# Measure of improvement in pre and post survey.

I did a survey to measure students perceived understanding of several topic at the beginning of the semester and few weeks later. The surveys are done anonymously and I cannot match the pre and post responses. I want to measure how much their understanding has improved. Here is a sample data:

   survey                 question          response count    percent
1 pre        I.understand.methods Strongly Disagree     5 0.05813953
2 pre        I.understand.methods          Disagree     7 0.08139535
3 pre        I.understand.methods           Neutral    19 0.22093023
4 pre        I.understand.methods             Agree    32 0.37209302
5 pre        I.understand.methods    Strongly Agree    23 0.26744186
6 post       I.understand.methods Strongly Disagree     0 0.00000000
7 post       I.understand.methods          Disagree     3 0.12500000
8 post       I.understand.methods           Neutral     4 0.16666667
9 post       I.understand.methods             Agree     8 0.33333333
10 post       I.understand.methods    Strongly Agree     9 0.37500000


It is safe to assume that the number of pre and post responses will be almost the same. In the data above it is not because I am still waiting on responses from the post survey.

What are possible metrics that I can use?

This question is related to How do I compare student pre-test scores with post-test scores to evaluate whether or not they "learned"? but different.

• For future studies of this kind, you could ask each student to give info such as mother's and father's birthday and last 2 digits of driving licence number on each survey. That way you could pair (almost) all without compromising confidentiality. // For the current data, I don't immediately see a valid analysis. Indep conditions of chi-sq $2 \times 5$ contingency table (Pre/Post by Opinion) would be not be met. // If graph is for all subjects, I'd hesitate to look for clear conclusion: Disagree and Strongly Agree both increased. // Also, not measuring improvement, but perception of it. Sep 10, 2016 at 17:48

Since I haven't gotten any answers here is a solution I found. I can use the mean rank to measure how the rankings in the pre and post differ. The mean rank can be calculated from the data. For the first survey: $$(5*1 + 7*2 + 19*3 + 32*4 + 23 * 5) / (5 + 7 + 19 + 32 + 23) = 3.71$$
For the second survey: $$(0*1 + 3*2 + 4*3 + 8*4 + 9*5) / (0 + 3 + 4 + 8 + 9) = 3.96$$
So, I can conclude that the ranking has improved by $3.96 - 3.71 = 0.25$