Economics and Student Affairs Project

Research question: find that there is statistically significant evidence that the responses to the question if your expectations for studying in Economics at UVic have been met? differ depending upon the respondent’s choice of department. If the distribution of responses varies considerably between the different study hours categories.

There are three types test we are able to do.

  1. test for Likert scale data.

Example two: Do Males and Females answer differently?

Example three: Do scoring tendencies differ by countries?

Scoring tenancies are calculated by using Likert scale. For example, in this case, we assign 1 to “not helpful”, 2 to “somewhat not helpful”, 3 to “neutral”, 4 to “somewhat helpful”, 5 to “helpful”, and 0 to “no basis to judge”.

  1. test correlation between two variables.

Example four: Whether Expectation and Faculty to Choose are correlated.

2. test for Likert scale data.

Example one:

Hypothesis test about likert scale data.

  • Mann Whitney test.

  • Kruskal Wallis test.

Data may also be combined into say two nominal categories Agree/Accept and Disagree/Reject, which allows us to carry out the:

  • Chi-square test.

  • Fisher exact test.

Example two: Do Males and Females answer differently?

Mann-Whitney test.

## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  Q34AcademicAdvising by Q71gender
## W = 782, p-value = 0.9491
## alternative hypothesis: true location shift is not equal to 0

From the Mann-Whitney test we get a p-value of 0.9491, hence we fail to reject the null hypothesis that Males and Females have the same scoring tendency at the 5% level. So there is no difference between two gender.

Example three: Do scoring tendancies differ by countries?

If we were interested in statistically testing if there were a significant difference between the scoring tenancies of people from different countries.

Unofficially we may conclude from the bar plot that there is seemingly no difference in the scoring tendencies of people from different countries. Using a Kruskal-Wallis we can officially test for a difference.

## [1] "China"                  "India"                 
## [3] "Other (please specify)" "United States"

Kruskal-Wallis Test.

To officially test for a difference in scoring tendencies of people from different country we use a Kruskal-Wallis Test.

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Q34AcademicAdvising by Q72country
## Kruskal-Wallis chi-squared = 8.6653, df = 3, p-value
## = 0.03409

The Kruskal-Wallis test gives us a p-vale of 0.03, hence we have evidence to reject our null hypothesis that there is no difference.

We are likely therefore to believe that there is a difference in scoring tendency between people from different countries.

Test Correlation

To test the correlation between categorical variable

  • Chi-square test.

  • Fisher exact test.

Example four: Whether Expectation and Faculty to Choose are correlated.

Test statistical significant

## 
##  Fisher's Exact Test for Count Data
## 
## data:  table(ECONSR1$Q2Faculty, ECONSR1$Q66expectationsMet)
## p-value = 0.2413
## alternative hypothesis: two.sided
## 
##  Fisher's Exact Test for Count Data with simulated
##  p-value (based on 1e+05 replicates)
## 
## data:  table(ECONSR1$Q2Faculty, ECONSR1$Q66expectationsMet)
## p-value = 0.2394
## alternative hypothesis: two.sided

Our Fisher’s Exact Test for Count Data with simulated p-value revealed that the expectation and faculty to chooser of student are independent ( p = 0.24 ).

expectation and gender

Test statistical significant

## 
##  Fisher's Exact Test for Count Data
## 
## data:  table(ECONSR1$Q71gender, ECONSR1$Q66expectationsMet)
## p-value = 0.1778
## alternative hypothesis: two.sided
## 
##  Fisher's Exact Test for Count Data with simulated
##  p-value (based on 1e+05 replicates)
## 
## data:  table(ECONSR1$Q71gender, ECONSR1$Q66expectationsMet)
## p-value = 0.1762
## alternative hypothesis: two.sided

Our Fisher’s Exact Test for Count Data with simulated p-value revealed that the expectation and gender of student are independent ( p = 0.17 ). The expectation of student did not differ by gender.

Analysis with incompleted dataset