Report a formal conclusion for the information beow includin

Report a formal conclusion for the information beow including the results of all tests.

Is there a significant relationship between the three variables?

SS(T) = 40.92

SS(BT)= 37.42

SS(A) = 6.76

SS(B)= 30.16

SS(AxB)=0.50

SS(W)=3.5

df(BT)=5

df(A)=1

df(B)=2

df(AxB)=2

df(W)=6

df(T)=11

MS(A)=6.76

MS(B)=15.08

MS(AxB)=0.25

MS(W)=0.58

F(A)= 11.66

F(B)= 25.86

F(AxB)=0.43

Solution

there are two variables. A,B

taking level of significance as 0.05

##at first we test whether A has any effect or not.

null hypothesis : A dos not have any effect    alternative: A has effect

the test statistic is F(A)=MS(A)/MS(W) which under null hypothesis follows an F distribution with dfs

df(A)=1 and df(W)=6

null hypothesis is rejected iff F(A)>F_0.05,1,6       where F_0.05,1,6 is the upper 0.05 point of an F distribution with dfs

df(A)=1 and df(W)=6.

now F(A)=11.66 > F_0.05,1,6=5.987378

hence the null hypothesis is rejected and the conclusion is that A has effect.

##now we test whether B has any effect or not.

null hypothesis : B dos not have any effect    alternative: B has effect

the test statistic is F(B)=MS(B)/MS(W) which under null hypothesis follows an F distribution with dfs

df(B)=2 and df(W)=6

null hypothesis is rejected iff F(B)>F_0.05,2,6       where F_0.05,2,6 is the upper 0.05 point of an F distribution with dfs

df(B)=2 and df(W)=6.

now F(A)=25.86 > F_0.05,2,6=5.143253

hence the null hypothesis is rejected and the conclusion is that B has effect.

##now we test for the interaction effect between A and B

null hypothesis : interaction effect between A and B is absent    alternative: interaction effect is present

the test statistic is F(AxB)=MS(AxB)/MS(W) which under null hypothesis follows an F distribution with dfs

df(AxB)=2 and df(W)=6

null hypothesis is rejected iff F(AxB)>F_0.05,2,6       where F_0.05,2,6 is the upper 0.05 point of an F distribution with dfs

df(AxB)=2 and df(W)=6.

now F(AxB)=0.43 < F_0.05,2,6=5.143253

hence the null hypothesis is rejected and the conclusion is that A and B dont have interaction effect.

hence there is significant relation between A and B as there is no interaction effect is present between them