What would be the appropriate statistical tool?

#1
Dear all,
I am a graduate researcher in the analysis phase of my research work. My research is an intervention research (n=14) trying to analyze the impact (pre and post) of the sports program. I don’t have a control group for this research. My dependent variables fall under ordinal, likert and continuous types, and my independent variable would be age and attendance. My question is, will paired t-test is suffice for this kind of data set? Does t-test work with binary variables? Is it worth running normality for binary data? Finally, kindly suggest another alternative for a data set with different type of dependent variables.

Your help and suggestions are welcomed and greatly appreciated.

Thanks and Regards
Jerrome
 
#2
Hi Jerrome,

the assumptions that the data follow a normal distribution will be violated if you consider ordinal data. Thus, a typical paired t-test would at best lack sensitivity, and at in the worst case provide biased estimates. However, there are non-parametric versions of the t-test which do not depend on the assumption of normality, e.g. the signed-rank test (= U-test). It is designed for paired comparisons on non-normal data.

Best
 
#4
the assumptions that the data follow a normal distribution will be violated if you consider ordinal data.
Ehh, wait a minute now! Isn't it possible for a continuous variable, which is ordinal, to be normally distributed?

The economists for example, are often talking about "utility" which is considered to be ordinal. Of course that can be normally distributed. For example, if I state my "utility" for chocolate (and do that repeatedly).

The IQ-scale, which is defined to be normally distributed, isn't that thought of as a ranking of all persons (thus ordinal) where the middle person, the median, is given the population mean of 100 and the values are spread out so that the standard deviation is 15 and the density is normal? I believe that it is defined in that way.


Thus, a typical paired t-test would at best lack sensitivity, and at in the worst case provide biased estimates.
It is a long time ago since I was reading about this, but if the variable is normally distributed, isn't it so that the parameter estimates of the means will be unbiased and the test uniformly most powerful?

(I appreciate mmmerker's willingness to answer, but I am not completely convinced that it is true.)