Question

What is the p value for the dataset below? determine whether a significant difference exists among groups A, B, and C? Use the format 0.999.

Chemical A	Chemical B	Chemical C
112	121	84
103	125	96
98	98	105
122	100	89
130	95	102
107	122	98
105	121	105
120	115	89
100	128	100
124	130	90

1. Referring to the results from your analysis of chemicals A, B, and C; which pair of groups had the greatest difference in their mean values?

   A		A-B
   B		A-C
   C		B-C
   D		Differences in the means between each group were all about equal

Answer 1

First, the ANOVA will be used to see if the means of three groups are equal.

H0: The mean of three chemicals is same

H1: There is difference in the mean of at least two chemicals

Following are the results for the same:

	Chemical1	Chemical2	Chemical3	Total
N	10	10	10	30
∑X	1121	1155	958	3234
Mean	112.1	115.5	95.8	107.8
∑X2	126791	134929	92272	353992
Std.Dev.	11.1898	13.0235	7.4207	13.6038

Source	SS	df	MS	F-val
Between-treatments	2217.8	2	1108.9	9.50788
Within-treatments	3149	27	116.6296
Total	5366.8	29

The p-value is .000748. The result is significant at p < 0.05. So we can conclude that there is difference between the mean of at least two chemicals.

To compare the means we will use Tukey's HSD Test: Test statistics is as follows

  

where Si,j is

Hi,j in the denominator is hormonic mean

treatments=k= Chemicals A, B & C= 3
degrees of freedom for the error term=27

Critical values of the Studentized Range Q statistic:

Qcritical α=0.05,k=3,df=27 = 3.5058

Treatments pair	Tukey HSD Q statistic	Tukey HSD p-value	Tukey HSD inferfence
A vs B	0.9956	0.7483732	insignificant
A vs C	4.7729	0.0061535	p<0.05
B vs C	5.7685	0.001014	p<0.05

From the table given we can say that, p-value for pair B&C is minimum.

So we can say that the difference is greatest between pairs B & C.