Which statistics to use?

Question

I have a medical research in which I have two sets of data

1. Control group: People who have no ailment.
2. Study group: People who have some particular ailment.

Within each category there are subgroups like age, gender, blood pressure ranges, cholesterol ranges, etc.

Now I got a few observations (around 50) for both control group and study group. I have observation of various parameter like blood pressure, cholesterol level etc. I want to prove statistical significance of these parameter (Blood pressure/cholesterol) in study group. What is the best way to do it? Should i use $t$ distribution or normal distribution?

Also when I calculate the $p$-value, should I compare each subgroup in study group (based on range) with corresponding subgroup in control group or calculate $p$-value as a whole for study vs control group?

Answer 1

use a Student's T-test.

Your setting is an unpaired sample and the parameter is on a continuous scale (we know that because it has a unit like BP - mmHg, cholesterol - g/dL).

BUT - remember that your sample is not a population and you have to ask yourself if you handpicked them or are those two samples of random people.

Probably this is not random and you should check if the parameters you are testing present as NORMAL DISTRIBUTION.

This is important because Student's T-test was designed for NORMAL DISTRIBUTION. If this assumption is true - you may use the test and conclude upon the p value.

Answer 2

You have to use the Student t test for unpaired data. For subset analysis, you can perform separate analyses for different subsets, but a better approach is to use two-way ANOVA. For example, considering group (study or control) and age subset as main factors, a two-way ANOVA would tell you not only whether differences exist between groups or between age subsets, but also whether differences between groups interact with age (i.e., whether between-group differences differ across age subsets).