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="C:/Users/jd/OneDrive - Indiana University/M311/Research/Final Paper/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 mindfulness, self-efficacy, and narcissistic traits. Specifically, mindfulness will be positively related to self-efficacy and negatively related to narcissistic traits, and self-efficacy will be positively related to narcissistic traits.

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':    3074 obs. of  7 variables:
##  $ ResponseID      : chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ edu             : chr  "2 Currently in college" "5 Completed Bachelors Degree" "2 Currently in college" "2 Currently in college" ...
##  $ usdream         : chr  "american dream is important and achievable for me" "american dream is important and achievable for me" "american dream is not important and maybe not achievable for me" "american dream is not important and maybe not achievable for me" ...
##  $ moa_independence: num  3.67 3.67 3.5 3 3.83 ...
##  $ mindful         : num  2.4 1.8 2.2 2.2 3.2 ...
##  $ efficacy        : num  3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...
##  $ npi             : num  0.6923 0.1538 0.0769 0.0769 0.7692 ...
# 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(mindful, efficacy, 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
## mindful     1 3074 3.70 0.84   3.73    3.71 0.79 1.13   6  4.87 -0.06    -0.14
## efficacy    2 3074 3.13 0.45   3.10    3.13 0.44 1.10   4  2.90 -0.26     0.48
## npi         3 3074 0.28 0.31   0.15    0.24 0.23 0.00   1  1.00  0.94    -0.70
##            se
## mindful  0.02
## efficacy 0.01
## npi      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(d2$mindful)

hist(d2$efficacy)

hist(d2$npi)

# 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(d2$mindful)

plot(d2$efficacy)

plot(d2$npi)

5 Check Your Assumptions

5.1 Pearson’s Correlation Coefficient Assumptions

  • Should have independence of observations 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.

# Standardize all three variables
z_mindful <- scale(d2$mindful, center=TRUE, scale=TRUE)
z_efficacy <- scale(d2$efficacy, center=TRUE, scale=TRUE)
z_npi <- scale(d2$npi, center=TRUE, scale=TRUE)

# Count outliers for each variable
sum(abs(z_mindful) > 3)
## [1] 2
sum(abs(z_efficacy) > 3)
## [1] 16
sum(abs(z_npi) > 3)
## [1] 0

5.2 Issues with My Data

Mindfulness and self-efficacy were approximately normally distributed, while narcissistic traits showed some positive skewness (0.94). Mindfulness had a kurtosis of -0.14 and 2 outliers, self-efficacy had a kurtosis of 0.48 and 16 outliers, and narcissistic traits had a kurtosis of -0.70 and no outliers. Outliers can distort the relationship between two variables and influence the direction and strength of Pearson’s correlation coefficient. Since mindfulness and self-efficacy contained outliers, correlations involving these variables should be interpreted with caution.

6 Run a Single Correlation

corr_output <- cor.test(d2$mindful, d2$efficacy)

7 View Single Correlation

corr_output
## 
##  Pearson's product-moment correlation
## 
## data:  d2$mindful and d2$efficacy
## t = 14.484, df = 3072, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2194344 0.2856263
## sample estimates:
##       cor 
## 0.2528262

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 
##          mindful efficacy   npi
## mindful     1.00     0.25 -0.02
## efficacy    0.25     1.00  0.16
## npi        -0.02     0.16  1.00
## Sample Size 
## [1] 3074
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##          mindful efficacy  npi
## mindful     0.00        0 0.22
## efficacy    0.00        0 0.00
## npi         0.22        0 0.00
## 
##  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 mindfulness, self-efficacy, and narcissistic traits would be correlated with each other, we calculated a matrix of Pearson’s correlation coefficients. Two of the variables (mindfulness and self-efficacy) approximately met the required assumptions of the test, with both meeting the standards of normality and containing relatively few outliers. One variable, narcissistic traits, had positive skewness (0.94), no outliers, and a weak negative relationship with mindfulness; so any significant results involving narcissistic traits should be evaluated carefully.

As predicted, we found that mindfulness and self-efficacy were significantly positively correlated (r = .25, p < .001). The effect size of this correlation was small (Cohen, 1988). Additionally, self-efficacy was found to be positively related to narcissistic traits (r = .16, p < .001), as predicted, with a small effect size. However, mindfulness was not significantly related to narcissistic traits (r = -.02, p = .22), so this prediction was not supported. Please refer to the correlation coefficients reported in Table 1.

[In your HW, revise the above two paragraphs to fit your results. Make sure to discuss ALL predicted correlations and whether supported or not. Always report the Pearson’s r and p-value for every prediction. If your p-values vary (some are < .05 while others are <.001), then you can say that they are all less than the largest of the major sig division: .05, .01, .001. Similarly, if your effect sizes vary, make sure to update the wording above and specify which were trivial/small/medium/large based on what you have (i.e., do not state any size you did not find). Delete this reminder in your HW.]

Table 1: Means, standard deviations, and correlations with confidence intervals
Variable M SD 1 2
Mindfulness 3.70 0.84
3.13 0.45 .25**
Self-Efficacy [.22, .29]
0.28 0.31 -.02 .16**
Narcissistic Traits [-.06, .01] [.13, .20]
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.