Not sure where to begin...

I'm planning a study in which I will survey about 300 people about their attitude towards a given subject area. They will answer questions on a likert scale, 1-5. My hypothesis is as follows:

H0: Participants have a negative attitude towards topic X (m<3).
Ha: Participants do not have a negative attitude towards topic X (m>=3).

What I THINK I want is a one sample t-test. However, my hypothesized mean is that the "mean will be less than 3", and not "m=3" I'm not sure how I would use the t-test without a single expected mean. I feel like there's a different statistic I'm missing.

Looking for a nudge in the right direction!

Much appreciated,


TS Contributor
your hypothesis is wrong, when you set H0 and H1, the "=" sign is always in H0, so you have a problem there, you need to change it.
m<3 is equal to m<=2 from logical point of view
now another point to take in mind. your variable is ordinal, it is not necessarily normally distributed. the t-test assume normality of the data . make sure you check it first before using this test.
Okay, that's interesting. In my case, I'm creating a composite score based on the responses to multiple questions, so 2 would be extreme. Would I be safe in saying:

H0: m <= 2.99 ?

Also, now I'm sort of lost (nothing new) on the proper test again...
The Polytomous Rasch model is common for this type of study, but I haven't studied it for a while and forget the specifics.


TS Contributor
I thought about the ordinal as discrete, that's why I said m<=2, but since you are using averages, then you are correct, m<=2.99 could be better.
regarding the test, the t-test assumes that your data is normally distributed, if it ain't, and you sample ain't big enough, then the test might give the wrong results.

what you need to do, is to examine your data, the distribution (you can do it using a histogram, or even better, a Q-Q plot - any statistical software can do it). If your data is even approximately normal, you can use the test, if it ain't, you should use a non-parametric test instead, in your case the Wilcoxon signed rank test.