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After normality test!

meelad

Dear All,

I normalized my data by log-normal or other functions. I used "Distribution>Fit" and check out it thorought "Goodness Fit ...".

For analysis by ANOVA, I used "Fit Model" and transformed the data based on its function that I used to normalize. ex. I used log-normal for normality, so I transformed it to log.

Did I do correctly?

I need means for mean comparison or report them. Should I report or use original data or transformed data? Also, I need standard error for them. Should I use standard error based on new data or not?

Because, if I use mean or standard error as tranformed form, it is different with orginal data.

Sorry, I know it is basic but I confused a little bit. Please help me.

Thank you so much for your time

Accepted answers

Peter_Bartell

I fundamentally agree with my colleague @Mark_Bailey's counsel. The only thing I'll add is in your reporting and PRESENTING of results, be mindful of your audience. If they need to make decisions or take action based on your study recommendations, there might be a time when you want to communicate to the audience using untransformed values. I'm not saying do the analysis in the untransformed fashion...but when communicating something along the lines of say, "The mean concentration for the material coming from reactor A is x and the mean concentration for material coming from reactor B is y." then it might be more beneficial to communicate this information in the untransformed units.

I always try to approach communicating findings from the perspective of the decision makers and not the statistician's point of view...those decision makers are making the money...not the statistician. The statistical details can be provided if needed as follow up or an appendix, etc.

Mark_Bailey

I hope that my previous reply did not confuse the point. You need to be consistent throughout the process. At the end, though, it might make sense to back-transform the results for presentation. You can't use the original data, but instead back-transform statistical results such as the mean or confidence intervals to the original scale.

All comments

Mark_Bailey

The analysis is based on the transformed data so be consistent. The process includes transformation, fit model (ANOVA), assess statistics, check assumptions (i.e. residuals) and so on. The conclusions and reports are based on the transformed data.

In science, we directly use pH all the time. We do not back-transform it to Hydronium activity. There is no need.

Peter_Bartell

meelad

Dear @Mark_Bailey

Thank you so much for your time and your explanation.

I mean that I report the ANOVA results and I report the mean comparison based on original data.

For example, I have a series of data in form of percentage. They were not normal and I transformed them by log and analyze them. Now, for mean comparison, should I use the data based on unnormalized or normalized data?

meelad

Dear @Peter_Bartell

Thank you so much for your time and your suggestion.

It is realy useful.

Mark_Bailey

meelad

Dear @Mark_Bailey

Thank you so much.

It was great,

Cheers,

Milad