Statistics: I am trying to do a Two-Way ANOVA on Minitab and Test for Interaction but I keep getting asterisks for my F and P Values.

Question

Help. I am doing a project and statistics and the basis is whether or not vaccination and region effect your chances of acquiring the flu. I did a Two-Way Anova Factorial design with the following Minitab Input and the results look normal. However, when I test for interaction, I keep getting asteriks instead of P or F values.

Minitab Input

Answer 1

Two factors: A and B, two replications per cell, 24 observations altogether. Fake data generated to have small B-effect, larger A-effect, no interaction effect. Command produced by menu in Minitab 17. All works as planned.

MTB > ANOVA Y = A + B + A*B.

ANOVA: Y versus A, B 

Factor  Type   Levels  Values
A       fixed       4  1, 2, 3, 4
B       fixed       3  1, 2, 3


Analysis of Variance for Y

Source  DF       SS      MS     F      P
A        3   42.227  14.076  4.15  0.031
B        2   21.391  10.696  3.16  0.079
A*B      6   19.061   3.177  0.94  0.503
Error   12   40.669   3.389
Total   23  123.349


S = 1.84095   R-Sq = 67.03%   R-Sq(adj) = 36.81%

My model: $Y_{ijk} = \mu + \alpha_i + \beta_j + \gamma_{ij} + e_{ijk},$ $i = 1,2,3,4$ levels of A, $j = 1,2,3$ levels of B, $k=1,2$ observations per cell, $e_{ijk}$ iid $\mathsf{Norm}(0, \sigma).$ I can have interaction term $\gamma_{ij}$ because it has different subscripts than error term $e_{ijk}.$

Correct model for your data: $Y_{ij} = \mu + \alpha_i + \beta_j + e_{ij},$ $i = 1,2,3,4,5$ States, $j = 1,2$ levels of Vacc, $e_{ij}$ iid $\mathsf{Norm}(0, \sigma).$ When you try to introduce interaction term $\gamma_{ij}$ it has same subscripts as error term. So interaction (if it exists) simply infates error variance, but is not distinguishable from error.