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

We predict that life satisfaction, mindfulness, need to belong, and social media use will all be correlated with each other. Additionally, we predict that life satisfaction will be negatively correlated with social media use, such that participants who report higher levels of social media use will report lower life satisfaction.

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':    2156 obs. of  7 variables:
##  $ ResponseId: chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ gender    : chr  "f" "m" "m" "f" ...
##  $ age       : chr  "1 between 18 and 25" "1 between 18 and 25" "1 between 18 and 25" "1 between 18 and 25" ...
##  $ swb       : num  4.33 4.17 1.83 5.17 3.67 ...
##  $ mindful   : num  2.4 1.8 2.2 2.2 3.2 ...
##  $ belong    : num  2.8 4.2 3.6 4 3.4 4.2 3.9 3.6 2.9 2.5 ...
##  $ socmeduse : int  47 23 34 35 37 13 37 43 37 29 ...
# 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, mindful, belong, socmeduse))

# 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 2156  4.43 1.33   4.50    4.49 1.48  1.00   7  6.00 -0.35
## mindful      2 2156  3.72 0.84   3.73    3.72 0.79  1.13   6  4.87 -0.04
## belong       3 2156  3.21 0.61   3.20    3.23 0.59  1.30   5  3.70 -0.27
## socmeduse    4 2156 34.26 8.59  35.00   34.52 7.41 11.00  55 44.00 -0.30
##           kurtosis   se
## swb          -0.50 0.03
## mindful      -0.15 0.02
## belong       -0.09 0.01
## socmeduse     0.20 0.19
# NOTE: Our fake variable has high kurtosis, which we'll ignore for the lab. You don't need to discuss univariate normality in the results write-ups for the labs/homework, but you will need to discuss it in your final project manuscript.

# also use histograms to examine your continuous variables

hist(d$swb)

hist(d$mindful)

hist(d$belong)

hist(d$socmeduse)

# last, use scatterplots to examine your continuous variables together, for each pairing

plot(d$swb, d$mindful)

plot(d$swb, d$belong)

plot(d$swb, d$socmeduse)

plot(d$mindful, d$belong)

plot(d$mindful, d$socmeduse)

plot(d$belong, d$socmeduse)

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: 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.

# We are going to standardize (z-score) all of our 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] 0
d2$mindful <- scale(d2$mindful, center=T, scale=T)
hist(d2$mindful)

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

sum(d2$belong < -3 | d2$belong > 3)
## [1] 2
d2$socmeduse <- scale(d2$socmeduse, center=T, scale=T)
hist(d2$socmeduse)

sum(d2$socmeduse < -3 | d2$socmeduse > 3)
## [1] 0

5.2 Issues with My Data

All four of my variables meet all of the assumptions of Pearson’s correlation coefficient. Two variables, a measure of mindfulness and a measure of need to belong met the standards of normality, but mindfulness had 1 outlier and need to belong had 2 outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction. Pearson’s r may underestimate the strength of a non-linear relationship and distort the relationship direction.

6 Run a Single Correlation

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

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$swb, y = d2$socmeduse)
## Correlation matrix 
##      [,1]
## [1,] 0.09
## Sample Size 
## [1] 2156
## 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

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|

Remember, Pearson’s r is also an effect size!

corr_output_m <- corr.test(d2)

9 View Test Output

corr_output_m
## Call:corr.test(x = d2)
## Correlation matrix 
##             swb mindful belong socmeduse
## swb        1.00    0.29  -0.15      0.09
## mindful    0.29    1.00  -0.22     -0.12
## belong    -0.15   -0.22   1.00      0.27
## socmeduse  0.09   -0.12   0.27      1.00
## Sample Size 
## [1] 2156
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##           swb mindful belong socmeduse
## swb         0       0      0         0
## mindful     0       0      0         0
## belong      0       0      0         0
## socmeduse   0       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

10 Write Up Results

To test our hypothesis that life satisfaction, mindfulness, need to belong, and social media use would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. All four of the variables (life satisfaction, mindfulness, need to belong, social media use) met the required assumptions of the test, with all four meeting the standards of normality. One variable, mindfulness, had 1 outlier, and another variable need to belong had 2 outliers, so any significant results involving the two variables should be evaluated carefully.

We found that all four variables were significantly correlated (all ps < .001). The effect sizes of all correlations were weak (rs = between |0.10| and |0.29|; Cohen, 1988). Our second hypothesis was not supported, that life satisfaction would be lower in participants who reported higher levels of social media use, as can be seen by the correlation coefficients reported in Table 1.

Table 1: Means, standard deviations, and correlations with confidence intervals
Variable M SD 1 2 3
Life Satisfaction 4.43 1.33
Mindfulness 3.72 0.84 .29**
[.25, .33]
Need to Belong 3.21 0.61 -.15** -.22**
[-.19, -.11] [-.26, -.18]
Social Media Use 34.26 8.59 .09** -.12** .27**
[.05, .13] [-.16, -.07] [.23, .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.