A psychologist wanted to determine whether having a job interferes with student academic performance. She measured academic performance as a grade point average (GPA) score on the 4.0 GPA scale, where higher scores indicate better performance. She selected a sample of 30 students - 10 did not work, 10 worked part-time, and 10 worked full-time during the previous semester - and recorded their GPA. Conduct an ANOVA test at 5 percent significance level whether there is a difference student performance by their work load (This is the same example we used in the class, same data)

a. What statistical test would you choose to analyze this type of data? Why this is an appropriate test?

b. Write hypothesis in a plain language

c. What is the Between Degree of Freedom? You may check ANOVA table or calculate yourself

d. Based on the ANOVA, state your decision regarding the hypothesis you have stated earlier

e. Would you be interested to conduct the post hoc test? If yes, which post hoc test would you choose? Why would you choose it?

f. State your conclusion in a plain language

This question g has three sub-questions

g. TSU always puts the success of our students first. The Academic Affairs is interested to make a policy. You made a brief presentation to the board and they are asking following questions to you. Please answer to them briefly as much as you can.

1. Should a student work (please note that the outside workload should not interfere student's performance i.e., GPA)? If yes, what should be their workload?

2. During your presentation, the TSU Vice President of the academic affairs asked, "our survey indicates that majority of our students work in a convenient store, gas station, field-based job, late night etc (not a desk-based work). Normally male students can handle those type of working situation very well", what do you suggest to us whether only male students should work, not the female? (this is a hypothetical question, please do not take it personally). What would be your answer?

3. Due to COVID-19, there will be a shortage of workforce in the market in the next few years. The graduate students need to maintain 3.0 or higher GPA. How many hours (maximum) they may work if they like to maintain the 3.0 GPA? Can you answer this question? If not, how would you develop a study that may help you to answer this question (just think beyond ANOVA?)

• R-Code

> ###################################################

> ###### Question 1 ######

> ###################################################

>

> Workload <- c('NW', 'NW', 'NW', 'NW', 'NW', 'NW', 'NW', 'NW', 'NW', 'NW',

+ 'PT', 'PT', 'PT', 'PT', 'PT', 'PT', 'PT', 'PT', 'PT', 'PT',

+ 'FT', 'FT', 'FT', 'FT', 'FT', 'FT', 'FT', 'FT', 'FT', 'FT')

>

> GPA <- c(3.4, 3.2, 3, 3, 3.5, 3.8, 3.6, 4, 3.9, 2.9, 3.5, 3.6, 2.7, 3.5, 3.8,

+ 2.9, 3.4, 3.2, 3.3, 3.1, 2.9, 3, 2.6, 3.3, 3.7, 2.7, 2.4, 2.5, 3.3, 3.4)

>

> data.gpa <- data.frame(Workload, GPA)

> # Assume that all assumptions are met for the test you supposed to do!!

> head(data.gpa)

Workload GPA

1 NW 3.4

2 NW 3.2

3 NW 3.0

4 NW 3.0

5 NW 3.5

6 NW 3.8

>

> library(agricolae)

> a.1 <- aov(GPA~Workload, data=data.gpa)

>

> # Post-hoc 1

> comp.gpa.hsd <- HSD.test(a.1, trt="Workload", group=TRUE, alpha=0.05)

> comp.gpa.hsd

$statistics

MSerror Df Mean CV MSD

0.1524815 27 3.236667 12.06453 0.4329854

$parameters

test name.t ntr StudentizedRange alpha

Tukey Workload 3 3.506426 0.05

$means

GPA std r Min Max Q25 Q50 Q75

FT 2.98 0.4341019 10 2.4 3.7 2.625 2.95 3.30

NW 3.43 0.3973523 10 2.9 4.0 3.050 3.45 3.75

PT 3.30 0.3333333 10 2.7 3.8 3.125 3.35 3.50

$comparison

NULL

$groups

GPA groups

NW 3.43 a

PT 3.30 ab

FT 2.98 b

attr(,"class")

[1] "group"

>

> # Post-hoc 2

> comp.gpa.lsd <- LSD.test(a.1, trt="Workload", group=TRUE, alpha=0.05)

> comp.gpa.lsd

$statistics

MSerror Df Mean CV t.value LSD

0.1524815 27 3.236667 12.06453 2.051831 0.358315

$parameters

test p.ajusted name.t ntr alpha

Fisher-LSD none Workload 3 0.05

$means

GPA std r LCL UCL Min Max Q25 Q50 Q75

FT 2.98 0.4341019 10 2.726633 3.233367 2.4 3.7 2.625 2.95 3.30

NW 3.43 0.3973523 10 3.176633 3.683367 2.9 4.0 3.050 3.45 3.75

PT 3.30 0.3333333 10 3.046633 3.553367 2.7 3.8 3.125 3.35 3.50

$comparison

NULL

$groups

GPA groups

NW 3.43 a

PT 3.30 ab

FT 2.98 b

attr(,"class")

[1] "group"

>

> # Post-hoc 3

> comp.gpa.Bon <- LSD.test(a.1, trt="Workload", p.adj="bonferroni", group=TRUE, alpha=0.05)

> comp.gpa.Bon

$statistics

MSerror Df Mean CV t.value MSD

0.1524815 27 3.236667 12.06453 2.552459 0.4457407

$parameters

test p.ajusted name.t ntr alpha

Fisher-LSD bonferroni Workload 3 0.05

$means

GPA std r LCL UCL Min Max Q25 Q50 Q75

FT 2.98 0.4341019 10 2.726633 3.233367 2.4 3.7 2.625 2.95 3.30

NW 3.43 0.3973523 10 3.176633 3.683367 2.9 4.0 3.050 3.45 3.75

PT 3.30 0.3333333 10 3.046633 3.553367 2.7 3.8 3.125 3.35 3.50

$comparison

NULL

$groups

GPA groups

NW 3.43 a

PT 3.30 ab

FT 2.98 b

attr(,"class")

[1] "group