For Each: How would I find which statistical test would you use?
- One-sample
t-test
- Two-sample (independent sample)
t-test
- Repeated measures
t-test
- Analysis of Variance (ANOVA)
Scenario 1
:
A researcher would like to examine how the chemical tryptophan, contained in foods such as turkey, can affect mental alertness. A sample of
n
= 9 college students is obtained and each student’s performance on a familiar video game is measured before and after eating a traditional Thanksgiving dinner including roast turkey. The average score dropped by = 14 points after the meal with
SS
= 1152 for the difference scores.
Scenario 2
:
A large company would like to assess the impact of using a professional trainer to conduct a confidence-building workshop with their salespeople. A sample of 16 workers is obtained. Half of them (n
= 8) attend the workshop, and the other half (n
= 8) do not, serving as a control group. Two weeks later, each of the participants is given a questionnaire measuring their level of self-confidence.The data are as follows:
Controls Workshop
= 17.5 = 22.7
SS
= 100
SS
= 124
Scenario 3
:
A teacher gives a third grade class (n
= 16 students) a reading skills test at the beginning of the school year. To evaluate the changes that occurred during the year, students are tested again at the end of the year. Their test scores revealed an average improvement of
x̅
D
= + 4.7 points on the reading skills test.
Additionally, what could be one potential problem (a confounding variable) in the measurement of students’ reading skills in this study?
Scenario 4:
As a member of admissions, you’ve collected data on SAT scores from all first-year students at Wheaton. You want to compare the average score for a first-year student at Wheaton (x̅
= 1240,s
= 81), to the 2018-2019 national average for high school seniors at the time, which was
µ
= 1059.
Scenario 5
:
You gather data from a sample of Wheaton students (n
= 72), who responded to your request to complete a survey. You asked them to complete a few questions, one of which is to indicate their levels of stress on a scale from 0 (no stress at all) to 100 (extremely stressed). You measure their stress at the beginning of the spring semester, and then email them again during finals week of the spring semester and ask them to fill out the same scale measuring their (0-100). You then compare these students’ average level of stress at the beginning of the semester to their average level of stress during finals week.
Scenario 6
:
We’ve collected data on the number of hours spent studying, on average, throughout the Spring 2020 semester for all Wheaton students. Through a colleague at Stonehill College in Easton, MA we were able to gather the same data for Stonehill students. You want to compare the average number of hours spent studying during the Spring 2020 semester for male students at Wheaton, female students at Wheaton, male students at Stonehill and female students at Stonehill.
Scenario 7
:
A psychologist examined the effect of chronic alcohol abuse on memory. In this experiment, a typical test of memory was used, because its scores are standardized. Scores from the general population form a normal distribution with
m
= 50 and
s
= 6. A sample of 22 alcohol abusers is given the memory test and the mean of that sample is 47.
Scenario 8:
You give all Wheaton students a measure of well-being (i.e. happiness) when they enter as first year students. You want to compare the average happiness scores for incoming first year students for the classes of 2020, 2021, 2022, and 2023.