# Confusion about small sample size, skew and t-tests

#### hedgefrog

##### New Member
Hi there

I'm doing a small research project with a sample size of 12. The data is slightly positively skewed but not strongly. The standards deviations are not that similar for the two sets of data. I've read that I cannot then do t-test if the standard dev's are different and the data is not of normal distribution.

I read about being able to transform the data so that it then matches the assumptions for doing a t-test. It said something about diving the data by the median in order to transform it?! I have no idea.

Does anyone have any ideas?

Alternatively I'll just have to discuss medians, interquartile ranges and such if I can't do parametric tests.

Thank you

#### hedgefrog

##### New Member
I also meant to ask... would this be ok or is my sample size of 12 too small?

#### Dragan

##### Super Moderator
Hi there

I'm doing a small research project with a sample size of 12. The data is slightly positively skewed but not strongly. The standards deviations are not that similar for the two sets of data. I've read that I cannot then do t-test if the standard dev's are different and the data is not of normal distribution.

I read about being able to transform the data so that it then matches the assumptions for doing a t-test. It said something about diving the data by the median in order to transform it?! I have no idea.

Does anyone have any ideas?

Alternatively I'll just have to discuss medians, interquartile ranges and such if I can't do parametric tests.

Thank you

You might want to consider the (rank based) nonparametric alternative test to the two-independent samples t-test - the Mann-Whitney U-test (or also called the Wilcoxon test).

Further, your sample sizes are most likely to small....but it really difficult to say for sure because I don't know the context of your experiment.

#### hedgefrog

##### New Member
Thank you
I don't think I'm able to do a mann whitney test as my data comes from two different populations. I was hoping to do an independent t-test.

The experiment is to test the intakes between two groups who are taking different textures of diets (e.g. swallowing problems etc).

Would you know anything about transforming data? How acceptable it is?

##### New Member
I do not see why you cannot do a non parametric test. It looks like it can be applied to this scenario.

Doing transformations is also acceptable.

#### Dragan

##### Super Moderator
Thank you

Would you know anything about transforming data? How acceptable it is?

You can perform tranformations. However, a common problem associated with this approach is that the null hypothesis changes and may be uninterpretable.

That said, the Mann-Whitiney U-test is appropriate in this case. It is the nonparametric alternative to the t-test that you're decribing.