Normality Issue in ratio data

[sbalugai...@gmail.com]

Respected sir/madam,

Whenever we try to bring normality in ratio data by using select cases in SPSS, the sample size is also reduces. Sometimes it reduces by 50% of the total sample size.  

Do we need to report this reduced sample size? 

Thanks & Regards,

Mr. Sagar Gaikwad

PhD Scholar

University of Mumbai. 

[Neeraj Kaushik]

Dear Sagar

Why do you wish to make data normal?

What purpose this will serve?

Plz aware.

Best wishes

Neeraj

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[sagar gaikwad]

Respected Sir,

SIr before applying parametric tests ( like correlation and regression) we need to check the normality of data but while eliminating outliers the sample size is reduces. 

So do we need to report this reduced sample size. 

Is it permissible to reduce the sample size and perform parametric tests

Thanks & Regards,

Mr. Sagar Gaikwad

Assistant Professor,

Vidyalankar School of Information Technology

Mob No: 9833376766

Online Profile: https://vsit.edu.in/faculty_sagar_gaikwad.html

ORCID ID : 0000-0002-3816-2801

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[Neeraj Kaushik]

Donalson (1968) observed that the results of ANOVA are robust even if there is no normality of the data.

So you shd go ahead applying t-test/ANOVA without worrying about the Normality of data.

Plz read this page:

https://books.google.co.in/books?id=AlNdBAAAQBAJ&pg=PA444&lpg=PA444&dq=donaldson+1968+on+normality&source=bl&ots=mWfgIp9CU3&sig=ItwTdB1TUx5-FZ7ZYZw_x051gkU&hl=en&sa=X&ved=0ahUKEwjK6afs8pXMAhWMi5QKHeCYBbQQ6AEIHjAA#v=onepage&q=donaldson%201968%20on%20normality&f=false

Best wishes

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[sagar gaikwad]

Respected sir,

I have read this thread before and tried to search for the article but couldn't find it. 

It is only related to anova, can we perform correlation & regression analysis if data is not normally distributed. If yes then which type of correlation and regression is applicable?

Thanks & Regards,

Mr. Sagar Gaikwad

Assistant Professor,

Vidyalankar School of Information Technology

Mob No: 9833376766

Online Profile: https://vsit.edu.in/faculty_sagar_gaikwad.html

ORCID ID : 0000-0002-3816-2801

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[Neeraj Kaushik]

Dear Sagar

You are correct. The work of Donaldson (1968) provides that ANOVA is robust for the violation of the assumption fo normality. While computing Correlation and regression, just ensure that 

(a) The variables under study are measured on ratio measurement (Not on Binary questions, MCQ, Ranking or Scale questions)

(b) There are no outliers in your work (Use Analyze-> Descriptive statistics-Explore in SPSS or refer https://www.youtube.com/watch?v=oJ3dJNkkBBY&list=PLzUJUtTJcj8TGQXfdrHsXE0tOlxThbCUy&index=6&t=1s)

If there are too many outliers in your work and you're not able to get rid of them then you shd collect more data.

Best wishes

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[sagar gaikwad]

Respected sir,

Thank you so much for the kind reply. 

If the variable is measured on reflective scale then cumulative score is used which means we convert scale variable to ratio  data now in this variable there can be an outlier or not.  

Thanks & Regards,

Mr. Sagar Gaikwad

Assistant Professor & Ph. D Coordinator

Vidyalankar School of Information Technology

Mob No: 9833376766

Online Profile: https://vsit.edu.in/faculty_sagar_gaikwad.html

ORCID ID : 0000-0002-3816-2801

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[Neeraj Kaushik]

Dear Sagar

Normality is never present in the Likert scale statements.

We shall discuss the why part whenever we'll meet in any workshop.

Measurements can be converted back like Ratio measurement can be converted to Nominal or Ordinal bu the reverse is not possible. Interval measurement can not be converted to Ratio.

Best wishes

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[sagar gaikwad]

Respected sir,

Thank you so much for your kind reply. 

Thanks & Regards,

Mr. Sagar Gaikwad

Assistant Professor & Ph. D Coordinator

Vidyalankar School of Information Technology

Mob No: 9833376766

Online Profile: https://vsit.edu.in/faculty_sagar_gaikwad.html

ORCID ID : 0000-0002-3816-2801

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[Sukhmani Singh]

Dear Neeraj Sir and Mr. Sagar,

Thank you for this discussion. Actually, I also faced similar kind of confusion some months ago when I read a paper in which it was mentioned that Dependent variable was non-normal and still the researcher went ahead with Regression, t-test and ANOVA. You can check the Paper here.

Neeraj sir, kindly share your guidance on the following three points as per your convenience:

1. Though ANOVA is robust to non-normality (Donaldson-1968, as mentioned in Andy Field, 2020) but there is one more condition …that ANOVA can be robust to the violations of normality and homogeneity of variance, if “Sample sizes are equal across all conditions.” 

Sir, should we give importance to this aspect also?…I am asking particularly with reference to this Paper in which samples sizes across all groups were not equal still they went ahead with ANOVA?

2. Secondly, Is it necessary that in Linear Regression, Dependent variable (cumulative score of likert statements) should be normally-distributed?

I am aware that assumptions of regression require- homoscedasticity (residuals should have same variance) and normally-distributed errors (residuals in the model should be normally-distributed) but I am not sure that whether regression requires normally-distributed DV also or not?

3. Lastly, in general, if t-test and ANOVA are robust enough to violate the assumption of normality then what the - Basic difference remains between Parametric and Non-Parametric tests?

Kindly guide sir.

Thankyou and Regards,

Dr. Sukhmani.

[Sukhmani Singh]

Dear Neeraj sir,

Good morning!

Your answer to any of the above mentioned 3 points will prove a great help in my learning. 

Thankyou and Regards.

Sukhmani.

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[sagar gaikwad]

Respected Neeraj sir and group members,

Thank you so much for your input on my query. 

After a little more research I came to know the following things if ratio data is not normally distributed.

1. Non-parametric tests can be used.

2. T test and Anova can also be used as both are robust tests.

3. Spearman Rank (Rho) correlation can be used if  ratio data is not normally distributed.

4. Non-linear regression  can be used if  ratio data is not normally distributed.

Please correct me if I am wrong. 

Thanks & Regards,

Mr. Sagar Gaikwad

Assistant Professor & Ph. D Coordinator

Vidyalankar School of Information Technology

Mob No: 9833376766

Online Profile: https://vsit.edu.in/faculty_sagar_gaikwad.html

ORCID ID : 0000-0002-3816-2801

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[Neeraj Kaushik]

First 3 are correct

I've not heard of Non-linear Regression

Moreover, there is no assumption of normality of DV or IDV in regression, its the residuals which shd be normally distributed.

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[sagar gaikwad]

Respected sir,

Thank you so much for your insights on my query. 

Thanks & Regards,

Mr. Sagar Gaikwad

Assistant Professor & Ph. D Coordinator

Vidyalankar School of Information Technology

Mob No: 9833376766

Online Profile: https://vsit.edu.in/faculty_sagar_gaikwad.html

ORCID ID : 0000-0002-3816-2801

To view this discussion on the web visit https://groups.google.com/d/msgid/dataanalysistraining/CAAd%3Dc8PyXMGO66PsxCCztNYXW1hmdidwJK0HTS31_Bx4-9_FoQ%40mail.gmail.com.