Beyond ANOVA (Part -3)

[Neeraj Kaushik]

Now lets start with the story of ANCOVA

At times when we have want to ascertain the effect of indep var on dep var (traditionally thinking of using ANOVA), there comes another var which influences the dep var (known as extraneous var). Now we shd minimize the effect of this extraneous var by somehow so that the true relationship between the dep & indep var can be computed.

So the technique used here is ANCOVA.

Assumptions of ANCOVA:
1. 1 dep var which is metric
2. 1 indep var which is categorical
(Both these are the assumptions of ANOCA too)

3. 1 indep var which is metric. Now this variable shd be correlated linearly to the dep var and we want to nullify its effect.
Other assumptions of ANOVA stands the same.

ANCOVA could be defined as a var that has a substantial correlation with the dep var & is included in the experiment to adjust the results for differences existing among subjects before the start of the experiment {Taken from SPSS for Windows Step by Step: George & Mallery}.

What we are doing conceptually is
We'll measure the effect of extraneous var (called co-variare here) and will nullify its effect by adjusting the mean value of dep var; so that now we can have the true relationship between the dep var & indep variables(s).

The inclusion of covariate or covariate(s) does not influence the cell means (i.e. the average mean scores of the various groups/indep var) in the initial output but it often has substantial influence (usually reduction) on the sum of squares (because the error term is reduced here) {Taken from SPSS for Windows Step by Step: George & Mallery}.

Lets understand it:
In ANOVA the total variations are believed to be the sum of chance variations & treatment variation but here one more var is present, which we believe is correlated with the dep var. So it must have a say in the overall variations.
But since we dnt want to measure its effect so we use this extraneous var as Co-variate. Now still the co-variate will explain some protion of the total variations.

So first we need some values which indicate how much every var (indep or co-variate) is contributing towards explaining the overall variations of dep var. This is something like r-square of regression.

This parameter is Eta squared value here which gives the proportion of varianve that is accounted by a particular var.

Rest of the things are like ANOVA. e.g. If sig value < 0.05 it means the Null hypothesis is rejected and the various categories of indep var are different. For checking the deatiled paired comparison we'll use Post hoc analysis.

We can see the plots too which gives a meaningful insight into the data.

So if the concept of ANCOVA is somewhat clear, then you may proceed by taking an example.

[Radha garg]

Thanks sir...... for make us understand this complicated concept in such a easy Language.

It make sense to me. So, please explain its example and also practical implication in SPSS.

Regards

Radha