# Perform 2 ways ANOVA in minitab with non normal data involved

Y

#### Yew Jin

Hi guys,

One of the assumptions is the data must in the normal distribution before study in ANOVA. I have a case that the intend to compare the 2 samples which 1 of the sample is in the non normal distribution.

We may use Johnson or Box Cox trasformation to change the non normal to normal set of data. But the question is how we want to use the transformation data in the sample versus the other set of original data which in normal distribution in this case for this study?

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S

#### shailendrasingh

Transform the non normal data using Box Cox transformation. Using the same lambda value convert the normal data set. This conversion will not affect the distribution of your normal data set,and then perform ANOVA using transformed data.

Other option is to perform nonparametric test equivalent to ANOVA i.e Kruskal Wallis test.This test is performed when any one of the data sets is not normal or if both sets are not normal.

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#### Yew Jin

But when we have the data which in the negative that we can't use the box cox, right?

Any other alternative beside we use the non normal method in this case?

S

#### shailendrasingh

Ahaan !!
Well we cant use Box Cox when data are negative.
A usual method of dealing with raw data where many of the values are less than 1 is to add an arbitrary constant to the entire data set and then transform; in this way we avoid dealing with negative numbers.

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#### Allattar

I have to ask about the data structure.
Is the data expected not to be normally distributed?
Is the data in each group normally distributed.

You probably realise this already, but just to confirm, the original data in an ANOVA does not need to be normally distributed, but the residual error should be. Well roughly normal at least.

An example of this could be

Line Shift
1 A
1 A
1 B
1 B
2 A
2 A
etc...

The criteria is that the results from each group, ie: line 1 shift A, line 1 shift B, line 2 shift A, line 2 Shift B, they would be normally distributed. But if you add all the results together in one column, they need not be normally distributed.
Lets say all combinations of line and shift have the same average and the same standard deviation, and are normally distributed, except line 1 shift B. Line 1 Shift B has an average muich higher than the other groups, it will make the data not normally distributed.

Apologies if you know this already, it is a common mistake, and one I have to explain often.

If you know the results from each combination are not expected to be normally distributed, ie: you are trying to analyse the standard deviation, which follows and exponential distribution. Then we can either transform the data, or run as suggested the Kruskal Wallis test, which is a test of medians, rather than means.

I wouldnt worry too much either if the residuals are not perfectly normal.

#### Miner

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