Social Media Use 34.45 8.55 .09**
[.06, .13]
Need to Belong 3.23 0.60 .30** .28**
[.27, .33] [.24, .31]
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.