# Generalization of results according to sample (n=41 -> 82% of population) despite not having a p-value in a contingency table

#### desun

##### New Member
Generalization of results according to sample (n=41 -> 82% of population) despite not having a p-value in a contingency table.

Hi. I'd appreciate your help.
I have basic statistical knowledge, and I'm trying to make sense of the following:

The population of my study is constituted of 50 universities, and 41 of them (82%) replied to the survey/questionnaire.
The questionnaire is composed of categorical variables, and I'm analyzing through "contingency tables" the association between variables.
I performed a Chi-square test using the following website:
http://vassarstats.net/newcs.html

Given of my tables with 2 rows X 3 columns
4 17 6
2 9 3
The chi-square test output informed my data doesn't fit the "expected cell frequency":
"The chi-square test is performed only if at least 80% of the cells have an expected frequency of 5 or greater, and no cell has an expected frequency smaller than 1".

Then I calculated the "Fisher Exact Probability Test 2x3" available in the same website: http://vassarstats.net/fisher2x3.html
The results are:
PA = 1.0
PB = 1.0
No. of tables evaluated = 69
In that case, it seems the two-tailed PA and PB = 1.0 suggests there is no association between rows and columns (not statistically significant).

=> Despite p-value, can I generalize my results for the population, giving my sample (n=41) represents 82% of the population (n=50)?

=> If not, would there be any heads-up I could write in the results to inform limitations of the associations I'm referring to in the contingency table?

Thank you very much,
Desun