This problem is to help conceptualize what an interaction effect looks like without any main effects.

The data is presented in parallel format.  Before entering into SPSS, you will need to put it into serial (column) format.  You will need to create a categorical variable for the first factor (days) and for the second factor (time of day).

The data presented shows exam scores for students randomly assigned to the sections meeting on these days at these times of the day:

Thursday		Friday
Morning	Afternoon	Morning	Afternoon
50.2 52.3 44.1 20.5 51.9 33.1 20.6 44.5 49.9 -6.5	-6.9 33.1 54.6 54.6 66.3 52.2 66.2 39.1 33.7 52.6	43.3 51.2 51.1 43.2 64.7 51 63.9 50.9 -7 32.4	46.6 28.5 46 28 37.2 45.9 40.6 -6.7 39.9 37.2

Conduct a 2-way fixed-effects ANOVA.  Have SPSS generate the descriptive statistics and a means plot.  For the means plot, select the Plots... option and select one of the categorical variables for Horizontal Axis: and the other categorical variable for Separate Lines:.  (Note:  You must click Add before you click Continue.)

First, find the group means for each level of the factors.  (Report answers accurate to 2 decimal places.)
Days:
    $\displaystyle {M}_{{\text{Thursday}}}=$
    $\displaystyle {M}_{{\text{Friday}}}=$
Time of day:
    $\displaystyle {M}_{{\text{morning}}}=$
    $\displaystyle {M}_{{\text{afternoon}}}=$

Question for reflection:  Based on the difference between the numbers, does there appear to be a difference in the means for the days or the difference in the means for the times of day?

Report the results of the ANOVA for the main & interaction effects.  (Report P-values accurate to 4 decimal places and F-ratios accurate to 3 decimal places.)
Day:
    $\displaystyle {F}_{{A}}=$
    $\displaystyle {p}=$
Time of day:
    $\displaystyle {F}_{{B}}=$
    $\displaystyle {p}=$
Interaction:
    $\displaystyle {F}_{{{A}\times{B}}}=$
    $\displaystyle {p}=$

Thoughts to consider:  First, notice which effects are significant and which are not?  Does this agree with what you observed above for the differences between the means?  What is the physical interpretation for non-significant main effects?  Look at the means plot generated by SPSS.  What is the interpretation of an interaction effect?