Writing Two-Ways

Case one, 2x2 with only main effects
The first example acting as if there was no interaction.

A 2 x 2 between-subjects ANOVA found a main effect of menu options such that hot items were rated spicier than mild items, F (1,16) = 90.00, p < .001, MSE = 0.50, a main effect of restaurant type such that food in a dive was rated spicier than the food in a fancy restaurant, F (1,16) = 10.00, p < .01, MSE = 0.50, and no interaction.  Figure 1 shows the mean spiciness ratings for each condition.

Since there are only main effects (no interaction), and since each IV only has two levels, you can mention the direction of the effect as part of the ANOVA.  Descriptive statistics can be given in paragraph, table, or graph.

Case two, 2x2 with an interaction
This is the first example that we have been investigating.

A 2 x 2 between-subjects ANOVA revealed a main effect of menu options such that hot items were rated as spicier than mild items, F (1,16) = 90.00, p < .001, MSE = 0.50, a main effect of restaurant type such that food in a dive was rated spicier than the food in a fancy restaurant, F (1,16) = 10.00, p < .01, MSE = 0.50, and a significant interaction, F (1,16) = 10.00, p < .01, MSE = 0.50.  Since there was no difference between restaurant types on ratings of mild menu items but there was a difference for hot items, the main effect of restaurant type appears to be an artifact of the interaction.  Figure 1 shows the mean spiciness ratings for each condition.

Since each IV only has two levels, you can mention the direction of the effect as part of the ANOVA.  Since there was an interaction, you need to describe how the effects of one IV depend of hte level of the other IV.  Descriptive statistics can be given in paragraph, table, or graph.

Case three, 3x2 with only main effects
This is like our example, acting as if we had no interaction.

A 3 x 2 between-subjects ANOVA found a main effect of menu options on spiciness ratings, F (2,30) = 16.875, p < .001, MSE = 1.60, a main effect of restaurant type on spiciness ratings, F (1,30) = 40.000, p < .001, MSE = 1.60, and no interaction.  Tukey HSD comparisons indicated that for menu options hot items were rated spicier than medium items, which were rated spicier than mild items (p < .05).  The food in dives was rated as spicier than the food in fancy restaurants.  Figure 1 shows the mean spiciness ratings for each condition.

Since one IV  has more than two levels, you can not mention the direction of the effects as part of the ANOVA.  Thus you report the main effects of the IV with 3 levels (menu options) from the outcome of a follow-up comparison (in this case Tukey's HSD).  Since one IV has just 2 levels, you give the direction there without reference to follow-ups since they were not needed.  Note that I followed the order laid done in the 3x2 statement.  The first IV is the one with 3 levels, thus it was first in the ANOVA statement, and first in the discussion of the direction of the effects.  Descriptive statistics can be given in paragraph, table, or graph.

Case four, 3x2 with an interaction

(1) A 3 x 2 between-subjects ANOVA found a main effect of menu options on spiciness rating, F (2,30) = 16.875, p < .001, MSE = 1.60, a main effect of restaurant type on spiciness ratings, F (1,30) = 40.000, p < .001, MSE = 1.60, and a significant interaction, F (2,30) = 4.375, p < .025, MSE = 1.60.  (2a) Tukey's pairwise comparisons for cell means showed that in the dive restaurant the mild menu option was rated less spicy than the medium or hot options (p < .05).  In the fancy restaurant there were no differences among the menu options.  (2b) In addition, for the mild menu option there was no effect of restaurant type but for both the medium and the hot options the food in dives was rated spicier than the food in fancy restaurants.  (3) Thus in the dive the differences among menu options was meaningful while in the fancy restaurant menu options had no effect, and the difference between the dive and the fancy restaurant was only apparent for medium and hot menu options .  (4) Figure 1 shows the means for each condition.

1.  ANOVA Statement
ME of IV1, ME of IV2, and Interaction
2.  Tukey follow-ups for simple effects
A. IV1
-- at level 1 of IV2
-- at level 2 of IV2
B. IV2
-- at level 1 of IV1
-- at level 2 of IV1
-- at level 3 of IV1
3.  Simple Summary explaining interaction (optional)
4.  Descriptive stats