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'.
Can I still use this approach? If not, please advise.
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!