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 life satisfaction, mindfulness, and need to belong. Specifically, life satisfaction will be positively related to mindfulness and negatively related to need to belong; and mindfulness will be negatively 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':    2103 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" ...
##  $ moa_independence: num  3.67 3.67 3.5 3 3.83 ...
##  $ 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 ...
# 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))

# 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 2103 4.43 1.33   4.50    4.49 1.48 1.00   7  6.00 -0.36    -0.49
## mindful    2 2103 3.71 0.84   3.73    3.72 0.79 1.13   6  4.87 -0.04    -0.15
## belong     3 2103 3.21 0.61   3.20    3.23 0.59 1.30   5  3.70 -0.27    -0.11
##           se
## swb     0.03
## mindful 0.02
## belong  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$mindful)

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$swb, d$mindful)

plot(d$swb, d$belong)

plot(d$mindful, d$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] 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

5.2 Issues with My Data

One of my variables, life satisfaction, meet all of the assumptions of Pearson’s correlation coefficient. Two variables, mindfulness and need to belong, had outliers. Mindfulness had one outlier and need to belong had two outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction. Mindfulness appears to have a positive relationship with life satisfaction and a non-linear relationship with need to belong. Need to belong has a non-linear relationship with life satisfaction and mindfulness. Pearson’s r may underestimate the strength of a non-linear relationship and distort the relationship direction. Any correlations with need to belong should be evaluated carefully due to these risks.

[Make sure to revise the above paragraph for your HW. If you do not have any non-linear relationships (which hopefully you won’t), remove those sentences as they will no longer be relevant. Delete this reminder in your HW.]

6 Run a Single Correlation

corr_output <- corr.test(d$swb, d$mindful)

7 View Single Correlation

corr_output
## Call:corr.test(x = d$swb, y = d$mindful)
## Correlation matrix 
## [1] 0.29
## Sample Size 
## [1] 2103
## These are the unadjusted probability values.
##   The probability values  adjusted for multiple tests are in the p.adj object. 
## [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 mindful belong
## swb      1.00    0.29  -0.16
## mindful  0.29    1.00  -0.22
## belong  -0.16   -0.22   1.00
## Sample Size 
## [1] 2103
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##         swb mindful belong
## swb       0       0      0
## mindful   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 life satisfaction, mindfulness 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, meeting the standards of normality and containing no outliers. Two variables, mindfulness and need to belong, met kurtosis standards, however, mindfulness had one outlier and need to belong had two outliers.

As predicted, we found that all three variables were significantly correlated (all ps < .001). The effect sizes of all correlations were weak (rs > 0.1; Cohen, 1988). Additionally, life satisfaction was found to be positively related to mindfulness and negatively related to need to belong as predicted. Furthermore, also as predicted, mindfulness was negatively related to need to belong. 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
Life Satisfaction 4.43 1.33
Mindfulness 3.71 0.84 .29**
[.25, .33]
Need to Belong 3.21 0.61 -.16** -.22**
[-.20, -.11] [-.26, -.18]
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.