Example Presentation of Results from a Two-Way Factorial …



Example Presentation of Results from a Two-Way Factorial ANOVA(

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Exercise 13.5 in David Howell’s “Statistical Methods for Psychology,” 4th 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. Note that I used individual rather than pooled error terms in the simple main effects -- not because of any great heterogeneity of variance, but just because that was easier and use of pooled error would not change the results.

Results

Rats were given a one-trial learning experience. Placed in the testing apparatus, which had a line drawn across the middle of the floor, they were given a mildly painful foot shock immediately upon crossing the line. Each rat was given electrical stimulation of the brain 50, 100, or 150 msec after this experience. It was thought that such brain stimulation would disrupt memory of the experience if delivered at a time that the stimulated area of the brain was in the process of consolidating the memory of the experience. For one third of the rats the area stimulated was an area thought not to be involved in learning and memory (area 0), for one third it was an area thought to be involved early on in the act of consolidation (area 1), and for the remaining third it was an area (area 2) thought to be involved in consolidation a little after area 1’s involvement. After its one-trial avoidance learning experience, each rat was placed back into the same apparatus and its latency to cross the line again was measured. Long latencies were interpreted as evidence that the rat remembered the event well, while short latencies were interpreted as evidence that the rat did not remember the event well (because the brain stimulation had disrupted the memorial process).

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 = .181 and the Area x Delay interaction, F(4, 36) = 3.17, p = .025, (2 = .189, but the main effect of delay fell short of statistical significance, F(2, 36) = 3.22, p = .052, (2 = .100. 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, 12) = 0.02, MSE = 36.1, p = .98, (2 = .003. Delay of stimulation did, however, have a significant effect on mean latency when area 1 was stimulated, F(2, 12) = 4.53, MSE = 28.1, p = .034, (2 = ..430, and when area 2 was stimulated, F(2, 12) = 6.42, MSE =23.7, p = .013, (2 = .517. 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. When the stimulation was delivered to brain 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.

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.

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.

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See SPSS Output

( Copyright 2010, Karl L. Wuensch - All rights reserved.

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