Anova

[Nidhi Dhankhar]

I want to find the significant difference  among the three category of farmers ( small, medium , large) for two different district  for different parameters like net price receive by farmer, marketing cost, production  cost etc. So for that purpose I want to apply Anova 

But the problem is that the number of small, medium and large farmers are different in my sample ( small farmer for one district 77  and for other 65 , medium farmer 25 and 37 and the large farmers are 12 and 16 ) 

So how can I do the analysis.  Is anova  appropriate tool for this or I have to shift to another tool 

[Neeraj Kaushik]

Plz refer to https://www.youtube.com/watch?v=DtXS2DDi50Y&list=PLzUJUtTJcj8Sx5nIJuje36cvDol6A_AXr&index=8

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[uma gulati]

Dear Nidhi

there are two things to understand.

you can apply anova but with unequal sample size, it reduces the statistical power of the test. With equal sample size there is greater probability of detecting true differences.

best wishes

Dr Uma

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[Neeraj Kaushik]

Andy Field, in his masterpiece Discovering Statistics using SPSS (Ed 4) writes:

The power of F also appears to be relatively unaffected by non-normality (Donaldson, 1968). This evidence suggests that when group sizes are equal, the F-statistic can be quite robust to violations of normality. However, when group sizes are not equal, the accuracy of F is affected by skew, and non-normality also affects the power of F in quite unpredictable ways (Wilcox, 2012).

It means ANOVA is very robust for violations of normality, provided the category sizes of the IDV are the same or similar.

AND randomly selecting some cases from the larger category can be comfortably done using the Select Case option.

Best wishes

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[Kanwalpreet Kaur Puri]

Sir,

Then, when is the Welch test used? 

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[Neeraj Kaushik]

Dear KKP

Here  is the correct sequence:

Check the Levene test for testing the assumption of homogeneity of variance

If p (of the Levene test) >0.05 => Use One-way ANOVA

If p (the Levene test) <0.05 but the sample size of all categories of IDV is comparable/similar => Use One-way ANOVA

If p (the Levene test)<0.05  but the sample size of all categories of IDV is not comparable/dissimilar =>

Use the Select Case option to randomly select the sample from the larger categories and make category sizes comparable then Use One-way ANOVA

else use Welch test

Best wishes

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[Kanwalpreet Kaur Puri]

Thank you so much sir for the detailed explanation.

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