Background

The Science Department of a university in Queensland has recently experienced high student attrition rates in its science programs. It was observed that most of the attrition occurred at the end of students' first year. In order to find out its causes, the department decided to collect data on the academic performance of its science students at the end of their first year of study. Academic performance is measured by their grade point average (GPA) after two semesters of study. Data were also collected on different variables as students entered their program. They include the students' high school scores in science, English and maths (recorded on a scale from 1 to 10), and their Australian Tertiary Admission Rank (ATAR)[1]. Department researchers are also interested to investigate the influence of students' social economic status (SES) and their gender on their GPA. Students' SES is measured by their parents' highest level of education. The sample consists of 224 first year students. A portion of the dataset[2] is presented below:

Legend:

GPA = Grade Point Average (max = 7)

HS_SCI = Science score in high school

HS_ENG = English score in high school

HS_MATH= Maths score in high school

ATAR = Australian Tertiary Admission Rank

PARENT EDUC = Parents' highest education where P, U and S denote respectively 'Post-graduate', 'Undergraduate' and 'Secondary school or below' qualification.

Task 1 (Boxplot and t-tests)

1.(a)Discuss the distributional aspects of the GPA for male and female science students, and support your statements using graphical (histograms of boxplots). You should be aiming to discuss aspects of central location, spread and skewness.(3 marks)

(b)Recent research showed that in mathematics "on average for 15-year-old Australian students, females achieved at a significantly lower level than male students" (p.2, Buckley 2016)[3] . However, there is also research evidence that, "despite the stereotype that boys do better in math and science, girls have made higher grades than boys throughout their school years for nearly a century" (APA 2014)[4]. So it is not certain if one gender performs better than the other at university. Test if there is any difference in GPA on average between male and female students in the Science Department at the level of significance of 5%.

1.Education literature has shown that students with higher socio-economic status (SES) tend to have stronger academic achievement.

(a)Test at the level of significance of 10% whether students whose parents have a post-graduate qualification have a higher GPA than students whose parents have only an undergraduate qualification.

(b)Test at the level of significance of 10% if students whose parents have an undergraduate qualification have a higher GPA than students whose parents have only a secondary or below qualification.

Note: When conducting a test in Q1 and Q2, you should discuss briefly whether it is a one or two tail test, the test statistics, any assumptions made and draw a conclusion based on Excel output.

Task 2 (Regression Analysis)

You plan to develop a regression model to further investigate how various factors influence students' GPA in the Science Department.

1.Before you conduct any regression analysis, you use Excel to construct a correlation matrix of all the quantitative variables in the dataset. Based on the correlation matrix, comment briefly on the direction and strength of linear associations between GPA and other quantitative variables (viz. HS_SCI, HS_ENG, HS_MATH and ATAR). Is there anything unusual about any of the signs of the correlations?

2.Based on the correlation matrix obtained in Question 3, would you say that:

(i)HS_SCI is a predictor of GPA?

(ii)HS_ENG is a predictor of GPA?

(iii)HS_MATH is a predictor of GPA?

(iv)ATAR is a predictor of GPA?

Conduct simple regression to support your answers to questions (i) to (iv).

3.You conduct a stepwise regression according to the following step by step procedure:

Step 1: HS_SCI only

Step 2: HS_SCI and HS_ENG

Step 3: HS_SCI, HS_ENG and HS_MATH

Step 4: HS_SCI, HS_ENG, HS_MATH and PARENT EDUC

Step 5: HS_SCI, HS_ENG and HS_MATH, PARENT EDUC AND GENDER

Step 6:HS_SCI, HS_ENG and HS_MATH, PARENT EDUC, GENDER and ATAR

Present the regression output for each of the six steps in a table outlining all of the relevant information

Choice of reference category: It is recommended that you choose U (undergraduate education) as the reference category for the categorical variable: PARENT EDUC.

1.For each of the independent variables contained in the regression model in Step 5, fully interpret the regression (slope) coefficients and comment on their statistical significance.

In discussing statistical significance of a regression coefficient, you have to justify your choice of a one or two tail test.

2.In stepwise regression Step 6 you noticed that the regression coefficient of ATAR is negative (!). Does this result surprise you, given the correlation of ATAR and GPA? Why/Why not? Does the inclusion of ATAR improve overall model fit? Discuss fully.

Task 3 (Summary Report)

As the chief project officer, you are asked to write a summary report (300 words) detailing all the findings from your data analysis. The issues you can discuss in your report should include (but are not limited to) the following:

There has been research evidence that SES and academic achievement are closely related[1]. Based on your analysis in this study, critically examine education researchers' claim that student SES has an impact on their academic performance.

Do you think there is any gender difference in academic achievement of Science students?

In stepwise regression from Steps 1 to 3 where HS_SCI, HS_ENG and HS_MATH are added to the model progressively, observe the changes to the regression (slope) coefficient of the independent variable, HS_SCI. Do you think HS_SCI is a good predictor of students' GPA?

Is ATAR a good predictor of GPA? Should ATAR be included in the model?

Based on this study, what is the final model you would recommend to the Head of the Science Department?

Comment on the overall adequacy of the final model.

Are there any other important factors influencing academic performance that were not included in this study? What are they?