Wednesday, October 22, 2008
What is the F?
Hello. I'm going through my notes and trying to drill Monday's lecture into my head and just came across the "F" in the ANOVA section. Unfortunately, I didn't write any notes on what this actually means and was wondering if there was a quick and easy way of defining it, its significance to the regression and the importance of reporting it? (I looked through both sets of notes and didn't see it, so I apologize if it's a matter of simple oversight).
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2 comments:
The F will be more important next quarter in ANOVA. In regression, however, you do not report the F-value. The ANOVA table in simple linear regression tells you one thing: whether or not R and R squared are statistically significantly different from zero. You make this call based on the p-value. If p is less than .05, you reject the null hypothesis and claim that R and R squared are different from zero. Generally speaking, the higher the F-value, the lower the p-value.
If you want a taste of ANOVA and how the F is calculated, read on. As you will find out next quarter, the F is the mean square (variance) between groups divided by the mean square (variance) within groups (aka, error). So, in the example in the slides, if you divide the mean square in the row labeled "Regression" (8200.573) by the mean square in the row labeled "Residual" (279.310), you get the F-value.
Justin has given you a clear, concise, and correct answer. However, there's just one thing I'd like to add/modify about his answer.
Unlike standardized and unstandardized beta, whose reporting is clearly spelled out in the APA Publication Manual on pp. 160-161, the reporting of the R, R squared, adjusted R squared, F, df, and p are not quite as black and white.
My preference is that you report the F along with its df, because these make completely and unambiguously clear (a) how many predictors were in your model and (b) your sample size.
It is possible to have this information clearly presented without the F, but it takes more words and more space, so for the homework, please do report the F corresponding to the test of whether or not your R statistics are significant.
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