Normal Distributions and Transformations

[#1]

Hi Everyone,

I have some measured data and when I try a continuous normal fit, I can see that my data is not normal.  However, I can see from the Goodness-of-Fit Test that the data is from the Johnson Su distribution.

This distribution has two shape, one location and one scale parameter.  From my research online, I can see how to calculate variance from these parameters and from that the standard deviation.  I used Excel to calculate that, but is there a way in JMP to do this?  From my understanding, the Summary Statics table from the "Distributions" analysis calculates these statistics assuming the data is from the normal distribution.

Thanks in advance!

Natalie

[#2]

Select "Save Transformed" from the red triangle in the Fitted Johnson SI outline box.  It will create a new column of data using the Johnson SI transformation

[#3]

Okay. After that should I run your script to transform that Johnson SI column to normality?

[#4]

Yes.....

[#5]

I understood that I needed to run your script. If I don't run it I can see that column normalised, but...

1. In which situation should I use those parameters from Capability Analysis?

2. When I ran the non-normal data in a repeated-measures design I could find a significant effect on the variable that I analysed across the timepoints through the results from the nonparametric muliple comparison test (e.g., Wilcoxon Each Pair). However, when I ran the data, which column had been transformed using Johnson SI, that significant effect disappeared across the timepoints. So, which result should I trust?

[#6]

1.  You will have to tell me what you want to do with the Capability Analysis.  My background is in both psycology and engineering.  You could use Cp/Cpk to get somewhat of an estimate of the capability is, but since you are using it within a single set of data, and not based upon real specification limits, I would find the statistic somewhat suspect.

2. The purpose of transforming the data is to transform the data into a distribution that is normally distributed.  The rational for this, is that many of the statistical tests are based upon the data being normally distributed.  The Wilconon  statistic is a NonParametric test.  It does not require a normal distribution.

[#7]

1. Although, I read the Capability Analysis "measures the conformance of a process to defined specification limits", unfortunately I didn't understand exactly its meaning in Statistics.

2. Therefore, when the new column "Johnson SI" is created, I really need to run your script. (Initially, I thought it wasn't necessary to run it). Anyway, I tried to run it. In my case, the data table is in column format. I attempted to adapt your script deleting the first part, which created the data table, and inserting the names of columns rather than PNP3 and "Johnson SI Transform PNP3", and I saved it on the top left box (below the name of the data file) inside the data file. When I ran it, nothing happened. (I don't know if I saved it correctly or occurred any parsing error in regards to the column names since they weren't in the script, but in the data file). Please, Jim (@txnelson), how can I run your script using a column-format data file? 

Thank you very much!

[#8]

I will ask again, but more directly, why do you think you need to run a Capability Analysis on the data?

That aside, concering the script not providing you with any visible output, are there any messages in the Log, indicating any errors?

[#9]

Regarding the Capability Analysis, I saw it set up in one of your previous post when you explained "the steps of how to transform non to normal data" to me in the URL: https://community.jmp.com/t5/Discussions/Normal-Distributions-and-Transformations/td-p/28662/page/2?...  (page 2)

It seems the "Capability Analysis" is measuring if a system can meet a set of specifications or requirements in a statistical process control, isn't it? So it doesn't apply to my case.

[#10]

Cp/Cpk analysis is completely dominated by the specification limits.  And yes, you can get 3k spec limits generated, however, using them on such a limited measurment space seems to me to be only and exercise in producing numbers, not anything of any real meaning. 

[#11]

Am I correct to think the Cp and Cpk aren't applied to the Psychology field, but to Engineering, Process Control and so on?