The outlier screening for Focalism and Affective forecasting

#the equation for screening outliers
BivariateAssumption.ListwisePS1 = lm (listwise.PS1$Happy ~ listwise.PS1$Focus)
#getting summary output for Cook's D values
summary(cooks.distance(BivariateAssumption.ListwisePS1))

##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## 0.0000000 0.0004877 0.0018014 0.0099331 0.0043961 0.2419474

There are zero outliers using Cook’s D standard of < 1.00.

plot(listwise.PS1$SREISavg, listwise.PS1$Happy, xlab = "Emotional Intelligence", ylab =  "Affective Forecasting")

####NHST

cor.test(listwise.PS1$SREISavg, listwise.PS1$Happy)

## 
##  Pearson's product-moment correlation
## 
## data:  listwise.PS1$SREISavg and listwise.PS1$Happy
## t = 0.80954, df = 134, p-value = 0.4196
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.09974105  0.23533241
## sample estimates:
##        cor 
## 0.06976314

There was NOT a significant correlation between emotional intelligence and affective forecasting, r = 0.070, p < 0.420, which showed no relationship between emotional intelligence and how people predicted their happiness.

Semi-Partial and Partial Correlation

library(ppcor) #for the partial COR

## Loading required package: MASS

##Loading the datafile

PSY772ProblemSet1 <- read_sav("C:/Users/John Majoubi/Downloads/Problem Set #1 (Linear Correlations)-20230303 (1)/Directions and Datafiles (PS1)/PSY772ProblemSet1.sav")

####EDA steps

Scatterplot array

#getting the column position:
names(listwise.PS1)

## [1] "Enjoy"    "Happy"    "Focus"    "SREISavg"

plot(listwise.PS1)

##scatterplot array (for practice)

plot(listwise.PS1[c(2,3:4)])

#focus and happy zero-order cor
cor.test(listwise.PS1$Happy, listwise.PS1$Focus)

## 
##  Pearson's product-moment correlation
## 
## data:  listwise.PS1$Happy and listwise.PS1$Focus
## t = 6.6683, df = 134, p-value = 6.194e-10
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3611713 0.6157516
## sample estimates:
##       cor 
## 0.4991569

cor.test(listwise.PS1$Focus, listwise.PS1$SREISavg)

## 
##  Pearson's product-moment correlation
## 
## data:  listwise.PS1$Focus and listwise.PS1$SREISavg
## t = 2.3722, df = 134, p-value = 0.0191
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.03355937 0.35702563
## sample estimates:
##       cor 
## 0.2007581

#emotional intelligence and happy zer-order cor
cor.test(listwise.PS1$SREISavg, listwise.PS1$Happy)

## 
##  Pearson's product-moment correlation
## 
## data:  listwise.PS1$SREISavg and listwise.PS1$Happy
## t = 0.80954, df = 134, p-value = 0.4196
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.09974105  0.23533241
## sample estimates:
##        cor 
## 0.06976314

#current mood and happy zero-order cor
cor.test(listwise.PS1$Enjoy, listwise.PS1$Happy)

## 
##  Pearson's product-moment correlation
## 
## data:  listwise.PS1$Enjoy and listwise.PS1$Happy
## t = 3.8027, df = 134, p-value = 0.0002166
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.1517295 0.4564447
## sample estimates:
##       cor 
## 0.3120912

It is significant

EDA step2: Screening for outliers using Cook’s D

#the equation for outlier screening 
Pcorrassumptions.listwise = lm(listwise.PS1$Happy ~ listwise.PS1$Focus + listwise.PS1$SREISavg + listwise.PS1$Enjoy)

#now the Cook's D
summary(cooks.distance(Pcorrassumptions.listwise))

##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## 5.000e-08 2.690e-04 1.418e-03 1.029e-02 6.038e-03 2.148e-01

There are zero outliers using Cook’s D < 1.00.

Semi-Partial correlation NHST for correlation between focalism and affective forecasting while controlling for emotional intelligence and current mood

spcor.test(listwise.PS1$Happy, listwise.PS1$Focus, listwise.PS1[,c("Enjoy" , "SREISavg")])

##    estimate      p.value statistic   n gp  Method
## 1 0.4609402 2.087735e-08  5.967562 136  2 pearson

We found a zero order correlation between focalism and affective forecasting, r = .499, p < .001, df = 134. Using a semi-partial correlation, there is a significant positive correlation, sr = .461, p < .001, df = 132, between focalism and affective forecasting when controlling for emotional intelligence and current mood on focalism only, r\(_{a(b.c+d)}\) = .461. Accordingly as focalism scores are increased so are individuals’ ability to predict their affective state removing both emotional intelligence and current mood from focalism only.

Semi-Partial correlation NHST for correlation between emotional intelligence and affective forecasting controlling for focalism and current mood

spcor.test(listwise.PS1$Happy, listwise.PS1$SREISavg, listwise.PS1[,c("Enjoy" , "Focus")])

##      estimate   p.value  statistic   n gp  Method
## 1 -0.05250231 0.5468546 -0.6040387 136  2 pearson

cor(listwise.PS1$SREISavg, listwise.PS1$Happy)

## [1] 0.06976314

We found NO zero order correlation between focalism and affective forecasting, r = .070, p > .469, df = 134. Using a semi-partial correlation, there is NO significant correlation, sr = -.053, p > .547, df = 132, between emotional intelligence and affective forecasting removing both focalism and current mood from emotional intelligence only, r\(_{a(b.c+d)}\) = -.063.

Partial correlation NHST for correlation between focalism and affective forecasting while controlling for emotional intelligence and current mood

pcor.test(listwise.PS1$Happy, listwise.PS1$Focus, listwise.PS1[,c("Enjoy" , "SREISavg")])

##    estimate      p.value statistic   n gp  Method
## 1 0.4854961 2.753404e-09  6.380322 136  2 pearson

We found a zero order correlation between focalism and affective forecasting, r = .499, p < .001, df = 134 Using a partial correlation, there is a significant positive correlation, pr = .486, p < .001, df = 132, between focalism and affective forecasting when controlling for both emotional intelligence and current mood, r\(_{ab.c+d}\) = .486. Accordingly as focalism scores are increased so are individuals’ ability to predict their affective state, when removing both emotional intelligence and current mood from this relationship.

##Getting the zero-order relationship

cor(listwise.PS1$Happy, listwise.PS1$Focus)

## [1] 0.4991569

Partial corr NHST for correlation between emotional intelligence and affective forecasting while controlling for focalism and current mood

pcor.test(listwise.PS1$Happy, listwise.PS1$SREISavg, listwise.PS1[,c("Enjoy" , "Focus")])

##      estimate   p.value  statistic   n gp  Method
## 1 -0.06312804 0.4686748 -0.7267355 136  2 pearson

cor(listwise.PS1$SREISavg, listwise.PS1$Happy)

## [1] 0.06976314

We found NO zero order correlation between focalism and affective forecasting, r = .070, p > .469, df = 134. Using a partial correlation, there is NO significant correlation, pr = -.063, p > .467, df = 132, between focalism and affective forecasting when controlling for both focalsim and current mood, r\(_{ab.c+d}\) = -.063.

Partial correlation removes the overlap of the third variable(s) from both the predictor and the outcome, where semi partial correlation does not remove the overlap from the outcome of interest, but only from the predictor.

APA Style Conclusion

We found a zero order correlation between focalism and affective forecasting, r = .499, p < .001, df = 134.Using a partial correlation, there was a significant positive correlation, pr = .486, p < .001, df = 132, between focalism and affective forecasting when controlling for both emotional intelligence and current mood, r\(_{ab.c+d}\) = .486. Accordingly as focalism scores are increased so are individuals’ ability to predict their affective state, when removing both emotional intelligence and current mood from this relationship.

Using a semi-partial correlation, there was a significant positive correlation, sr = .461, p < .001, df = 132, between focalism and affective forecasting when controlling for emotional intelligence and current mood on focalism only, r\(_{a(b.c+d)}\) = .461. Accordingly as focalism scores are increased so are individuals’ ability to predict their affective state removing both emotional intelligence and current mood from focalism only.

We found NO zero order correlation between focalism and affective forecasting, r = .070, p > .469, df = 134.Using a partial correlation, there was NO significant correlation, pr = -.063, p > .467, df = 132, between focalism and affective forecasting when controlling for both focalsim and current mood, r\(_{ab.c+d}\) = -.063.

Using a semi-partial correlation, there was NO significant correlation, sr = -.053, p > .547, df = 132, between emotional intelligence and affective forecasting removing both focalism and current mood from emotional intelligence only, r\(_{a(b.c+d)}\) = -.063.

Problem Set #1

John Majoubi

2023-03-06

Bivariate Correlations

Pearson Zero-Order Correlation

Data screening

Scatterplot for Focalism and Affective Forecasting