multiple criteria

[deadbanana]

Hi all,
I am dilettanet in statistics But I need to analyze some lab data.
I am wondering if there is a method for comparing multiple criteria as a whole? For example, say I have 2 products, product A and product B. And I want to know if their composition is identical. Say they are composed of sugar, butter, and cocoa. I measure the following:

A
sugar 70, 80, 72%...avg=74%
butter 20, 25, 10 %..avg=18.3%
cocoa 10, 5, 18%....avg=11%

B
sugar 65, 90, 70%...avg=75%
butter 30, 5, 15 %..avg=16.7%
cocoa 5, 5, 15%....avg=8.3%

Now I want to know if the compositions of A and B are different.
Do I need to test each of the components separately using a t-test, say test hypothesis if sugar content in A is different from B etc, or is there a way to test the composition collectivelly?
I guess I have to test each component separately but I want to be sure.....Thanks.

[vinux]

You can do 'Test of homogeneity' . It is a chi-square test. It is similar to test of independence.

Regards
Vinux

[dmmarathe]

You will have to do test for equality of means for all 3 components as a sure way.

[jamesmartinn]

A 3 x 3 Between Subjects ANOVA.

[deadbanana]

Thanks!
I think I'll look into the chi-square test of homogeneity. That looks promising.
Sorry I don't know what does it mean to do "3x3 between subject ANOVA". I googled but haven't found anything useful yet.
If all fails, I know how to test the equality of means for individual categories
db

[jamesmartinn]

The 3 x 3 Between Subjects ANOVA will test the overall equality of means for your different conditions and let you know if there are significant differences between some of your pairs.

If you were to do multiple T-Tests for each comparison, you would greatly inflate the chance of a Type I error. The ANOVA can do the samething, but will not increase the chances of a Type I error. In a sense, the T-Test is a special case of the ANOVA, where you only have k = 2 groups.



The 3 x 3 Notation simultanouesly informs you how many factors and how many levels of each factor. You have two factors, that have 3 conditions each:

A(sugar, butter, coca) => 1 factor, with three levels
B(sugar, butter coca) ==> 1 factor, with three levels

Taken together, 3x3 = 2 factors, the first having 3 levels, and the second having also 3 levels.


Perhaps you should use 'factorial anova' as your search query for further reading. Hope this helps.

[deadbanana]

I thought one would use ANOVA when you want to compare means of multiple things, like say I determine 5x how much suger there in green icecream, 5x in red icecream and 5x in blue icecream. I would calculate mean + SD and then test if the means are equal after doing F-test to make sure the variations are the same. If I would only have 2 icecreams, I would use t-test. If I want to compare all 3 together, I would use anova, right? That's what I remember from stat classes...but maybe I am wrong.
But now the difference is that I am looking not only on sugar but many other characteristics, and I didn't know ANOVA can deal with multiple criteria.

The example I gave was just an example. In fact I am looking at chemical composition of subjects let's call them A and B, and I have 14 compounds.
So according to your scheme,
A(c1,c2,....c14)
B(c1,c2,....c14),
and I have 4 experiments.
c1..14 are expressed as % of total.
I averaged the experiments, and claculated SD for each ci.
OK, now I don't really know how to do ANOVA on these. Do you have any suggestions about how to organize the data and do it in excel (is it possible?)?
My data looks like this:

              A                          B
         avg     SD                 avg    SD
c1       
c2
c3
.
.
c14

[deadbanana]

...concerning the chi square homogeneity test: I guess I would organize my data like this and run the test on them and that the output would be P that the ratio between the individual components in A and B are the same.

        sugar          butter       cocoa
A       74                18            11

B       75                17             8

....but in this case the information about the variation of each of the measurements gets lost..? if say sugar in A iwould be 60+-30 and in B 80+-10 and I would ignore the +- part, it may lead to wrong results, no?
Does this test require that the variations are comparable or is there a way to correct for that?