Question

A researcher is testing 4 different blood coagulation drugs. The drugs are labeled A,B,C and D. He is interested in how the drugs affect the blood coagulation rates of mice. The coagulation rate is the time in seconds that it takes for a cut to stop bleeding. He has 16 mice available for the experiment, so he will use 4 on each drug, randomized.

A	B	C	D
62	63	68	56
60	67	66	62
63	71	71	60
59	64		61
64

a. Perform CRD (completely randomized design) manually. You need to write the STEPS clearly.

Answer 1

Let y_ij be the jth observation of the ith drug ; i = a,b,c,d

Null Hypothesis

Alternative Hypothesis H!: Atleast two means are different.

Grand Total (G)

Raw Sum of Square (RSS)

Correction Factor (C.F.)

Total Sum of Square (TSS) = RSS - CF = 64907-64643.0625 = 263.9375

Between (drugs ) Sum of Squares

Within (drugs) sum of Squares = TSS - Between SS = 263.9375 -174.5708 =89.3667

Degrees of freedom

For TSS = N-1= 15

For Between Drugs SS = k-1= 4-1= 3

For ESS = 15-3 =12

ANOVA TABLE

Source of variation	df	SS	MSS	F ratio
Between Drugs	3	174.5708	174.5708/3 =58.1903	58.1903/7.4472 =7.814
Within Drug (Error)	12	89.3667	89.3667/12 =7.4472
Total	15	263.9375

The Critical value of F for 3,12 df , at 5% significance level is 3.490

Since calculated F is gretare than tabulated F, Reject H0.

Hence, we reject H0 at 5% significance level and conclude that the drugs differ significantly.