A new treatment meant to help those with chronic arthritis pain was developed an

Question

A new treatment meant to help those with chronic arthritis pain was developed and tested for its long-tern effectiveness. Participants in the experiment rated their level of pain on a 0 (no pain) to 9 (extreme pain) scale at three-month intervals. Participant Before 3 mo 6 mo 9 mo 6 3 6 4 4 4 a. Compute the F value for the above ANOVA analysis - (Express your answer in 2 decimal digits) (b) Compute the F critical value for the above ANOVA analysis Express your answer with two decimal digits (C) Was the treatment effective? .05.

Explanation / Answer

Before=8 6 7 5, X1=6.5

3 mo=7 5 6 5, X2=5.75

6 mo=6 5 6 4, X3=5.25

9 mo=6 4 5 4, X4=4.75

X=5.5625, n=16, c=4

SSA=4(6.5-5.5625)2+4(5.75-5.5625)2+4(5.25-5.5625)2+4(4.75-5.5625)2=6.6875

SSW=(8-6.5)2………(4-4.75)2=13.25

MSA=6.6875/ (4-1) =2.229

MSW=13.25/ (16-4) =1.104

FSTAT=2.229/1.104=2.0188 and FCRIT is 3.49

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Before 4 26 6.5 1.666666667 3 mo 4 23 5.75 0.916666667 6 mo 4 21 5.25 0.916666667 9 mo 4 19 4.75 0.916666667 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 6.6875 3 2.229166667 2.018867925 0.165053233 3.490294819 Within Groups 13.25 12 1.104166667 Total 19.9375 15 Since FSTAT is < FCRIT and hence it does not lie in the rejection region and hence, we should not reject the null hypothesis

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