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COPE ratings are ratings of congressional votes. A high COPE rating indicates prolabor votes. Each observation is a member of congress. Suppose that you want to determine if COPE ratings vary by political party and by region of the country. You also want to test for an interaction between region and party.
Assume two variables: PARTY & REGION
Here's a table of the means
in the raw data:
COPE Rating Example
| Region/Party | Democrat | Republican | Mean/number |
| North | 100 | 80 | 90 |
| n=20 | n=20 | n=40 | |
| South | 20 | 30 | 25 |
| n=20 | n=20 | n=40 | |
| West | 90 | 40 | 65 |
| n=20 | n=20 | n=40 | |
| Mean | 70 | 50 | |
| number | n=60 | n=60 |
Between Row SS
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Between Column SS
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Between Subclass SS
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| Interaction | ||
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Here's the results of an SPSS analysis of variance on the data:
SPSSWIN PRINTOUT
| Source of Variation | SS | DF | MS | F | Sig of F |
| WITHIN + RESIDUAL | 171,000 | 114 | 1500 | ||
| PARTY | 12,000 | 1 | 12000 | 9.0 | .001 |
| REGION | 86,000 | 2 | 43000 | 28.7 | .000 |
| PARTY BY REGION | 18,000 | 2 | 9000 | 6.0 | .005 |
| (Model) | 116,000 | 5 | |||
| (Total) | 287,000 | 119 | |||
| R-Squared = | .400 | ||||
| Adjusted R-Squared = | .370 |
Here is the results of analyzing the identical data in EXCEL, along with a graph of the results that clearly shows and interaction effect. Do you know why an interaction is indicated?
| Anova: Two-Factor With Replication | |||||
| SUMMARY | Democrat | Republican | Total | ||
| North | |||||
| Count | 20.0 | 20.0 | 40.0 | ||
| Sum | 2000.0 | 1600.0 | 3600.0 | ||
| Average | 100.0 | 80.0 | 90.0 | ||
| Variance | 1783.9 | 2628.6 | 2252.3 | ||
| South | |||||
| Count | 20.0 | 20.0 | 40.0 | ||
| Sum | 400.0 | 600.0 | 1000.0 | ||
| Average | 20.0 | 30.0 | 25.0 | ||
| Variance | 782.2 | 994.9 | 891.4 | ||
| West | |||||
| Count | 20.0 | 20.0 | 40.0 | ||
| Sum | 1800.0 | 800.0 | 2600.0 | ||
| Average | 90.0 | 40.0 | 65.0 | ||
| Variance | 1510.9 | 1292.9 | 2007.0 | ||
| Total | |||||
| Count | 60.0 | 60.0 | |||
| Sum | 4200.0 | 3000.0 | |||
| Average | 70.0 | 50.0 | |||
| Variance | 2601.1 | 2057.9 | |||
| ANOVA | |||||
| Source of Variation | SS | df | MS | F | P-value |
| Sample | 86000.0 | 2.0 | 43000.0 | 28.7 | 0.0 |
| Columns | 12000.0 | 1.0 | 12000.0 | 8.0 | 0.0 |
| Interaction | 18000.0 | 2.0 | 9000.0 | 6.0 | 0.0 |
| Within | 170878.0 | 114.0 | 1498.9 | ||
| Total | 286878.0 | 119.0 |
If there was no interaction the lines would be parallel with each other.(return)
  
  
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