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How should I transform non-normal data and perform ANOVA from the transformed data

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Occasional Contributor
Posts: 5

How should I transform non-normal data and perform ANOVA from the transformed data

Hi,

 

I have performed the residual analysis for my samples and noticed that some of them are not normally distributed. I expect to do a transformation for the separate datasets and perform ANOVA by combining the samples as well. I am trying to figure out how to use proc transreg (model BoxCox). Is this approach for the transformation suitable for my objective?

 

Options nocenter pageno=1;

data one;

input Entry Block Measure;

cards;

 

Every data set is arranged in 3 columns. In my experiment, dependent or independent variables are not defined. How should I modify the proc transreg code for this?

Esteemed Advisor
Posts: 5,521

Re: How should I transform non-normal data and perform ANOVA from the transformed data

Posted in reply to Nadishika

ANOVA is quite robust to departures from normality. You might not need to transform at all. Please tell us more about your ANOVA analyses (models) and your sample sizes.

 

Posting some histograms or QQ plots would also be very useful.

PG
Occasional Contributor
Posts: 5

Re: How should I transform non-normal data and perform ANOVA from the transformed data

Hello PG,

 

Thanks for your reply. I have 5 samples(datasets), each sample size is 177 with 2 blocks. The model for the ANOVA is the mixed model considering the blocks as the random factor. Here I have attached two histograms and plots of residual*predicted for two datasets. The Kurtosis values were way too high ( ex: 8.1). Shapiro-Wilk test was considered as the test for normality and the Pr<W were mostly <0.0001. The residual*predicted plots appears in fan shaped.Do I still have the chance to use these sample data as it is without a transformation?

 

Thanks,

Nadishika

 

 

Capture 1.PNGCapture 2.PNGCapture 3.PNGCapture 4.PNG

 

Occasional Contributor
Posts: 5

Re: How should I transform non-normal data and perform ANOVA from the transformed data

@PGStats

What is your opinion on the importance of normality for the LS-means (in a mixed procedure)? Does the departure from normality make much effect in LS-means?

SAS Super FREQ
Posts: 4,238

Re: How should I transform non-normal data and perform ANOVA from the transformed data

Posted in reply to Nadishika

> In my experiment, dependent or independent variables are not defined. 

 

I don't understand what you mean by this statement. Please post the code you used to run the ANOVA model.

Occasional Contributor
Posts: 5

Re: How should I transform non-normal data and perform ANOVA from the transformed data

[ Edited ]

 

Hi Rick,

 

This would be my code for the ANOVA model ( 5 samples, 177 Entries and 2 blocks).

proc mixed data=one covtest cl;                                                              

class Sample Entry  Block;                                                       

model Measure = Sample  Entry  Sample*Entry/ddfm=kenwardroger;                                  

random Block;                                                  

run;       

Please ignore this sentence  'In my experiment, dependent or independent variables are not defined'.Measure is the dependent variable in the model statement. Before performing ANOVA, I  checked the normality for the residuals in individual samples. Please check some of the results of the residual analysis in my reply to PG. Any advice is much appreciated.

Thanks

 

Occasional Contributor
Posts: 5

Re: How should I transform non-normal data and perform ANOVA from the transformed data

Posted in reply to Nadishika

@Rick_SASand @PGStats, I really appreciate further support.

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