Percentile Rank vs. Mean or Group Median
The mean of an individual question is not used in the calculation for percentile rank, but the rank of the mean within a population is important. The mean is calculated from the raw responses in the population. The percentile rank is based on a formula that compares a report’s mean against the mean of each report in the population.
Note that CoursEval Evaluation reports can also be configured to calculate Pct Rank vs. group median. If your strategy is to show the mean it is advised to calculate percent rank vs. mean. Similarly, if you are showing group median on the report, percent rank should be configured to calculate against group median.
Percentile Rank Calculation
The percentile rank of a given score is the percentage of scores in its population frequency distribution that are the same or lower than the given score.
The formula is:
Where:
- c is the number of items found in the group whose values are less than the value being compared.
- f is the number of times the value occurs (frequency) within the group. Includes the value being compared. This helps to deal with ties.
- N is the total number in the group including the value being compared.
The N number can be found on the Evaluation report by hovering over the Pct Rank column value.
Example
In this example the mean in the comparison group is less than the mean score for an individual course and instructor, yet, the percentile rank is only 39 (the score falls in the 39th percentile). The data table below shows that other reports in the population will see a similar result. In fact, the percentile rank does not appear above the 50th percentile until the 12th ranked report. There are 4 reports with a higher mean than the department, but with a percentile rank below 50.
Report
Raw Data for Percentile Rank
There were 22 reports in the population (this equates to 22 means to compare against). Note that percentile rank is not weighted based on # of responses since the comparisons for percentile rank are against the mean for other courses and individuals in the same population. The highlighted mean is the one used in the example above. Note that there are ties for other data points.
Note that all of the reports in this population compare the mean for the example question to a department mean of 4.62. The department mean is weighted and has no bearing on the percentile rank!
Sample Calculation
Now simply apply the formula where:
c = 8 are less than the compared mean
f = 1 is the number of times that particular value appears
N = 22 comparison means
- (8 + .5(1)) / 22 = .386364
-
Rounded and multiplied by 100 gives us a percentile rank of 39
Ties in Percentile Rank
If we apply the same formula to one of the ties (mean of 4.9231 – tied for 4th) we would have:
c = 17 are less than the tied, compared, means
f = 2 is the number of times that particular value appears
N = 22 comparison means
- (17 + .5(2)) / 22 = .81812
- Rounded and multiplied by 100 gives us a percentile rank of 82
Highest and Lowest Achievable Ranks
Percentile Rank is not like a normal percentage where you can achieve a maximum of 100% and a minimum of 0%. Let’s investigate the minimum and maximum based on the first and last ranked items in the list in the example
Applying the rule to the top values in the list (mean of 5.00 with 3 ties) gives:
c = 19 are less than the tied, compared, means
f = 3 is the number of times that particular value appears
N = 22 comparison means
- (19 + .5(3)) / 22 = .9300
- Rounded and multiplied by 100 gives us a percentile rank of 93
- In this example the highest percentile rank that can be achieved would be to be included in the 93rd percentile.
Applying the rule to the bottom value in the list (mean of 3.625, only one) gives:
c = 0 are less than the tied, compared, means
f = 1 is the number of times that particular value appears
N = 22 comparison means
- (0 + .5(1)) / 22 = .0200
- Rounded and multiplied by 100 gives us a percentile rank of 2
- In this example the lowest percentile rank that can be assigned would be the 2nd percentile.