# Successful t-test, how to analyze causality?

I have a basic question regarding t-test. I have a dataset where I observed an effect between two groups. I analyzed the effect via a t-test and the p value is sufficiently low.

The data set describes two groups of patients who are treated differently. The measurement is on a metric scale (imagine observed lung volume).

In my interpretation is that there is an effect with statistical significance.

My question is now what are the next steps, in order to analyze if there is a causality between treatment and effect.

Many would say this is a philosophical question rather than a statistical one. But it is one statisticians are called upon to answer. Here are several kinds of issues to ponder:

1st, was a diverse group of people randomized into treatment and control groups. If so, this helps to eliminate disease status, age, gender, education, income, etc, as 'lurking' explanatory variables. (Rich people can afford to take better care of themselves, and there were more rich people in the experimental group; what do you expect?")

2nd, was the treatment specifically designed to achieve the observed effect, or is this a surprise? (What factors led to expecting the observed result?)

3rd, was the study double-blind, thus eliminating various kinds of bias? ("The doctors took better care of subjects in the treatment group because they wanted to show the treatment works.")

4th, were the instruments used to get data on success relevant, reliable and established ones? (Are the data you put into your t test obviously relevant and established lab results? Are any patient surveys you analyzed well-vetted instruments for reliably detecting exactly what is relevant?)

• Agreed. This totally depends on the experiment design, and how well confounding variables are controlled in the experiment. – yueyanw May 7 at 21:44
• Thanks! So basically the t test shows that there is a correlation and the experiment design needs to be discussed to prove that there's a causality. – guerda May 8 at 21:28
• In some cases, it may be difficult to 'prove' causality. If A,B,C are correlated, do A and B cause C? Does C cause both A and B? Etc. // It took some years to work past unhelpful arguments and questionable "data" from companies and tobacco-growing states to make a strong case that smoking is one major cause of lung cancer. – BruceET May 8 at 21:40