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

I predict that Exploitativeness and Narcissistic Personality Disorder will be correlated with each other.

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" ...
##  $ npi       : num  0.6923 0.1538 0.0769 0.0769 0.7692 ...
##  $ exploit   : num  2 3.67 4.33 1.67 4 ...
##  $ stress    : num  3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
##  $ swb       : num  4.33 4.17 1.83 5.17 3.67 ...
##  $ party_rc  : chr  "democrat" "independent" "apolitical" "apolitical" ...
##  $ edu       : chr  "2 Currently in college" "5 Completed Bachelors Degree" "2 Currently in college" "2 Currently in college" ...
# 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(exploit,npi))

# 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
## exploit    1 3141 2.39 1.37   2.00    2.21 1.48   1   7     6 0.94     0.36
## npi        2 3141 0.28 0.31   0.15    0.24 0.23   0   1     1 0.94    -0.69
##           se
## exploit 0.02
## npi     0.01
# 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(d2$exploit)

hist (d2$npi)

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

plot(d2$exploit, d2$npi)

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.

rm(NEW_DATAFRAME)
## Warning in rm(NEW_DATAFRAME): object 'NEW_DATAFRAME' not found
d2$exploit <- scale(d2$exploit, center=T, scale=T)
hist(d2$exploit)

sum(d2$exploit < -3 | d2$exploit > 3)
## [1] 33
d2$npi <- scale(d2$npi, center=T, scale=T)
hist(d2$npi)

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

5.2 Issues with My Data

One of my two variables meets all of the assumptions of Pearson’s correlation coefficient. One variable, Exploitativeness, had mild kurtosis (0.36) and had 33 outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction. Exploit and Npi appear to have a grid-like, linear relationship. Pearson’s r may underestimate the strength of a non-linear relationship and distort the relationship direction. Any correlations should be evaluated carefully due to these risks.

[Make sure to revise the above paragraph for your HW.]

6 Run a Single Correlation

corr_output <- corr.test(d2$exploit, d2$npi)

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$exploit, y = d2$npi)
## Correlation matrix 
##      [,1]
## [1,] 0.36
## 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

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 
##         exploit  npi
## exploit    1.00 0.36
## npi        0.36 1.00
## Sample Size 
## [1] 3141
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##         exploit npi
## exploit       0   0
## npi           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 my hypothesis that Exploitativeness and Narcissistic Personality Disorder would be correlated with one another, I calculated a series of Pearson’s correlation coefficients. Neither of the two variables (exploit, npi) met the required assumptions of the test, because one had outliers and neither had a normal distribution. One variable, Exploitativeness, had 33 outliers and a linear relationship with Narcissistic Personality Disorder or Inventory; so any significant results involving Exploitativeness should be evaluated carefully.

As predicted, I found that my two variables were significantly correlated (ps < .001). The effect size of the correlation was medium (rs < .5; Cohen, 1988).

[In your HW, revise the above two paragraphs to fit your results. Make sure to discuss ALL predicted correlations and if sig or not.]

Table 1: Means, standard deviations, and correlations with confidence intervals
Variable M SD 1
Exploit 2.39 1.37
Npi
0.28 0.31 .36**
[.33, .39]
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.