If I have an experiment documenting the recovery of 1,000 patients who were given access to a medication.
- MEN taking the drug. 2 out of 2 recover (100% recovery).
- MEN not taking the drug. 400 out of 498 recover (80.3% recovery).
- WOMEN taking the drug. 30 out of 498 recover (6.02% recovery)
- WOMEN not taking the drug. 0 out of 2 recover (0%recovery).
People taking drug: 32 out of 500 recover (6.4% recovery). People not taking the drug: 400 out of 500 recover (80% recovery).
Can I conclude the next statement?
- 100% (drug) vs 80.3% (no drug) recovery for men and
- 6.02% (drug) vs 0% (no drug) recovery for women,
Therefore: the drug is indisputably helpful.
Is there any flaw in my logic?
(data is fake, but my question is about my conclusion, whether the conclusion is plausible given the data…)
I know I exagerated the sample size... but he is still comparing samples, which is more than 3 times larger!! (270 men no drug, to 80 women no drug), how is he comparing them as equal? and besides, how he arrives to such huge 'indisputably' claim without even doing any statistical test?