Question

II. An experiment to ascertain the effect of chocolate on cardiovascular health was performed using three different "types" of chocolate: (1) 100 gm. Dark Chocolate (DC); (2) 100 gm. Dark Chocolate with 200 ml. full fat chocolate milk (DC+MK) and (3) 100gm. Milk Chocolate (MC). The chocolate Factors were given on separate days with an assay for antioxidant level measured one hour after ingestion. The data was presented in the following table: TABLE 3.12 Levels <One Hour Follow ing Chocolute Consuemption Subjects (Observatlons Factor DC.MK ite.4 101.1 102 7 y7,1 HS.., УХ.9 100.0 w.sing.uawic4.s ,s SMC What is an appropriate analysis? Experiment with the analysis, if needed. Show your conclusions. The data is in file Chocolate.xlsx on Canvas. Use two tests at least one is nonparametric. If there is a difference in the types of chocolate, which are similar? Different? (30)

Answer 1

We can use parametric test (ANOVA) where our Null Hypothesis: there is no difference between the means

Alternate Hypothesis: at least one pair of mean is different

When we compute we get the following results:

Source of Variation	SS	df	MS	F	P-value
Between Groups	1952.644	2	976.3219	93.5756	2.52E-14
Within Groups	344.3058	33	10.43351
Total	2296.95	35

  So the p-value is `~ 0

thus we reject the null hypothesis and say there is at least one pair of mean which is different

Also computed Kruskal-Wallis Test, which is a non parametric one with the same hypothesis above,

Since it is observed that $\chi ^{2}$ = 23.568 > $\chi ^{2}$ = 5.991, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p ~ 0, and since p <0.05, it is concluded that the null hypothesis is rejected.

Now we compute t-statistics for all pairs:

	P value
DC & MK	3.82E-10	Different
DC & ( DC + MK)	5.7E-10	Different
(DC + MK) & DC	0.41915	Same

So only the (DC + MK ) and DC has same effect and the rest two are different