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 stress, independence, and support. Specifically, higher levesl of perceived stress will be negatively related to both independence and perceieved support. Individuals that report more stress will report lower levels of independence and lower levels of support.

4 Check Your Variables

# We're going to create a fake variable for this lab, so that we have four variables. 

# NOTE: YOU WILL SKIP THIS STEP FOR THE HOMEWORK! DELETE LINES 48-52!


# 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':    3078 obs. of  7 variables:
##  $ ResponseID      : chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ gender          : chr  "f" "m" "m" "f" ...
##  $ income          : chr  "1 low" "1 low" "rather not say" "rather not say" ...
##  $ efficacy        : num  3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...
##  $ stress          : num  3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
##  $ moa_independence: num  3.67 3.67 3.5 3 3.83 ...
##  $ support         : num  6 6.75 5.17 5.58 6 ...
# 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(stress, moa_independence, support))

# 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
## stress              1 3078 3.05 0.60   3.00    3.05 0.59 1.3 4.7   3.4  0.03
## moa_independence    2 3078 3.54 0.47   3.67    3.61 0.49 1.0 4.0   3.0 -1.44
## support             3 3078 5.54 1.13   5.75    5.66 0.99 0.0 7.0   7.0 -1.11
##                  kurtosis   se
## stress              -0.17 0.01
## moa_independence     2.52 0.01
## support              1.48 0.02
# 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$stress)

hist(d$moa_independence)

hist(d$support)

# 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$stress, d$moa_independence)

plot(d$stress, d$support)

plot(d$moa_independence, d$support)

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$stress <- scale(d2$stress, center=T, scale=T)
hist(d2$stress)

sum(d2$stress < -3 | d2$stress > 3)
## [1] 0
d2$moa_independence <- scale(d2$moa_independence, center=T, scale=T)
hist(d2$moa_independence)

sum(d2$moa_independence < -3 | d2$moa_independence > 3)
## [1] 51
d2$support <- scale(d2$support, center=T, scale=T)
hist(d2$support)

sum(d2$support < -3 | d2$support > 3)
## [1] 43

5.2 Issues with My Data

Two of my variables meet all of the assumptions of Pearson’s correlation coefficient. One variable, independence, had high kurtosis (2.52) and 51 outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction. Any correlations with independence should be evaluated carefully due to these risks.

6 Run a Single Correlation

corr_output <- corr.test(d2$stress, d2$support)

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$stress, y = d2$support)
## Correlation matrix 
##       [,1]
## [1,] -0.21
## Sample Size 
## [1] 3078
## 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 
##                  stress moa_independence support
## stress             1.00            -0.02   -0.21
## moa_independence  -0.02             1.00    0.10
## support           -0.21             0.10    1.00
## Sample Size 
## [1] 3078
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##                  stress moa_independence support
## stress             0.00             0.17       0
## moa_independence   0.17             0.00       0
## support            0.00             0.00       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 stress, independence, and support would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. Two of the variables (stress and support) met the required assumptions of the test, with both meeting the standards of normality and containing no extreme outliers . One variable, independence, had high kurtosis (2.52), 51 outliers; so any significant results involving independence should be evaluated carefully .

We found that only two variables were significantly negatively correlated (all ps <0.001). Perceived stress was not significantly correlated with independence (r=-0.02, p=0.17), and this prediction wasn’t support. Independence was significantly positively correlated with support (r=0.10, p<.001 Cohen, 1988). Overall, two of the three predicted correlations were support,but the effect sizes ranges from trivial to small. 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
Stress 3.05 0.60
Independence 3.54 0.47 -.02
[-.06, .01]
Support 5.54 1.13 -.21** .10**
[-.25, -.18] [.06, .13]
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.