# Mercury Definitions

Display of course evaluation results

### Total Number of Completed Evaluations

The number of students who submitted evaluations.

### Total Enrollment in Course

The number of students enrolled in the course.

### Response Rate

The “Total Number of Completed Evaluations” divided by the “Total Enrollment in the Course or Course Section”, expressed as a percentage.

### Valid responses

The number of students who selected one of the options provided for the question.

### Blank responses

The number of students who did not select an option for the question. Blank responses are NOT included in any calculations. Note: The number of “Valid responses” plus the number of “blank responses” should equal the “Total Number of Completed Evaluations”.

The number of students who entered a comment for the question.

### Mean

The sum of all “valid responses” divided by the number of “valid responses”. Note: The closer the mean is to 5, the closer it is to “strongly agree/ excellent”.

### Standard Deviation

The standard deviation is a measure of the variation of the distribution of a data set. The standard deviation provides information about the distribution of responses, and underlines the danger of looking at the mean alone without considering the variance.

Note: For example, the following three cases illustrate how the same mean, 3, summarizes three data sets with completely different features. Clearly, the estimated standard deviation is needed in conjunction with the sample mean to better describe a data set.

Case 1: Student responses: 5 x “1” and 5 x “5”
Data set: (1, 1, 1, 1, 1, 5, 5, 5, 5, 5)
Mean: 3, σ(SD): 2.1

Case 2: Student responses: 2 x “1”, 2 x “2”, 2 x “3”, 2 x “4” and 2 x “5”
Data set: (1, 1, 2, 2, 3, 3, 4, 4, 5, 5)
Mean: 3, σ(SD): 1.5

Case 3: Student responses: 10 x "3"
Data Set: (3, 3, 3, 3, 3, 3, 3, 3, 3, 3)
Mean: 3, σ(SD): 0

Formula: The standard deviation is calculated as the square root of the arithmetic mean of the squares of the deviation from the arithmetic mean. As this is a calculation on a sample rather than the population, the result is an estimated standard deviation and is expressed in the same units as the data.

### The Standard deviation of the Mean

This is an estimate of how representative the sample mean (those responding to the questionnaire) is of the population mean (the whole class).

Formula: The variability of the sample mean is, naturally, smaller than the variability in the individual observations. This is usually taken to be the estimated standard deviation of the observations, divided by the square root of the sample size. When sampling from a “small” finite population this variability will be reduced. A finite population estimator of the standard deviation of the sample mean is given by:

### Dept Mean

This is the mean calculated treating all courses as if they were combined into one. It is the sum of all valid responses for a question in all courses in the department divided by the total number of such responses.

### Dept Course Mean

This is calculated as the “mean of means” and gives equal weight to mean evaluations from classes of different sizes. For this mean, the sum of the mean for each question per course is divided by the number of courses. It is calculated to avoid any weighting due to large courses in a department but perhaps gives undue weight to mean evaluations reported for classes with very small enrolments.

Which mean to use?

The decision about which mean to use depends on the course size and number of respondents. The Dept. Mean is more commonly used when there is little difference (+-.1) between the two means. This usually occurs when courses within a department have relatively uniform enrolments and there are similar response rates for all courses.
However, a range of course sizes or number of respondents within a department usually results in differences between the two means. Therefore, to compare like to like, large courses should be compared to the Dept Mean and small courses to the Dept Course Mean.

For example, Dept X has enrolments ranging from 6 to 400. For a given semester, the question, “Overall, this is an excellent course,” gives a Dept Mean of 3.4 and a Dept Course Mean of 3.7.

Case 1: Prof. A is teaching a course of 28 students and received 15 responses (53.6% response rate). The result for this question was a mean of 4.1, σ 0.9. To compare to similar smaller courses, the Dept Course Mean should be used, as this removes the weighting due to the number of students in large classes.

Case 2: Prof. B is teaching a course with 400 students and received 149 responses (37.3% response rate). The result for this question was a mean of 3.2, σ 1.0. To compare to similar large courses, the Dept Mean should be used, as this removes the weight of courses with small enrolments.