set up dataset

Internal validity of WBA 4

Check distribution of each question of WBA 4

  1. Quick Statistical Summary
## === BASIC STATISTICAL SUMMARY ===
##  wba1_currlife     wba9_dirctn      wba23_posemo    wba24_negemo_r  
##  Min.   : 0.000   Min.   : 0.000   Min.   : 0.000   Min.   : 0.000  
##  1st Qu.: 5.000   1st Qu.: 5.000   1st Qu.: 6.000   1st Qu.: 4.000  
##  Median : 7.000   Median : 8.000   Median : 8.000   Median : 6.000  
##  Mean   : 6.274   Mean   : 6.944   Mean   : 6.956   Mean   : 5.983  
##  3rd Qu.: 8.000   3rd Qu.: 9.000   3rd Qu.: 9.000   3rd Qu.: 8.000  
##  Max.   :10.000   Max.   :10.000   Max.   :10.000   Max.   :10.000
  1. Visual Assessment

  1. Normality Tests
## wba1_currlife p-value: 5.372362e-12
## wba9_dirctn p-value: 1.710766e-17
## wba23_posemo p-value: 2.666999e-17
## wba24_negemo_r p-value: 1.166408e-13
## Interpretation: p-value > 0.05 suggests normal distribution

All the 4 items are not exactly normally distributed, which is expected in large sample size.

Correlation Coeffience Matrix (see how variables relate)

##                wba1_currlife wba9_dirctn wba23_posemo wba24_negemo_r
## wba1_currlife      1.0000000   0.5816440    0.5897343      0.3801483
## wba9_dirctn        0.5816440   1.0000000    0.6650213      0.4598965
## wba23_posemo       0.5897343   0.6650213    1.0000000      0.5468707
## wba24_negemo_r     0.3801483   0.4598965    0.5468707      1.0000000

Summary

The data show internal construct validity. The distribution show good variability ( spread across the scale), covering the full range, with no extreme outliner, and meaningful distribution (although not normal distributed, but it is expected in large dataset(>100)).

Correlation test show goods internal construct validity. Life satisfaction, positive emotions and direction in life are highly positively related (r=0.59,r=0.67). Negative emotions_r are less positive correlated with the other three. But all are positively related, and no excessively high correlation which may suggest redundancy(when r>0.85).

Convergent Validity with Ryff

Test the reliability and distribution of the sum of Ryff’s items.

## Cronbach's Alpha for Ryff scale: 0.871

Cronbach’s alpha for ryff is 0.871, which shows good reliability of Ryff in our collected data.

Also see the distribution of the sum of ryff.

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   33.00   80.00   95.00   92.54  106.00  126.00

Convergent validity test between the sum of wba4 and the total of ryff.

Check the normality of total scores

## 
## --- DESCRIPTIVE STATISTICS ---
##              Mean     SD Median Skewness Kurtosis
## WBA_Total  26.321  7.776     28   -0.720    3.051
## Ryff_Total 92.544 17.323     95   -0.408    2.672
## 
## --- STATISTICAL NORMALITY TESTS ---
## WBA TOTAL SCORE:
##   Shapiro-Wilk test: W = 0.9562 , p = 7.14e-11
## RYFF TOTAL SCORE:
##   Shapiro-Wilk test: W = 0.98 , p = 2.88e-06

p > 0.05: suggests normal distribution. p < 0.05: suggests non-normal distribution. The two sums show some non-normality, which is common in large sample size.

Visual Assessment
Although the graphs look almost normal distributed, both scales show some non-normality, which is common in large dataset(n>100)

Pearson correlation

## Correlation coefficient (r): 0.727
## 95% Confidence Interval: [ 0.682 , 0.766 ]
## p-value: <2e-16
## Sample size (N): 489

Spearman correlation

## Spearman's rho: 0.71
## p-value: <2e-16

Interpretation :

Both Pearson and Spearman test show robost positive correlation (0.71/0.72) which are statiscally significant. The sum of WBA4 and Ryff are highly positively correlated.

Convergent validity test: the correlation of each item of wba4 with ryff

## 
## === CORRELATIONS WITH RYFF PSYCHOLOGICAL WELL-BEING SCALE ===
WBA Scale r p-value 95% CI
Current Life Satisfaction 0.487 0 [0.416, 0.552]
Direction in Life 0.678 0 [0.627, 0.723]
Positive Emotions 0.626 0 [0.568, 0.677]
Negative Emotions (Reversed) 0.542 0 [0.476, 0.602]

All four items of wba4 are positively related with the ryff.

Divergent correlation with a negetive dataset

Multitrait-multimethod matrix