Weeks 17 and 18 Flashcards
The following ANOVA table is for a 1-way design with k = 3 treatment groups and n = 18 participants per treatment. Some values have been removed from the table. Restore the missing values for df.
Source SS df MS F
Between 112
Within
Total 214
Between df = 2
Within df = 51
Total df = 53
The following ANOVA table is for a 1-way design with k = 3 treatment groups and n = 18 participants per treatment. Some values have been removed from the table. Restore the missing values for SS.
Source SS df MS F
Between 112
Within
Total 214
SS Within 102
The following ANOVA table is for a 1-way design with k = 3 treatment groups and n = 18 participants per treatment. Some values have been removed from the table. Restore the missing values for MS, and F.
Source SS df MS F
Between 112
Within
Total 214
MS between = 56
MS within = 2
F = 28
2) The following ANOVA table is for a 1-way design with k treatment groups and N = 80 participants overall. Some values have been removed from the table. Restore the missing values for df.
Source SS df MS F
Between 1 1
Within 600
Total
df between = 1
df within = 78
df total = 79
2) The following ANOVA table is for a 1-way design with k treatment groups and N = 80 participants overall. Some values have been removed from the table. Restore the missing values.
Source SS df MS F
Between 1 1
Within 600
Total
MS between = 600
SS between = 600
SS within = 46,800
SS total = 47,400
In a 2-way ANOVA, both of the independent variables should be nominal in nature.
a) True
b) False
a) True
Explanation … In a 2-way ANOVA there are 2 nominal independent variables with no sense of order or interval. Each treatment group in this sort of design is characterized by the simultaneous presence of some level of each variable. The thing that separates a 1-way ANOVA from a 2-way ANOVA is that in a 1-way ANOVA, each experimental group is thought of as exposed to some level of a single treatment whereas in a 2-way ANOVA, each group is simultaneously exposed to 2 different treatments.
In a 2-way design, if there are no simple effects of either treatment, then there must also be NO main effects.
a) True
b) False
a) True
Explanation … The best way to think about this is using interaction plots. Imagine an interaction plot of the results from, for instance, a 2 3 design where there are no simple effects anywhere. The only way to have no simple effects is to have all cell means be the same. The interaction plot would therefore appear as below (where some means have been slightly offset so you can see them).
You can see from this that not only are there no simple effect, but there are no main effects either.
In a 2-way design, if there are no main effects then there must also be no simple effects.
a) True
b) False
Explanation … Main effects may be masked by interactions. Thus, if no main effects are apparent in the results of an experiment it may be because they are hidden by an interaction. If this is the case then we would then look at the simple effects in order to see what is really happening. In the example shown below, a complete crossover interaction has eliminated all main effects (i.e., all marginal means have the same value) but there are substantial simple effects of the treatments. This is a counterexample to the situation outlined in the question so the statement contained in the question must be false.
If the lines in an interaction plot do not cross, then no interaction is present.
a) True
b) False
b) False
Explanation … One way of recognizing an interaction is to note that the lines in an interaction plot are not parallel. Since the lines can be nonparallel and still not cross, this means that you can have an interaction in such a case, contrary to the statement in the question. The interaction plot below shows a situation like this.
An interaction is present in a 2-way design if the simple effects of one of the variables are different at different levels of the other variable.
a) True
b) False
a) True
Explanation … The interaction plot below shows a situation where the simple effect of B is small at level 1 of A, larger at level 2 of A, and even larger at level 3 of A. The changing simple effects of B are what cause the lines to be nonparallel and so there is an interaction. In the situation diagrammed below you could also say (equivalently) that the simple effects of A are different at level 1 of B and level 2 of B. In particular, there appears to be no simple effect of A at level 2 of B but there is a substantial effect at level 1 of B. Either way, the changes in simple effect signal the presence of an interaction.
6) The interaction plot below shows the results of observations in a 2 x 3 design. Of the 5 possible simple effects that could be tested here, how many do you think are zero effects (i.e., the means involved are all the same)?
A graph with A1, A2, and A3 on the bottom, with B1 and B2 lines in the graph, with kB2 being straight, and B1 curving up to meeting the middle dot of B2, and then curving down
a) 1
b) 2
c) 3
d) 4
b) 2
Explanation … In the interaction plot it appears that there is a simple effect of A on the dependent variable at level 1 of B but not at level 2 of B. This is because at level 2 of B all 3 means are the same whereas at level 31 of B the means differ as you travel from one level of A to another. Likewise, there seems to be no simple effect of B on the dependent variable at level 2 of A. This is because, at level 2 of A, both means are the same. At the other levels of A there do seem to be simple effects of B on the dependent variable since in these cases the means at level 2 of B are higher than those at level 1.
In total then, there are 2 simple effects that are have gone missing in these results, the simple effect of A at B2 and the simple effect of B at A2. You can think of these as zero effects.
Which of the statements about the interaction plot below is false?
a graph with A1, A2, and A3 at the bottom, and B1 and B2 in lines. B2 is straight across, and B1 curves downwards (underneath B2) and then up, but never intersects with B2
a) There are apparent main effects of both A and B on the dependent variable
b) There is an apparent interaction between A and B
c) There is an apparent simple effect of B on the dependent variable at level 1 of A
d) There is an apparent simple effect of A on the dependent variable at level 2 of B
d) There is an apparent simple effect of A on the dependent variable at level 2 of B.
Explanation … The simple effect of A on the dependent variable at level 2 of B The figure shows 1) an apparent main effect of A on the dependent variable because after collapsing across B the marginal means for A1 and A2 are both lower than the marginal mean for A2, 2) an apparent main effect of B on the dependent variable because, after collapsing across levels of A the marginal mean at level 2 of B is higher than the marginal mean at level 1 of B, 3) simple effects of AThe interaction plot below shows a situation where the simple effect of B is small at level 1 of A, larger at level 2 of A, and even larger at level 3 of A. The changing simple effects of B are what cause the lines to be nonparallel and so there is an interaction. In the situation diagrammed below you could also say (equivalently) that the simple effects of A are different at level 1 of B and level 2 of B. In particular, there appears to be no simple effect of A at level 2 of B but there is a substantial effect at level 1 of B. Either way, the changes in simple effect signal the presence of an interaction.
How many different main effects can be tested n a 3 x 5 factorial design?
a) 1
b) 2
c) 3
d) 5
e) 8
b) 2
Explanation … In a 2-way ANOVA there are 2 independent variables and you can talk about the presence of absence of a main effect for each variable. It doesn’t matter how many levels each variable has. A variable has some sort of main effect if its different levels are associated with different marginal means and it has no main effect if the different levels all have the same marginal mean. Of course in a real experimental situation some of the marginal means may differ from each other by accident even if there is no real main effect. But this is the sort of thing that an F-test of a main effect is meant to sort out.
How many different simple effects can be tested in a 3 x 5 factorial design?
a) 1
b) 2
c) 3
d) 5
e) 8
e) 8
Explanation … In a 2-way ANOVA, each variable can have a different simple effect at each and every level of the other variable. Thus, treatment A can have a different simple effect at levels 1, 2 , 3, etc. of level B and treatment B can have separate effects at levels 1, 2, 3, etc., of treatment A. Thus, in a design with variables A and B, there are a + b simple effects that may need to be sorted out.
Suppose that the analysis of a x 2 x design reveals a significant interaction, a significant simple effect of B at level 1 of A, a significant simple effect of A at level 2 of B, and no other significant simple effects. Which of the interaction plots below is compatible with these results?
a) Two B lines change amounts to meet on A2
b) B2 is straight, B1 is below but both meet together at A2
c) B1 is straight, B2 is below but both meet together at A2
d) B1 is straight, B2 is at the same height at A1, and B2 descends
d) This one has no simple effect of B at A1 (i.e., both means are the same there), so it can’t be the correct answer.
The question says that there is only one simple effect of A. This means that the correct plot must have only one diagonal line. Choice a) has 2 diagonal lines so it can’t be the correct answer.
At this point there are only 2 answers left in the running, b) and c). The question states that there is a simple effect of A at level 2 of B but not at level 1 of B. Visually this means that the solid line (the one for B2) should be slanted but the other one (the one for B1) should be horizontal. Clearly, choice c) is the plot where this is so.
