Example Presentation of Results From a Factorial ANOVA
Exercise 13.5 in David Howell’s “Statistical Methods for Psychology,” 7th edition,
provided the data for this analysis. It was in earlier editions of his “Fundamental
Statistics for the Behavioral Sciences,” but was dropped from the 4th edition of that
text. Here I present an example of how to write up the results from such an analysis.
Please note that I used the pooled error term when testing the simple effects but
individual error terms when computing eta-squared for the simple effects.
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Subjects were rats in a one-trial passive avoidance learning task
Put in the experimental apparatus, they were shocked when they crossed a line.
Later they were put back in. The dependent variable was their latency to cross
that line again.
They were given brain stimulation at 50, 100, 150 msec after the training shock.
This stimulation was delivered to Area 0, 1, or 2.
Such stimulation would be expected to disrupt the consolidation of the memory
when delivered to an area that is involved in such consolidation.
It was hypothesized that the stimulation would have no effect in Area 0 but would
in the other two areas.
My program, Area_x_Delay.sas, available on my SAS Programs Page, contains
the data and will do the analysis. Here are the results, presented in APA style.
The latency data were analyzed with a 3 x 3, Area x Delay, factorial ANOVA.
Each effect was tested with a MSE of 29.31. Significant (p < .05) effects were found for
the main effect of area, F(2, 36) = 6.07, p = .005, 2 = .18, 90% CI [.04, .29], and the
Area x Delay interaction, F(4, 36) = 3.17, p = .025, 2 = .19, 90% CI [.01, .26], but the
main effect of delay fell short of statistical significance, F(2, 36) = 3.22, p = .052, 2 =
.10, 90% CI [.00, .19]. As shown in Table 1, the latencies were, as expected, higher in
area 0 than in the other two areas.
More interesting than the main effect of area, however, is how the effect of delay
of stimulation changed when we changed the area of the brain stimulated. The
significant interaction was further investigated by testing the simple main effects of
delay for each level of the brain area factor. When the area stimulated was Area 0, the
area thought not to be involved in learning and memory, delay of stimulation had no
significant effect on mean latency, F(2, 36) = 0.02, p = .98, 2 = .00, 90% CI [.00, .00].
Delay of stimulation did, however, have a significant effect on mean latency when Area
1 was stimulated, F(2, 36) = 4.35, p = .020, 2 = .43, 90% CI [.08, .55], and when Area 2
was stimulated, F(2, 36) = 5.19, p = .010, 2 = .52, 90% CI [.16, .62].
As shown in Table 1, the disruption of consolidation of the memory produced by
the brain stimulation in Area 1 was greater with short delays than with long delays.
Pairwise comparisons using Fisher’s procedure indicated that the mean latency was
significantly less with 50 msec delay than with the 150 msec delay, but with the smaller
differences between adjacent means falling short of statistical significance.
Table 1. Mean latency (sec) to cross the line.
Delay of Stimulation
Area
50
100
150
marginal
0
28.6A
28.0A
28.0A
28.2
1
16.8A
23.0AB
26.8B
22.2
2
24.4B
16.0A
26.4B
22.3
marginal
23.3
22.3
27.1
Note: Within each row, means with the same
letter in their superscript are not significantly
different from one another.
When the stimulation was delivered to Area 2, a different relationship between
latency and delay was obtained: Stimulation most disrupted consolidation at 100 msec.
Fisher’s procedure indicated that mean latency with 100 msec delay was significantly
less than with 50 or 150 msec delay, with mean latency not differing significantly
between the 50 and 150 msec conditions.
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Mean Latency to Cross
Please note that you could include your ANOVA statistics in a source table
(referring to it in the text of your results section) rather than presenting them as I have
done above. Also, you might find it useful to present the cell means in an interaction
plot rather than in a table of means. I have presented such an interaction plot below.
30
28
26
24
22
20
18
16
14
12
10
Area 0
Area 1
Area 2
50 msec
100 msec
Delay of Stimulation
Karl L. Wuensch, June, 2010.
150 msec