# log tranformation on two sample t test help

## log tranformation for two sample t test

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#### bayoote

##### New Member
Hi All,

I need help on a two sample t test question.
I have two sets of numbers:
X
54.5
67.35
4.1
and
Y
1510.5
3462.6
1045.4

I want to compare the mean to say that they are statistically different at 95% confidence interval
Since the two sets of number has unequal variances, I used a Welch's test. However, the p value for the test is 0.1192. The test is not significant. Why is that?

Then I took a log transformation on X and Y and they don't have unequal variances problem. I used a pooled t test. The P value is 0.0007. It is significant now.
The problem is I took a log transformation and I have the log difference and log difference confidence interval. If I take anti log on the difference, it is going to be the ratio of median and its confidence interval.

My question is how can I transform it back to get the confidence interval of the mean X-Y on its original scale?

Thanks a lot for any help!

#### hlsmith

##### Less is more. Stay pure. Stay poor.

I don't think it is possible to get be to the mean after the natural log transformation.

#### obh

##### Active Member
Hi Bayoote,

I assume this is a theoretical question?

Your sample size is very small ...
With such a small sample size you can only make assumptions. t-test assumes reasonable symmetrical data but you can't check it on 3 values ...

If you don't have a good reason to believe it is equal variances, you should use the unequal t-test.

Playing with logs on a sample size of 3 values doesn't make sense...

You may intuitively expect significant results.
But despite the big differences between the 2 groups' values, your sample size is extremely small and this reduces the test power dramatically.

Now you stay on the edge of significant results depend on the significance level you chose.
So this reveals the power differences between different tests. (with α=0.05 for example, the pooled variance test is almost significant while
the Welch t-test or the Mann-Whitney U test is not significant