Hello Everybody;

I would like some advice regarding my results. I carried out two surveys - one involving teachers and the other involving students - and in both surveys I used the same questionnaire. The participants were asked to rank components on a 5 point scale. Here are the results for one of the components

- one sample t-test against benchmark of 4 with results of teacher's survey.

Component A had the following results:

mean: 3.3
p-value: 0.0048
95% C.I: -Infinity and 3.6913
reject null hypothesis (mu >= 4) and accept alternative hypothesis (mu < 4)


- one sample t-test against benchmark of 4 with results of student's survey:

Component A had the following results:

mean: 3.9565
p-value: 0.4262
95% C.I: -Infinity and 4.3529
accept null hypothesis (mu >= 4)

- two sample t-test with equal variance comparing means of both samples:

p-value: 0.0933
95% C.I: -1.4298 to 0.1167
Accept null hypothesis (mu1 == mu2)


My question is this:

The teacher's sample suggests that the mu < 4 for component A. The student's sample suggests that the mu >= 4 for component A. The two-sample t-test suggests there is not significant difference between the samples. What conclusion can be made here or what other test can I do to decide if overall mu < 4 or mu >= 4?

Any advice would be greatly appreciated.

hi Prins
did you mean mu as the "u"? Thanks for asking this question at the forum.

Maybe somebody can explain it better than me but here goes anyway--

First of all, I don't think the one-sample test is relevant here, as you have two groups and they used the same questionnaire. So if you want to test the difference between the teaachers and students, it would be a two sample t-test (the 2nd one you did).

So you would report:

There were no significant differences between responses from teachers (M = 3.3, SD = report value) and those of students (M = 4.0, SD = report value), T(df) = value, p >.05.

About the mu , 4 for teachers and >= 4 for students, it just shows you that there may be a difference between how teachers and students score their responses, but reasons are speculative, as your results did not reach significance.

hope this helps
love satchi

Hello Satchi;

Thanks for the response.

The one-sample t-test was needed because in the first case I was looking at the teachers and students separately. The logic is basically as follows:

1) I have a framework with a number of components
2) Experts evaluate framework and rank components using scale 1 (not important), 2 (slightly important), 3 (important), 4 (very important) or 5 (essential)
3) I keep component in framework if it has a mean of 4 or more
4) A one-sample t-test is performed against benchmark of 4
5) Results reveal experts believe component A is not very important (i.e. mean is below 4)
6) I run another survey but this time with students who use the same ranking scale
7) I carry out one-sample t-test against a benchmark of 4 as before
8) Results reveal that students believe component A is very important (i.e. mean is 4 or more)
9) I check if there is a significant difference between the two results by carrying out an f-test followed by a t-test
10) Two-sample t-test reveals no significant difference

So the question I am left with is whether or not component A is very important i.e. should it be left in the framework?

I was wondering whether the confidence interval could be used for this purpose?

I hope the above makes sense.

Think you need to justify use of a t-test, as your data appears to be ordinal, rather than continuous.
In that context, mean and confidence intervals are meaningless.

hi Prins, hi Thesisfun
Prins, this benchmark of 4 is what I don't understand, because the value of 3 also carries weight in justifying people's responses, as much as value 4 or 5 or even 2.
So your true "benchmark" may not be 4? I don't know your framework so I can't tell if component A is very important. You could use the confidence interval to use the range but there is no measure of change so it would be that using the CI to interpret could not tell us anything, as commented by thesisfun.

love satchi

Hello Thesisfun, Satchi;

Based on my research and from what I have understood t-tests can be used and are widely used with ordinal scales in surveys. Here is a journal paper on the matter: http://pareonline.net/pdf/v15n11.pdf

I think although the data is not continuous a value such as 3.5 would still have some meaning in this context.

The scale was presented to respondents as follows:

(not important) 1 2 3 4 5 (essential)

So 3 could be interpreted as important or neutral.

Any benchmark value could have been used from 3 - 5 (I would say that it should be slightly more than 3). The reason for using 4 is based on research that suggests 80% is a good benchmark so I am using 80% of 5 i.e. 4.

I think even if I change the benchmark value you could still end up in the situation described earlier where one group regards a component to be important whilst another does not.


At the moment the conclusion seems to be that there is no significant reason to drop component A from my framework.

I think you are going to need a very strong argument for reporting means and using a t-test.

To me, that paper suggests that there is little point using a t-test if a mann-whitney has equivalent power.

I don't know how to interpret 3.5- at a rough guess, it means slightly less important than very important.
Also, is your data actually normally distributed?