Situation: Comparing mean scores of level of satisfaction across multiple institutions and overall.
Let's say there are 50 institutions, all with different sample sizes.
Level of satisfaction is rated 1 to 5.
I was asked to perform a t-Test to determine outliers and significance of the score differences, with a control range for 1 SD and 2 SD.
Eg. Institute = Mean score
Institute A = 3.8 Institute B = 3.9 Institute C = 4.1 . . . Overall = 4.0
This is so that we can rank the institutions based on their mean score.
So here's my question:
- How do I make a fair comparison of the mean scores? It is possible?
- How does a t-Test determine statistical significance in this scenario?
- Do I look at P-value or overlap in distribution to assess usefulness of the test?
- I conducted multiple t-Tests for 2 groups (eg. Institute A & Overall, Institute B & Overall, Institute C & Overall, ...) but I'm aware that it is not appropriate to conduct multiple t-Tests comparing 2 groups at a time. What should I do?
Please kindly help. I am quite lost and confused.