IAI q14 nov 10

Hi
how to find the paratmers SSb , SST in this case?
Rajeev compared protein intake among three groups of women:
- women eating a standard India diet (STD)
- women eating a lacto-vegetarian diet (LAC) and
- women eating a strict vegetarian diet (VEG)
The mean and standard deviation of protein intake as well as the group sizes are presented in
the table below.
Group Mean Standard Deviation Number of women in group

STD 75 9 10
LAC 57 13 10
VEG 47 17 6
Is there any alternate formula to calculate SSt becuase here individual numbers are not given. In the formula for SST given in table , this corresponds to yij. Without that how to solve?

 

But why do you want to calculate SST? The data given is sufficient to calculate SSB and SSR, which are the two quantities required for ANOVA-test.

And if for some reason you want to find SST, then you can always use this equality..

SST = SSB + SSR

 

I generally calcualte SSB and then SST and the formula in the actuarial table says that
SST-SSB=SSR so it is SST first then SSR. But which formula to use for calculating SSR alone.
May be I need to cram this one from the book. I always thought that anova and regression's formulaes are there in the actuarial table and no need of memorizing any more

 

Cramming is not a good idea. It's better to have a good understanding of these formulas.

For ANOVA the test statistic is

F = Variance between samples / Variance within samples

Numerator is just "SSB / (k - 1)" &
Denominator is "SSR / (n - k)"

Numerator is always easy to calculate. Denominator is just the weighted average of sample variances i.e.

SUM [ (ni - 1) * si^2 / (n - k) ]

In this particular question we are given means and SDs for all samples instead of individual sample values. So SSR was easier to calculate than SST

Hope this clears your doubt.

 

Thanks this is almost new for me. Of all the questions in acted material, I think it is first we calculate SST , sSB and then from that SSR.
SSR=summation (Yij-Yibar)^2
I couldn't find that SSR is nothing but weighted sample variance. Can u pls point out in the acted material text?

 

Not SSR, but SSR / (n - k) is the weighted average of sample variances.
SSR is equal to what you've mentioned.

And if you multiply and divide this by "ni - 1", you'll get same result which I've mentioned excluding the denominator "n - k"

SUM [ (ni - 1) * si^2 ]

I can't see this written anywhere in the study material. This is something you can make a note of.

 

I confess I would have calculated the sums from the means and the sum of squares from the standard deviations and then stuck those in the SST and SSB formulae...

 

Thanks suraj and bobbathejobba

 

It's worth looking at Q9 of IAI Nov 2012 paper.
It is easier to adopt a similar approach for this one as well.

 

Thanks bapan for pointing out!!