Three kinds of sleeping pills do the trial against white mice. Recorded the time in seconds from start until the mice given the drug slept. Prove whether the effects are the same for three types of drugs Drug 1 Drug 2 Drug 3 47 55 54 53 58 50 49 54 51 50 61 51 46 62 49

Given Data :

Calculating Sum of Squares :

$$\sum_{i,j} X_{ij} = {245} + {290} + {255} = 790$$ 

$$\sum_{i,j} X_{ij}^2 = {12035} + {16870} + {13019} = 41924$$

Total sum of squares=$$SS_{total} = \sum_{i,j} X_{ij}^2 - \frac{1}{N} \left(\sum_{i,j} X_{ij}\right)^2 = 41924 - \frac{ 790^2}{ 15} = 317.333$$

Within sum of squares =  $$SS_{within} = \sum SS_{within groups} = {30} + {50} + {14} = 94$$ 

Between sum of squares =  $$SS_{between} = SS_{total} - SS_{within} = 317.333 - 94 = 223.333$$

Total sample size = $N = 15$

Total degrees of freedom = $$df_{total} = 15 - 1 = 14$$ 

Groups = k = 3

Between-groups degrees of freedom = $df_{between} = 3 - 1 = 2$ 

Within-groups degrees of freedom = $$df_{within} = df_{total} - df_{between} = 14 - 2 = 12$$ 

Calculating the mean sum of squares :

$$MS_{between} = \frac{SS_{between}}{df_{between}} = \frac{ 223.333}{ 2} = 111.667$$

$$MS_{within} = \frac{SS_{within}}{df_{within}} = \frac{ 94}{ 12} = 7.833$$