Beyond ANOVA (Part 7.4 b) {Clearing the doubts)

[Neeraj Kaushik]

Now we confronted with the question that graphically there seems big differences between teachers A & D but why the same is not shown in analysis?
 
There's one more thing: Isn't the contrasts giving partial information?
So If you get as much annoyed as I'm then lets use the Post hoc for one time comparison between all 4 categories of teachers.
But here is a problem. Post hoc provides multiple comparisons between the Between subjects Factor only (ex. gender here)
So how to use Post hoc for rest of the factors? and which method of Post hoc to use?
Ans: We'll use Post hoc for teachers by Options menu (This is the same menu which we saw in MANOVA).

But, what is the difference between the Post hoc results obtained by Post Hoc Menu and by Options Menu?
Post hoc Menu is used for getting Post hoc on the basis of Between subject Factor while Options used for getting Post hoc in any variable.

Next question: Which methods (Equal variance method OR Not equal variance method) to be used?
Ans:  It still depends on the same Levene's test
Get Levene's test results from clicking on "Homogenity Tests" in Option Menu. But if we use it here, we'll get the warning (error) that since there're only 2 categories of Between subject Factor so this table will not be shown.
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Click on Options
On top, send teachers to 'Display Means for' pane.
Click on Compare main effects & from drop Menu choose method Bonferroni.

{Here we've 3 methods: LSD, Bonferroni & Sidak
Andy Field claims LSD to eb the weakest hence not preferred. Rest of the 2 are gud}
 
Click on Continue then OK
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In SPSS output directly come to the table of Paired Comparison.
The results are same. Teachers A & D differ significantly.
 
Now the question was that when mean differences between A & D is 11.5 why the Sig value > 0.05
Answer lies in the value of Std error 4.946
F-ratio is calculated by dividing mean differences by std error. Since std error is large here so F-value comes small as compared to first case (difference between 1 & 2).
So its not just the mean scores but the std dev as well as std error are also to be considered while analysing.
 
Here we learnt one more thing that Contrast gives only partial info so better to use Post hoc.
 
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Now another observation here is that while working on marks & teachers, in previous case/example we've concluded that no significant difference exists between teachers regarding their grading but with the same dataset now we're concluding that difference exists. 
One more thing to note is that in case (b) we've not considered the gender while evaluating the relation between teachers & marks. So results from case (a) & (b) shd be same. So why it is so???
 
Well, if in case (a) we wud have considered the 'Sphericity assumed' row then the conclusion of the both cases (a) & (b) would have been same.
We can crosscheck by taking Sphericity assumed {though we can't do it technically as assumption is violated here, but just for curosity we're checking it} and running Post hoc {By using Option Menu}, we'll get exactly the same results as in the case (b).
 
So basic difference comes from the Mauchly's test table.
Now lets explore the 2 tables of Mauchly's test.
 
When gender is not assumed, Mauchly's W value is 0.131 and subsequent Chi sq value is 11.628
Plz remember Chi sq test evaluates the differences between the observed & expected figures, hence higher the value of Chi sq, it indicates higher difference. and the resulting p-value will be reduced.
 
By including gender in our analysis, Mauchly's W value reduces to 0.096 and so do the Chi sq value 11.053. Hence p-value increases.
But I've no answer, as of now, why inclusion of gender reduced Mauchly's W value?
 
In this case, the value of sig is just on the border. Without gender it is 0.043 and after including gender Sig value become 0.055, hence the overall difference in analysis creeped in.
 
So what'll we do? 
We'll proceed as we've done it so far.
 
Conclusion: When gender is not considered in the analysis there does not seem the differences between the grades/marks given by teachers but when gender is considered the teachers A & B seems different. Though there was no significant impact of the gender*teacher interaction.
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Another confusion may be that the Multivariate Tests table (given in the start of output) in both cases suggests that teachers and marks are not related, so we've considered it in case (a) but not in case (b). Why??
 
Ans: Plz see this table is to be considered only when Sphericity assumption is violated, so we consulted it in case (a) biut not in case (b). Even if there's a conflict between this table and subsequent analysis, then we'll give more weightage to later tables. This table is just a supplementary table.
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Lastly we've used Gender in the plots only to have a graphical representation of entire data, there's no other purpose of inclusion of gender in plots .

 
Happy learning
Neeraj

[Radha garg]

Thanks for the all clarification sir.....

Now, we should proceeds with our next example.

Regards

Radha