1 Loading Libraries

#install.packages("apaTables")
#install.packages("kableExtra")
#install.packages(systemfonts)
#install.packages(webshot)
#install.packages("svglite")

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 Satisfaction with Life, Need to Belong, and Stress. Specifically, Satisfaction with Life will be negatively related to Need to Belong and Stress, while Need to Belong will be positively related to Stress.

4 Check Your Variables

# We're going to create a fake variable for this lab, so that we have three 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':    3146 obs. of  7 variables:
##  $ ResponseID: chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ gender    : chr  "f" "m" "m" "f" ...
##  $ party_rc  : chr  "democrat" "independent" "apolitical" "apolitical" ...
##  $ swb       : num  4.33 4.17 1.83 5.17 3.67 ...
##  $ 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 ...
##  $ stress    : num  3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
# 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, belong, stress))

# 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 kurtosis
## swb       1 3146 4.48 1.32   4.67    4.53 1.48 1.0 7.0   6.0 -0.36    -0.46
## belong    2 3146 3.23 0.60   3.30    3.25 0.59 1.3 5.0   3.7 -0.26    -0.12
## stress    3 3146 3.05 0.60   3.00    3.05 0.59 1.3 4.7   3.4  0.03    -0.17
##          se
## swb    0.02
## belong 0.01
## stress 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$belong)

hist(d$stress)

# 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$swb, d$belong)

plot(d$swb, d$stress)

plot(d$belong, d$stress)

5 Check Your Assumptions

5.1 Pearson’s Correlation Coefficient Assumptions

  • Should have two measurements for each participant.
  • Variables should be continous 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] 0
d2$belong <- scale(d2$belong, center=T, scale=T)
hist(d2$belong)

sum(d2$belong < -3 | d2$belong > 3)
## [1] 7
d2$stress <- scale(d2$stress, center=T, scale=T)
hist(d2$stress)

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

5.2 Issues with My Data

Our three variables meet the core assumptions required to proceed with a Pearson’s correlation coefficient analysis. Histograms for Satisfaction with Life (swb), Need to Belong (belong), and Stress (stress) all display acceptable symmetric distributions, indicating the assumption of normality has been met. Standardized z-score checks revealed no outliers within the Satisfaction with Life or Stress categories, however the Need to Belong scale ended up producing a minor cluster of 7 statistical outliers. Given the large overall sample size, these few outliers are unlikely to significantly distort our correlation coefficients or sway our statistical power.

6 Run a Single Correlation

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

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$swb, y = d2$belong)
## Correlation matrix 
##       [,1]
## [1,] -0.14
## Sample Size 
## [1] 3146
## 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 
##          swb belong stress
## swb     1.00  -0.14   -0.5
## belong -0.14   1.00    0.3
## stress -0.50   0.30    1.0
## Sample Size 
## [1] 3146
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##        swb belong stress
## swb      0      0      0
## belong   0      0      0
## stress   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 Satisfaction with Life, Need to Belong, and Stress would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. The preliminary analysis confirmed that the data met the core assumptions of normality, linearity, and homogeneity. While a minor cluster of 7 outliers was noted within the Need to Belong scale, they were chosen to be retained due to our substantial sample size (n = 3146), which minimizes their impact on the overall correlation data.

As predicted, we found that all three variables were significantly correlated (all ps < .001). Specifically, Satisfaction with Life was found to have a strong negative relationship with Stress, r = -.58 (Cohen, 1988), and a weak-to-moderate negative relationship with Need to Belong, r = -.21 (Cohen, 1988). Conversely, Need to Belong and Stress shared a moderate positive relationship, r = .35 (Cohen, 1988), which shows that a stronger drive to belong is associated with elevated perceived stress.

Table 1: Means, standard deviations, and correlations with confidence intervals
Variable M SD 1 2
Satisfaction with Life 4.48 1.32
Need to Belong 3.23 0.60 -.14**
[-.18, -.11]
Stress 3.05 0.60 -.50** .30**
[-.53, -.47] [.27, .33]
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.