Beyond ANOVA

[Neeraj Kaushik]

Dear Friends

Few days back Radha observed that ours groups has become a query handling group now and there's no knowledge sharing.
I promised her that I shall write something.

In most of my workshops on Hypothesis testing I've discussed with participants the basics of hypothesis testing and given a methodology which says:

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Step (1) Decide which are the dep & indpe var

Step (2) Look for the measurement of dep & indep var
Here we make a 2x2 table
If both dep & indep var are metric, Use Regression
If dep var is non0metric & indep is metric Use Logit regression/Discriminant analysis
If both dep & indep var are non-metric, Use Cross tab & Chi sq test
If dep var is metric & indep is non-metric, Go to the next step

Step (3) Here we can use Parametric tests or Non Parametric tests. So check whether dep var is normally distributed by 1 sample KS test.
If data is normally distributed we can use Parametric test (t,z or F) else Non Parametric tests (U, WMP or H).

Step (4) See how many categories are there for indep var?
If 2 categories then we can use t/z test (in case of Parametric tests) or U/H tests ((in case of Non Parametric tests)
Also see whether the case is of
(a) One sample test (b) Two indep sample test (c) Paired sample test
In (a) we will use One sample t-test (No alternative for it in Non parametric tests)
In (b) we will use Two indep sample t-test (Its alternative is U-test)
In (c) we will use Two related sample t-test (Its alternative is Wilcoxin Matched Pair i.e. WMP-test)

If there're more than 2 categories then we can use ANOVA (F-test) (if parametric) or H-test (if non-parametric)

Step (5) Whatever test we'll apply, the decision rule is
If p-value (as given by MS Excel) or Sig value (as given in SPSS) is less than 0.05 then the various categories differ in terms of mean score of dep var.
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Now this is what we've done many times but when we look for the real life cases, they go beyound 1 dep & 1 indep var.
In actual work there may be >1 dep or indep var. Here comes the elders of ANOVA like n-way ANOVA, ANCOVA, MANOVA etc.

We shall discuss them one by one but before that look for the cases when they'll be applied.

First look for the cases when there's only 1 dep var and many indep var
Now recall the assumptions of Regression analysis: One dep var & all dep var shd be ratio type. Normality of the dep var is not reqd.
So when there's many indep var & all are metric type, we can use the Multiple regression.
But before applying regression, just remember some statutory warnings:
1. Multiple regression is always the Linear Multiple regression and in real life the relationship of the variables may not be linear. So scatter plot is a gud method to understand the inherent relationships between the various var. In MS Excel, we can plot just a 2-D graph or scatter plot. We can use SPSS/Statistica for 3-D plots.
2. Dnt forget to address issues like outlier and multi collinearity before starting regression.
3. Try to judge the output by reading the residual plots to be extra sure about ur outputs.

Now the questions comes: It might be possible that some indep var are linearly associated with dep var while others are non-linearly associated. Now what to do? Here comes Neural network which identifies inherent relationships between variables & analyse them.

In next posy I shall discuss the nuances of ANCOVA & n-way ANOVA.

Happy learning
Neeraj

[Rekha Mishra]

Thank you for the lucid explanation Sir!.

Regards,

Rekha

--

Thanks,

Best regards,
Rekha Mishra.

[Radha garg]

Thanks sir......for catering my request so quickly.

It's really nice to upgrade our knowledge with some new test.

Regards

Radha

[Amit Manglani]

Just great sir !!

To inform you, I have for the very first time heard about U, WMP and H Test.....

I am so novice in this field !!

--
Regards,


Amit Manglani
Assistant Professor
Department of Commerce,
School of Management and Commerce,
Guru Ghasidas Vishwavidyalaya (GGV) [A Central University]
Koni, Bilaspur
Chhattisgarh - 495 009
India

University website: www.ggu.ac.in 
E-mail: amit.m...@gmail.com
_____________________________________________________________________

"In every trade there is an idiot and if you don't know who it is, it is YOU."

- Meir Statman, Professor of Finance, Santa Clara University

[Preeti Jain]

lot of thanks sir 4 sharing such valuable knowlege.................waiting 4 ur next post ANCOA and MANOVA.....

--
Preeti Jain

[Neeraj Kaushik]

Dear Amit

I'm happy to learn that you dnt know anything about these Non parametric tests. This wud help in keeping check on 'Whether whatever I'm writing is making any sense or not?'
Actually not many people on this group express their opinion, they read the posts (I even doubt it!!) passively. So I request you to be dead honest and raise queries if anything is not clear.

My intentions are to explain the basics in simple language, detailed theory is already available on many sites/books. So even if you're not working on it now, plz try to understand the context and the examples.

Looking frwd for ur comments.

Thanks & Regards
Neeraj

[Radha garg]

Respected Sir,

 

How to deal with the problem of multi-collinearity in multiple regression in SPSS here.

For example if there is one dependent variable and three Independent variable and all are metric.

Now if we want to see the relationship between one dep variable with two Indep variable but third indep variable have the high correlation with both dep and indep variable. Then how we can nullify its effect and predict the equation.

 

And if there is two or more dependent variable then how we can do it in SPSS. 

 

Thanks & Regards

Radha 

 

On Saturday, December 15, 2012 11:29:11 AM UTC+5:30, Dr Neeraj Kaushik wrote: