1 Introduction

This report addresses the results of an online survey done to analyze the student satisfaction of college business undergraduate students from two regional universities. The survey was voluntary and anonymous and the participation rate was unknown. A nonprobability sampling plan was used in this survey. The sample size of the first college was 151, and the second was 183.

This report examines the consulting question on internal consistency for the multi-item questions in the survey, those being the following: 4) Students’ Engagement in Learning 5) Student Learning Styles 6) Writing and Reading Load 8) Remedial Experience 9) Encouragement and Support 10) Growth and Development 11) Campus Resource Utilization (had three subsets of responses) 12) Retention 13) How Students Pay for College

survey = read.csv("C:/Users/qinfa/Desktop/school/STA490/at-risk-survey-data.csv", head = TRUE)
survey <- na.omit(survey)

engagement <- survey %>% select(q41:q421)
learning <- survey %>% select(q51:q56)
wr_load <- survey %>% select(q61:q63)
remedial <- survey %>% select(q81:q89)
encouragement <- survey %>% select(q91:q97)
growth <- survey %>% select(q101:q1015)
resource1 <- survey %>% select(q111.1:q119.3)
resource2 <- survey %>% select(q1110.1:q1110.3)
resource3 <- survey %>% select(q1111.1:q1111.3)
retention <- survey %>% select(q121:q125)
pay <- survey %>% select(q131:q136)

2 Validity and Reliability

The dataset was already cleaned, so there were not issues of missing data. This gave a dataset of 332 total observations. For the multi-item questions listed above, the following report seeks to report measures of validity and reliability for each of the sections.

2.1 Students’ Engagement in Learning

To begin, the internal consistency of question four was assessed by looking at its pairwise correlation plot.

M=cor(engagement)
corrplot.mixed(M, lower.col = "purple", upper = "ellipse", number.cex = .7, tl.cex = 0.7)

The shape of an ellipse represents the correlation. The skinnier the ellipse, the higher the correlation. The direction reflects whether a correlation is positive or negative. The off-diagonal direction implies s positive correlation while the main diagonal direction implies a negative association.

The moderate correlations present between individual variables implies the ability to use PCA. The internal consistency is measured through Cronbach’s Alpha, as presented below.

cronbach.alpha(engagement, CI=TRUE)
## 
## Cronbach's alpha for the 'engagement' data-set
## 
## Items: 21
## Sample units: 332
## alpha: 0.878
## 
## Bootstrap 95% CI based on 1000 samples
##  2.5% 97.5% 
## 0.848 0.898

Cronbach’s alpha is calculated as being 0.878 with a 95% confidence interval of (0.851, 0.898), which suggests that the items for this question have a relatively high internal consistency.

The same will be done to assess the internal consistency of the other sections.

2.2 Students’ Learning Styles

M=cor(learning)
corrplot.mixed(M, lower.col = "purple", upper = "ellipse", number.cex = .7, tl.cex = 0.7)

cronbach.alpha(learning, CI=TRUE)
## 
## Cronbach's alpha for the 'learning' data-set
## 
## Items: 6
## Sample units: 332
## alpha: 0.847
## 
## Bootstrap 95% CI based on 1000 samples
##  2.5% 97.5% 
## 0.816 0.874

The moderate to high correlation present in the pairwise correlation plot implies the relevance of PCA in future analysis. The calculation of Cronbach’s alpha gives a result of 0.847, confidence interval (0.816, 0.873), which is a relatively high internal consistency for question six.

2.3 Writing and Reading Load

M=cor(wr_load)
corrplot.mixed(M, lower.col = "purple", upper = "ellipse", number.cex = .7, tl.cex = 0.7)

cronbach.alpha(wr_load, CI=TRUE)
## 
## Cronbach's alpha for the 'wr_load' data-set
## 
## Items: 3
## Sample units: 332
## alpha: 0.491
## 
## Bootstrap 95% CI based on 1000 samples
##  2.5% 97.5% 
## 0.383 0.581

The correlations of the pairwise correlation plot appear to be low to moderate, which may mean that PCA is less viable than for other subsections. Cronbach’s alpha gives a relatively low calculation of 0.491 as well, 95% CI(0.381, 0.581). Therefore, the internal consistency of this question appears to be lower than previous sections.

2.4 Remedial Experience

M=cor(remedial)
corrplot.mixed(M, lower.col = "purple", upper = "ellipse", number.cex = .7, tl.cex = 0.7)

cronbach.alpha(remedial, CI=TRUE)
## 
## Cronbach's alpha for the 'remedial' data-set
## 
## Items: 9
## Sample units: 332
## alpha: 0.807
## 
## Bootstrap 95% CI based on 1000 samples
##  2.5% 97.5% 
##  0.77  0.84

The pairwise correlation gives moderate correlation values. The Cronbach’s alpha calculation is once again relatively high, 0.807 95% CI(0.771, 0.840)

2.5 Encouragement and Support

M=cor(encouragement)
corrplot.mixed(M, lower.col = "purple", upper = "ellipse", number.cex = .7, tl.cex = 0.7)

cronbach.alpha(encouragement, CI=TRUE)
## 
## Cronbach's alpha for the 'encouragement' data-set
## 
## Items: 7
## Sample units: 332
## alpha: 0.833
## 
## Bootstrap 95% CI based on 1000 samples
##  2.5% 97.5% 
## 0.799 0.859

The pairwise correlation for question 9 gives moderate correlation values. The Cronbach’s alpha calculation is once again relatively high, 0.833 95% CI(0.799, 0.859).

2.6 Growth and Development

M=cor(growth)
corrplot.mixed(M, lower.col = "purple", upper = "ellipse", number.cex = .7, tl.cex = 0.7)

cronbach.alpha(growth, CI=TRUE)
## 
## Cronbach's alpha for the 'growth' data-set
## 
## Items: 15
## Sample units: 332
## alpha: 0.947
## 
## Bootstrap 95% CI based on 1000 samples
##  2.5% 97.5% 
## 0.936 0.956

The pairwise correlation plot for question 10 gives correlation values that are moderate to high, indicating that PCA will likely be relevant for this subsection. The value calculated for Cronbach’s alpha is also high, 0.947 95% CI(0.937, 0.955).

2.7 Campus Resource Utilization

The eleventh question has three subsets of responses which will each be considered on its own.

2.7.1 Subsection 1

M=cor(resource1)
corrplot.mixed(M, lower.col = "purple", upper = "ellipse", number.cex = .7, tl.cex = 0.7)

cronbach.alpha(resource1, CI=TRUE)
## 
## Cronbach's alpha for the 'resource1' data-set
## 
## Items: 27
## Sample units: 332
## alpha: 0.903
## 
## Bootstrap 95% CI based on 1000 samples
##  2.5% 97.5% 
## 0.886 0.916

The pairwise correlation for question 11, subsection 1 gives moderate correlation values. The Cronbach’s alpha calculation is relatively high, 0.903 95% CI(0.884, 0.916).

M=cor(resource2)
corrplot.mixed(M, lower.col = "purple", upper = "ellipse", number.cex = .7, tl.cex = 0.7)

cronbach.alpha(resource2, CI=TRUE)
## 
## Cronbach's alpha for the 'resource2' data-set
## 
## Items: 3
## Sample units: 332
## alpha: 0.903
## 
## Bootstrap 95% CI based on 1000 samples
##  2.5% 97.5% 
## 0.884 0.921

The pairwise correlation for question 11, subsection 1 gives high correlation values. The Cronbach’s alpha calculation is relatively high, 0.903 95% CI(0.883, 0.921).

M=cor(resource3)
corrplot.mixed(M, lower.col = "purple", upper = "ellipse", number.cex = .7, tl.cex = 0.7)

cronbach.alpha(resource3, CI=TRUE)
## 
## Cronbach's alpha for the 'resource3' data-set
## 
## Items: 3
## Sample units: 332
## alpha: 0.866
## 
## Bootstrap 95% CI based on 1000 samples
##  2.5% 97.5% 
## 0.825 0.897

Once again, the correlations for the individual components for question 11 subsection 3 are high. Cronbach’s alpha is also relatively high, 0.866 95% CI(0.832, 0.897).

2.8 Retention

M=cor(retention)
corrplot.mixed(M, lower.col = "purple", upper = "ellipse", number.cex = .7, tl.cex = 0.7)

cronbach.alpha(retention, CI=TRUE)
## 
## Cronbach's alpha for the 'retention' data-set
## 
## Items: 5
## Sample units: 332
## alpha: 0.773
## 
## Bootstrap 95% CI based on 1000 samples
##  2.5% 97.5% 
## 0.720 0.812

Looking at the pairwise correlation plot for retention, the correlation values are moderate. Cronbach’s alpha is calculated as 0.773, 95% CI (0.725, 0.813), which is still relatively high, albeit lower than most of the previous questions.

2.9 How Students Pay for College

M=cor(pay)
corrplot.mixed(M, lower.col = "purple", upper = "ellipse", number.cex = .7, tl.cex = 0.7)

cronbach.alpha(pay, CI=TRUE)
## 
## Cronbach's alpha for the 'pay' data-set
## 
## Items: 6
## Sample units: 332
## alpha: 0.168
## 
## Bootstrap 95% CI based on 1000 samples
##   2.5%  97.5% 
## -0.071  0.329

Finally, in considering question 13, the correlations are low. Cronbach’s alpha is calculated as 0.168, 95% CI (-0.048, 0.335), which indicates low internal consistency for this question.

3 Conclusions

Internal reliability is a measure of how well the survey consistently measures the same information with the same results. Therefore, in this report, questions with multiple items were tested to see if the items came with consistent results. Across the board, most of the questions had results with moderate correlations and relatively high Cronbach’s alpha values, which indicate acceptable levels of reliability for the survey instruments. Of the 9 multi-item questions considered, two had noticeably lower values for Cronbach’s alpha: 6) Writing and Reading Load and 13) How students pay for college. The subsections can be checked for reversed scoring, which should be changed back and the correlation and Cronbach’s alpha recalculated.