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Nov 19, 2016 6:07 AM
(2400 views)

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Nov 21, 2016 11:05 AM
(4659 views)

Solution

It appears from the article that the author applied one of the family of Johnson transformations to the variables of interest. Within JMP there's a couple workflows to do something similar with Johnson transformations.

Workflow 1: Create a usual Distribution platform report using the untransformed original units variable. From the Distribution platform report, from the JMP hot spot above the frequency distribution graphic, choose the Continuous Fit drop down option, then the desired Johnson transformation. You can save the transformed variable to the data table from the Johnson Transform graphic hot spot by selecting Save Transformed.

Workflow 2: I think you can use only if you are running JMP version 12 or higher is, from the JMP data table select the specific column you want to transform, then from the column header, right click, New Formula Column -> Distributional -> Johnson Normalizing. This workflow creates a new column in the data table corresponding to the Johnson Sb transform.

13 REPLIES

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Nov 21, 2016 8:51 AM
(2347 views)

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Nov 21, 2016 10:22 AM
(2341 views)

Thank you for the response. The reason as to why I want to normalize the data is, I want to be able to generate norms for the scale that I have developed and to establlish psychometric properties. I have been reading this article https://ia801404.us.archive.org/27/items/ERIC_ED353271/ERIC_ED353271.pdf, which is similar to what I want to do.

I need help to execute this curve fitting in JMP. Thanks again.

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Nov 21, 2016 11:05 AM
(4660 views)

It appears from the article that the author applied one of the family of Johnson transformations to the variables of interest. Within JMP there's a couple workflows to do something similar with Johnson transformations.

Workflow 1: Create a usual Distribution platform report using the untransformed original units variable. From the Distribution platform report, from the JMP hot spot above the frequency distribution graphic, choose the Continuous Fit drop down option, then the desired Johnson transformation. You can save the transformed variable to the data table from the Johnson Transform graphic hot spot by selecting Save Transformed.

Workflow 2: I think you can use only if you are running JMP version 12 or higher is, from the JMP data table select the specific column you want to transform, then from the column header, right click, New Formula Column -> Distributional -> Johnson Normalizing. This workflow creates a new column in the data table corresponding to the Johnson Sb transform.

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Nov 21, 2016 10:45 PM
(2313 views)

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Nov 28, 2016 7:20 AM
(2230 views)

From my previous post, after couple of weeks of mind boggling and extensive research, I have come up with these steps -including a section of my chapter writing. Can somebody please peer review and validate, if this is okay? Thanks.

**Norms Development**

Development of the subscales and Challenging Behavior Composite (CBC) norms was done in several stages. The procedures were adopted from the works of Jing-Jen Wang (1992)[1] and Sparrow, Cicchetti & Balla (2005)[2]. The ages (4-58) were divided into 12 age groups and the corresponding mean, standard deviation, skewness and kurtosis of the raw scores distribution were computed for the five subscales in each of the age groups. Line graphs of the 12 means against age were drawn separately for each subscale, and a smooth line was traced through the mean. In the same manner, standard deviations across 12 age groups were plotted and smoothed.

The smoothed means and standard deviations, and the unsmoothed skewness and kurtosis values of each age group for each subscale were further input into several stages of standardization. The raw scores were transformed into standard scores, which in turn were generated into another distribution based on the smoothed mean and standard deviation. The distribution (with smoothed mean and standard deviation) was input to generate Johnson bounded distribution[3], which in turn were converted into Challenging Behaviour Rating Scale (CBRS) scores[4] (Mean=15, SD=3). To obtain norms beyond range, linear regression with raw scores and CBRS scale scores was performed. The predicted values were used as CBRS scaled scores.

In the next step, the conversion for the 12 age groups was expanded to include 55 age groups (4-58). Linear interpolation (for missing values between adjacent age groups) was used to fill the gaps. ( I tried extrapolation for missing values beyong age groups- results were not meaningful, so didnt do that)

[1] Jiing-Jen Wang. (1992). An Analytical Approach to Generating Norms for Skewed Normative Distributions. Paper presented at the Annual Meeting of the National Council on Measurement in Education, San Francisco, California.

[2] Sparrow, S.S., Cicchetti, V.D., & Balla, A.D. (2005). Vineland-II Survey Forms Manual. NCS Pearson Inc. United Sates of America

[3] Johnson Curves are fitted using moments (γ, δ, θ, σ) generated with values of mean, standard deviation, skewness and kurtosis of the distribution

[4] Vineland-II uses a scale score with mean (15) and standard deviation (3) for its maladaptive behavior scale. It is considered to be a relative measure to the scaled scores of many other tests.

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Nov 28, 2016 9:44 AM
(2214 views)

You need to read Dr. Donald Wheeler's paper:

Transforming the Data Can Be Fatal to Your Analysis

The misguided love affair with the normal distribution must come to an end!

Steve

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Nov 29, 2016 12:02 AM
(2205 views)

Yes, Thank you. I surely will. But I also think, I do not have enough knowledge to contest this viewpoint and also accept the fact that it can be a debate like- wholism Vs reductionism, quantiative Vs qualitative, type I error Vs type II error etc. The only defense I can make up for my work is that the scale will be more useful at system level- to classify those who need intensive therapy, those of whose parents or teachers can be educated on behaviour modification and therefore avert potential problems and never the less, them who need positive behavioural suppot. Its more like system based provisions (response to intervention model) rather than individual approach. A child walking into a therapy clinic will still be worked upon criterion referenced.

Thank you for the suggestion.

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Nov 29, 2016 12:19 PM
(2187 views)

bj,

Based on your latest input, perhaps you need to analyse your data with some predictive modelling technique such as neural networking or partitioning.

Steve

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Nov 29, 2016 6:21 PM
(2177 views)