A professor teaches two different subjects (history and sociology) in an ethnically diverse college. She wants to know how much interest students have in prominent political figures. She reasons that knowing this will help her plan for future lectures.
She asked students to rate each person listed with a Lickert scale (a continuum with five being high and 1 being of low interest). Upon looking at the data results, she concluded that there is no need to emphasize any political figure more than the others. Indeed, she reckoned, students in each subject area rated the figures similarly, so she can pace her lessons just as she has in the past.
History students’ scores:
John Maynard Keynes 3.6
Jesus 4.1
Martin Luther King Jr. 4.0
Karl Marx 2.5
Patricia Ireland 2.6
Abraham Lincoln 4.5
Sociology students’ scores:
John Maynard Keynes 3.7
Jesus 4.2
Martin Luther King Jr. 3.9
Karl Marx 4.1
Patricia Ireland 4.0
Abraham Lincoln 3.8
Is her conclusion solid? Please provide a statistical assessment using Spearman rs to evaluate her decision. Explain the practical significance of the test as well as its implications, if any, for her decision.
To assess the solidity of the professor's conclusion, we can perform a statistical assessment using the Spearman's rank correlation coefficient (rs). The Spearman's rs measures the strength and direction of the monotonic relationship between two variables. In this case, we can use it to determine if there is a significant correlation between the students' ratings of political figures in history and sociology.
To calculate Spearman's rs, we use the following steps:
Step 1: Rank the scores in each subject separately from lowest to highest, assigning the rank number 1 to the lowest score and so on.
History students' ranks:
Karl Marx 1
Patricia Ireland 2
John Maynard Keynes 3.5
Martin Luther King Jr. 3.5
Abraham Lincoln 5
Sociology students' ranks:
Karl Marx 1
Patricia Ireland 2
Abraham Lincoln 3
John Maynard Keynes 4
Martin Luther King Jr. 5
Step 2: Calculate the difference between the ranks for each student in both subjects.
History ranks - Sociology ranks:
Karl Marx 0
Patricia Ireland 0
John Maynard Keynes -0.5
Martin Luther King Jr. -1.5
Abraham Lincoln 2
Step 3: Square each difference calculated in Step 2.
Squared differences:
Karl Marx 0
Patricia Ireland 0
John Maynard Keynes 0.25
Martin Luther King Jr. 2.25
Abraham Lincoln 4
Step 4: Sum up all the squared differences.
Sum of squared differences = 0 + 0 + 0.25 + 2.25 + 4 = 6.5
Step 5: Calculate Spearman's rs using the formula:
rs = 1 - (6 * sum of squared differences) / (n * (n^2 - 1))
In this case, n is the total number of scores (6 in both subjects).
rs = 1 - (6 * 6.5) / (6 * (6^2 - 1))
rs = 1 - 39 / (6 * 35)
rs = 1 - 0.1857
rs = 0.8143
The calculated value of Spearman's rs is 0.8143.
Now, let's evaluate the practical significance of this test and its implications for the professor's decision.
A Spearman's rs value ranges from -1 to 1. A value of 1 indicates a perfect positive monotonic relationship, while a value of -1 indicates a perfect negative monotonic relationship. A value of 0 indicates no correlation.
In this case, the calculated rs value of 0.8143 suggests a strong positive monotonic relationship between the students' ratings of political figures in history and sociology. This means that the rankings of political figures by students are similar across both subjects.
Practically, since there is a strong positive correlation between the rankings from history and sociology students, the professor's conclusion that there is no need to emphasize any political figure more than others seems solid. The professor can continue to pace her lessons as she has in the past, as the students' interest in prominent political figures appears consistent across both subjects.