# One-Way ANOVA with Non-Normal Distribution

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- This topic has 8 replies, 3 voices, and was last updated 6 months, 1 week ago by Fausto Galetto.

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- March 10, 2020 at 6:39 am #246596

Fausto GalettoParticipant@fausto.galetto**Include @fausto.galetto in your post and this person will**

be notified via email.I analysed the data in the attached file.

There I present my computations made with Minitab 19.

The goal of the analysis is “

**Can we assess IMPROVEMENT**of sample 2 versus sample 1?”.From the nalysis of the data the conclusion has to be

**NO IMPROVEMENT***Can anybody see***IF I MADE a very STUPID ERROR?**Thanks

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- ONE-WAY-ANOVA-with-NON_normal-data.docxYou must be signed in to download files.

1March 12, 2020 at 2:36 pm #246640@fausto.galetto Since you were not able to reject the null hypothesis and see a difference, I would want to know the Power of your tests. Given the small sample sizes is there no difference as you state or is the lack of noticeable difference due to a low power?

0March 14, 2020 at 5:27 am #246663

Fausto GalettoParticipant@fausto.galetto**Include @fausto.galetto in your post and this person will**

be notified via email.Using Minitab, at “Power and Sample Size” I think I found that 10+10 items should give at least 90% power for the differences to be assessed…. IF I used Minitab properly!!! (at “Power and Sample Size”)…………

It could be that the “non-rejection of the H0” could depend on the methods used…

- This reply was modified 6 months, 1 week ago by Fausto Galetto.

0March 14, 2020 at 3:23 pm #246665Not sure I understand what values you put into Minitab for difference in means.

*I think I found that 10+10 items should give at least 90% power for the differences to be assessed*0March 15, 2020 at 6:51 am #246686

David007Participant@David007**Include @David007 in your post and this person will**

be notified via email.The power test is applicable only to the parametric t test, not the nonparametric.

Aside from that, the two-sample t test is quite robust to the assumption of normality.

0March 15, 2020 at 4:29 pm #246691P-value for normality for Sample 1 is .485 and for Sample 2 is .020. Close enough with respect to the normality assumption. In that case, maybe the 2 sample t can be used. The p values for the equal variances are just a bit above .05 so maybe close enough. Bottom line is that maybe the 2 sample will work in this case. Since no difference was seen and the sample size is small there is still a possible issue with Power.

The p-value for the 2 sample t is .092 which is a marginal conclusion of no difference. The mathematical difference between the two means is 615. I ran a Power and Sample Size calculation for a difference of 600 and the power turned out of be .38, not too strong.

Bottom line here is that the data sets are probably too small to be of any use in answering the original question of whether there is any statistically significant differences between the two samples. Run everything with an alpha of .10 and conclusions will probably change.

0March 16, 2020 at 4:52 am #246694

Fausto GalettoParticipant@fausto.galetto**Include @fausto.galetto in your post and this person will**

be notified via email.I used mu2-m1=600

0March 16, 2020 at 11:38 am #246702Then you can see above that the power for your data is only 38% which means if there is a difference you only have a 38% chance of seeing it. With a sample size of only 10, there will be a significant overlap of the two confidence intervals so it will not be easy to see a difference. I would not make a decision that the two groups are statistically the same with such a low power value. To achieve a minimally acceptable power of 80% you will need at least 27 data points for each group. Then you can run the test again and see whether you have a difference or not.

0March 16, 2020 at 12:31 pm #246703

Fausto GalettoParticipant@fausto.galetto**Include @fausto.galetto in your post and this person will**

be notified via email.**Perhaps I MISUSED Minitab….****Power and Sample Size**2-Sample t Test

Testing mean 1 = mean 2 (versus <)

Calculating power for mean 1 = mean 2 + difference

α = 0,05 Assumed standard deviation = 400

**Results**Difference -600

Sample Size 10

Target Power 0.92

Actual Power 0.942864

The sample size is for each group.0 - ONE-WAY-ANOVA-with-NON_normal-data.docx
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