Question

Match the research design to the correct test statistic. Each research design may be used more than once.

Jack Pearson is interested in whether race of applicant (Black, Hispanic, White, Asian) and the type of college (Ivy League, HBCU, Public, or Private-Liberal Arts) impacts the amount of financial aid an applicant is awarded. Donald Trump is interested in how his Twitter activity impacts his approval ratings. He gathers a group of 1000 followers, shows them his Twitter activity on a particularly heavy activity day (20+ tweets in a day), measures their approval ratings, and then shows them his Twitter activity on a slow day (less than 2 tweets in a day), and measures their approval ratings again. Professors are interested in the relationship between location of parking spots and quality of cars. The Philadelphia Eagles are interested in how a quarterback change can impact the number of points scored in a football game. They follow the number of points the Eagles score in the first half of the season with Carson Wentz as quarterback, and the number of points the Eagles score in the second half of the season with Nick Foles at quarterback and analyze how they changed. Federal prosecutors are interested in whether the leniency of plea deals (strict, moderate, lenient, illegally lenient) will impact the likelihood that high profile defendants will plead guilty. The Yankees are interested in the impact of age started playing baseball (pre-elementary school, elementary school, middle school, high school) and muscle strength (low, moderate-low, moderate-high, high, super high) on batting average. Betty is interested in how the information about the Black Hood (a serial murderer) is given to citizens of the town (via text versus via newspaper) of Riverdale will impact how scared they become on a scale of 1 (Come and get me, Black Hood; I’m not scared of you) to 10 (I’m never leaving the confines of my barricaded house again). Researchers are interested in the impact of crime show watching on jurors’ expectations of forensic evidence in a trial. They compare importance ratings of forensic evidence between those jurors who watch crime shows and those who don’t. In the NYC subway system, a subway train is, on average, 5 minutes late. The NYC transit authority thinks a new signal system may improve on-time performance, but have some serious budget concerns. On Monday, they measure how late all trains are with the old signal system, on Tuesday, they measure how late all trains are with a new, expensive signal system, and on Wednesday, they measure how late all trains are with a new, less expensive signal system. Retailers are interested in the relationship between Christmas music prevalence on the radio and sales in the month of December. Stockton wants to evaluate whether new students’ understanding of consent increases as a result of an in-depth sexual assault training at orientation. They give the students a survey about consent before the training and then again after the training to see if there is an increase in their understanding. Doctors in an uncivilized country with no medical ethics laws are interested in how effective different treatments are for Ebola. They take a group of patients with Ebola, give them no treatment and monitor their progress, then 1 week later, give them Treatment A and monitor their progress, and then 1 week later, give them Treatment B and monitor their progress.

A.

Factorial ANOVA

B.

Dependent samples t-test

C.

Correlation

D.

One-way ANOVA

E.

Independent samples t-test

F.

Repeated Measures ANOVA

Answer 1

Note:

Hey there! Thank you for the question. As you have posted a question with multiple research designs and the choice of test statistic for the different research designs are independent of each other, we have treated each design as a sub-part, and identified the suitable test statistic for the first 4 research designs. If you need help with the other designs, please re-post them separately.

1.

There are 4 different races given, and 4 types of colleges mentioned. The race and type of college of an applicant are the two independent variables, the effect of which on the amount of financial aid received by them is to be mentioned. The amount of financial aid is the response variable, which is continuous in nature, and the two independent variables are categorical.

The various levels of the race would potentially interact with the various levels of the type of college, so that the interaction effect on the amount of aid received would also be a variable of interest.

Hence, the suitable test statistic for this study is A. Factorial ANOVA.

2.

A group of 1,000 followers are first shown the activity on a heavy activity day and their approval ratings are obtained; then, the same group of 1,000 followers are shown the activity on a slow day and their approval ratings are obtained. Thus, two sets of observations are obtained from the same group of individuals.

As the same group of individuals yield the two sets of data, the two sets are correlated.

Hence, the suitable test statistic for this study is B. Dependent samples t-test.

3.

The relationship between location of parking spots and quality of cars is to be explored. The correlation coefficient helps to measure the linear relationship between two variables.

Hence, the suitable test statistic for this study is C. Correlation.

4.

The number of points scored by a team on an average with the presence of two different, independent quarterbacks in the team are compared.

Hence, the suitable test statistic for this study is E. Independent samples t-test.