A study has a 2(Target: Ingroup vs. Outgroup) x 2(Memory: Positive vs. Negative) between-subjects design. If an interaction is significant, the maximum number of possible simple effects are:

In a 2x2 between-subjects design, there are two independent variables, each with two levels. If an interaction is significant, it means that the effect of one independent variable depends on the level of the other independent variable.

The maximum number of possible simple effects is calculated by adding the number of levels of each independent variable and then subtracting the number of independent variables.

So, in this case, we have:

• 2 levels of the first independent variable (Target: Ingroup vs. Outgroup)
• 2 levels of the second independent variable (Memory: Positive vs. Negative)

Adding these together gives us 4. We then subtract the number of independent variables (2), which gives us a maximum of 2 possible simple effects.

However, it's important to note that each simple effect is a comparison of the means at one level of one independent variable, holding the other independent variable constant. So, in this case, we could have up to 4 simple effects:

1. The effect of Target (Ingroup vs. Outgroup) at the level of Positive Memory
2. The effect of Target (Ingroup vs. Outgroup) at the level of Negative Memory
3. The effect of Memory (Positive vs. Negative) at the level of Ingroup Target
4. The effect of Memory (Positive vs. Negative) at the level of Outgroup Target

So, depending on how you define "simple effects", the maximum number could be either 2 or 4.