I conducted a study on faculty improvement programs, whether they had an impact on teaching practices of faculty members. Sample size was 15. One of the categorical variable observed was 'Is the teacher on time for lecture?' with two possible responses, either Yes or No. This variable was observed with each of the 15 faculty members at two intervals of time, one year apart. Now I want to compare the percentage of teachers coming on time for lecture a year before and a year after the faculty improvement programs. Can I apply any test of statistical significance on these two percentages from the same sample of 15 members? What would be the most appropriate test in this regard? Thanks in advance
I think you can use a Chi-Square-Test. This page provides more information about the test and you can commit the test right there: http://www.quantpsy.org/chisq/chisq.htm
In short, Chi-Square-Test compares the measured distribution of variable to the expected distribution of the variable in case of no dependency. If the measured distribution is not dependent on the other variable then the chi-square value will be small (in case of identical distributions 0) and if it is dependent the value will be large. However, the value is dependent on size of the table and sample. So to decide if the two distributions are different you need to also look at the degrees of freedom.
In this case, you would see the two time moments as two different groups and measure if time had any influence on the distribution of variable 'Is the teacher on time for lecture?'. You enter the distribution in real numbers (not %s) to the table and calculate the chi-square-statistic. The page will advice you to use either Pearson statistics or Yates statistics (in case any of expected frequency is below 1 or if the expected frequency is less than 5 in more than 20% of your cells). The calculation will give you chi-square-value, degrees of freedom and p-value.
Hope this helps.