# power analysis with different sample distributions

I need to perform a (two-sample) power analysis, however my data are differently distributed in both samples and I am not sure whether I can a standard approach through t-test.

Please see the distribution of a variable ('scale') in two samples:

and the data:

scale   scale
0   8   214.0
1   8   230.0
2   9   246.0
3   13  284.0
4   14  469.0
5   16  506.0
6   25  551.0
7   29  585.0
8   62  593.0
9   63  751.0
10  71  753.0
11  71  784.0
12  91  789.0
13  97  868.0
14  134 881.0
15  160 964.0
16  256 1089.0
17  258 1313.0
18  259 NaN
19  344 NaN
20  381 NaN
21  477 NaN
22  479 NaN
23  653 NaN
24  858 NaN


Where

• mu_1 = 194
• mu_2 = 660
• pooled_std = 350

and based on these figures, to achieve a power of 80% and a level of significance of 5% (two sided), for detecting a true difference in variable 'scale' means between the two groups, I need only 9 samples. So it seems like, based on these calculations and the sample size and the distribution of the variable scale.

However, obviously, that the distributions are skewed/not equal and a bit far from 't'.

UPDATE

To put a bit of context into the numbers. For example, consider a case where you would like to measure a glucose level ('scale') in people with diabetes and without (disease/healthy) and this is what you find (the table in above, higher values of glucose associated with a disease).

Then, based on the data, you decide to introduce a new screening tool with a certain threshold. If a new observation will be above (below) your threshold, than it will be suggested as a (not) disease.

My question is: based on the data distribution (see pics in above) and clearly obvious difference in means of both groups, can I say the I have enough power in this study?

Thanks!

• Could you explain what you need a power analysis for? The differences between the two datasets are large and seemingly obvious. Are these data actually paired, as suggested by your presentation of them? If so, what do the "NaN" values mean? These are much more important issues to address than any question of power. – whuber Sep 5 '18 at 12:35
• This is what I was asked by a reviewer ('underpowered study') and I wanted to demonstrate that the difference is indeed significant, despite the fact there are only few samples. These are NOT paired observations, but rather measurements of a certain variable 'scale' in twogroups (healthy and disease groups).Please see my updated question for more explanations. – Arnold Klein Sep 5 '18 at 14:08
• Your reviewer is very confused. Power is a useful question only when you are contemplating obtaining more samples. For the purpose of assessing the evidence you have, it is irrelevant. – whuber Sep 5 '18 at 15:10
• Great, thanks. Can you elaborate please on 'much more important issues' you mentioned in your comment in above? – Arnold Klein Sep 5 '18 at 15:14
• Most are moot based on your previous clarification: I was referring to the need to respect paired data, rather than analyze them separately, and to accommodate missing values appropriately. Despite the appearance of "NaN" in your data display, you have no missing values: you only have two independent datasets of different sizes. Perhaps what matters most now is your experimental protocol: when you designed this experiment, what method(s) did you nominate for testing your hypothesis and what result(s) did they give? – whuber Sep 5 '18 at 15:17