Normal quantile transformation

[#1]

Hi all,

I would like to do a normal quantile transformation for my data, because it is not normally distributed and I cannot do a 3-way ANOVA on it.

I read a suggestion to do the normal quantile transformation and then run the 3-way ANOVA on this.

First, is this appropriate?

Second, can I do this analysis in JMP?

[#2]

Transformations can be very helpful. You might try using the Box-Cox Transformation built into Fit Least Squares, which can easily perform the 3-way ANOVA. I suggest you try this general solution first before resorting to the more specialized solution that might not be necessary.

See the JMP Help about this transformation.

[#3]

Thanks, Mark. I have a couple more questions regarding your response. 

First, the link attached shows that the Box-Cox transformation is only appropriate for positive Y responses. Some of the data in my current work are negative values. What then could be done?

Also, for the ones that are all positive values, when I get the box-cox transformation section, what exactly do I deduce from this? Reading from the link, it says we can save transformed data. So when I save transformed data, is this what I use going forward for the Tukey test for significant differences?

[#4]

I think what you are asking about is related to Van der Waerden test 

Though the test was developed for one-way ANOVA, but I think it should work for three-way ANOVA as well, given the null hypothesis is that none of the effects are significant (main and interactions). I am not sure it still work if your hypotheses are sequential.

To actually do it, you need ranks of the observations, then map the ranks to normal quantiles. See the following code snip to see the steps.

Names Default To Here( 1 );
dt=Open( "$SAMPLE_DATA/Big Class.jmp" );
New Column( "Height Rank", Formula( Col Rank( :height, <<tie( "average" ) ) ) );
New Column( "Normal Quantile Transform", Formula( normal quantile(:Height Rank/(nrow(dt)+1) ) ) );
dt << Oneway( Y( :Normal Quantile Transform ), X( :sex ), Means( 1 ) );

[#5 · Accepted solution]

You can also do normal quantile transformation using the Distribution platform.  For large tables this can be faster than using column formulas.