Beyond ANOVA (Part 7.4 b) {RMA Case-b}

[Neeraj Kaushik]

RMA Case (b): 1 measure with within group variations as well as between group (gender) variations

Working on previous file: repeat measure anova.sav
 
Background: Marks given by 4 teachers to 8 essays (4 from boys & 4 from girls). 
Here each essay was evaluated by 4 teachers and we want to see whether 
1> there's any difference between the 4 teachers 
2> there's any differences in gardes on the basis of gender?
 
Measure (Dep var): Marks
Within Sub Factor (Indep var): Teachers
No.of levels (How many teachers?): 4
Between subject Factor: Gender
 
Click on Analyze->General Linear Model->Repeated Measures
 
Within Sub Factor (Indep var): Teachers
No.of levels (How many teachers?): 4
Click on Add
 
Measure (Dep var): Marks
Click on Add
 
Click on Define
-----------------------
Send 'Teacher A' to 'Teacher D' to Right hand side pane
Send Gender to Between subject Factor
 
Click on OK
 
//Here we're looking for the within group as well as between group variations.
 
SPSS Output:
Table-4 Mauchly's test of sphericity indicates that assumptions of sphericity is tenable (maintained).
 
So in the next table Tests of Within subjects Effects we'll see the resultd from the row of Sphericity assumed. 
From the teachers row, we find significant difference between the teachers is present.
While teacher*gender intercation is not significant.
 
The next Table of contrast (Polynomial) does not give us any significant thing.
 
Then the Table of Between Subject effects repeats (what we already know) there's no influence of gender on marks i.e. both gender & marks are not connected.
-------------------------
Since teachers were found to be different so now we can use the other options of Plots, Contrast, Post hoc
 
Here contrast is always given (whether we ask for it or not).
Post hoc for gender will not be applicable as there's only 2 categories of males & females and for Post hoc we need min 3 categories.
 
So lets re-run the analysis
This time we'll click on some additional menus:
Click on Contrast
Change Contrast (from drop menu) to Repeated {Repeated contrast compares group 1st with 2nd, group 2nd with 3rd, group 3rd with 4th} and Click on Change
{We wont provide any Contrast between Gender for the 2 reasons: (1) There're only 2 categories & Post hoc needs min 3 categories (2) Gender is not significantly related with marks, as given by earlier analysis}
Click on Continue
 
Click on Plots
Send teacher to Horizontal axis
Send gender to Separate lines
Click on Add & then on continue
 
Click on Post hoc
We see only 1 option Gender here. 
We wont use Post hoc on Gender 
But note one important thing here: post hoc is possible only for Between Factor(s).
So Click on Cancel here.
 
Click on OK
----------------------
SPSS Output:
Table given in first analysis are same so lets move straight to 
Tests of Within subjects Contrasts. Now onwards we'll just discuss the Contrasts.
 
 
In the teacher's row, Sig value of Level1 & Level2 is 0.04 indicating a significant difference between the grades given by teacher A & B.
 
Look at the plot & it seems the difference shd be there in Teacher A & D. But the contrast we choose didn't give this info. So better to use the 'simple' contrast (which compares a particular category with the rest of all categories).
 
Re-run the analysis and choose Contrast to simple.
In SPSS output table` of Test of within subject Contrasts we see the sig value of Level 1 vs Level4 is 0.059 indicating these 2 categories does not differ.
 
By looking at the plots, the obvious question is why there's no difference between the Teacher A & D while their plots are so different? 
 
Answer in next post..........
 
Happy Learning
Neeraj

[Radha garg]

Respected Sir,

Here i want to ask three question.

1. Why the grades given by teachers is become significant here after the inclusion of gender yet gender is found insignificant with teacher.

Like in previous example, there was no significant result was found between the marks given by the teachers.

So, why it so here..

2.Suppose the variable entered in  between subject factor have three categories, then in post hoc test which test will be considered for analyzing the difference the categories as there is no such assumption of homogeneity of variance.

So, shall be considered the Sphericity test for equality of variance or some other criteria will be used for the same.

3. why we use the gender option in the plots as we already found that there is no significant relation between gender and teachers.

And the last question is already asked by you which we will be found in next post.

So, i will wait for that.

Thanks and Regards

Radha

[VARUN ARORA]

The answer to these questions are as follows:
1. Within same gender there is diversity in granting grades among the teachers, which is neutralized when gender is set aside, however, there is no bias in granting grades based on gender by the same teacher.
2. Post-hoc tests show assessment on one-to-one basis i.e. post-hoc tests provide results of a univariate assessment. This is just like responding to the question based on the result that among teachers there is significant difference in granting grades - then whether for males there is a significant difference in grades granted by teacher A and B, teacher A and C, teacher A and D, teacher B and C, teacher B and D and teacher C and D, i.e. while ANOVA gives generalized results, post-hoc tests try to actually point out where exactly these differences exist. In plain terms - every multivariate analysis ends up in a univariate assessment and every univariate assessment should be looked up for its multivariate impact. RMA ANOVA followed by post-hoc tests gives the opportunity to do this.

3. When we say gender has no impact in a multivariate assessment, then it does not mean that it has no impact at all. In a multivariate assessment we measure both independent as well as interactive impact of a variable.A variable might not have an independent impact but might be acting as a regressor or aggressor for some other variable.

Hope the above will explain the problem to some extent.

VARUN

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[Neeraj Kaushik]

Nice explanation Sir !!

[Radha garg]

Respected Sir,

Thanks for clearing my doubt here.

Regards

Radha

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