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From |
David Hoaglin <[email protected]> |

To |
[email protected] |

Subject |
Re: st: My ANOVA and regression results don't agree |

Date |
Mon, 6 Jan 2014 20:34:18 -0500 |

Hi, Jess. Please say more about the way in which the ANOVA and regression approaches do not correspond. As Phil mentioned, they produce the same fitted values. In that sense, the ANOVA and the regression always agree. In what sense are the p-values from the regression "wrong"? It would help me to see more information on your data and your analyses, such as the output that you got from the various commands. One consideration is whether the data for the ANOVA are balanced. (If you assigned subjects randomly to levels of adcontent, but not randomly to the combinations of adcontent and sex, your data would be balanced on adcontent, but not on the combination of the two factors.) Assuming that your data are balanced, with K observations in each of the 6 cells, the ANOVA decomposes the variation (about the overall mean) in the data into four sums of squares: adcontent (2 degrees of freedom) sex (1 degree of freedom) adcontent*sex (2 degrees of freedom) residuals or "error" (6K - 6 degrees of freedom) (the overall mean accounts for the other degree of freedom). The usual F-tests are concerned with each factor or interaction as a whole. For example, (mean square for adcontent)/(error mean square). The predictors in the regression are indicators that correspond to individual degrees of freedom: adcontent2 adcontent3 sex2 adcontent2_sex2 adcontent3_sex2 (and _const, which corresponds to adcontent1 and sex1), and each predictor has its own p-value. The residual sum of squares in the regression equals the residual sum of squares in the ANOVA. When the F-test in an ANOVA says that a factor is "significant," the null hypothesis being rejected is that the effect of each level of that factor is 0 (i.e., no differences among the levels). That result alone does not tell which levels differ significantly from which others, and all sorts of patterns are possible. For example, with the effects in the order adcontent1 < adcontent2 < adcontent3, adcontent2 might not differ significantly from adcontent1, and adcontent3 might not differ from adcontent2. Investigating and summarizing the patterns has a sizable literature. I would say that the person who wrote the code on the UCLA site chose to treat the highest level of each factor as the reference category. When you use factor variables in Stata, as in i.adcontent in your -regress- command, the first category is the default for the base category. You should see that in the output from that -regress- command. I hope this helps. David Hoaglin On Mon, Jan 6, 2014 at 5:53 PM, Pepper, Jessica <[email protected]> wrote: > Thanks for sending that link. I followed those instructions and got results that made sense. I just have 2 follow-up questions: > > 1. I understand that the 2 approaches (ANOVA and regress/test) don't correspond. When I follow the UCLA procedure that you sent the link to, it confirms what I initially found in the ANOVA and also shows me the contrasts, which is what I really need. All that is great. But why, in essence, should I "trust" the ANOVA over the regression? Why are the p values from the regression wrong? > 2. The procedure on the UCLA site defaults to treating the highest level of the variable as the reference category. That doesn't matter for my two level variable, but it does for my 3 level variable, correct? And if so, is there an easy way to tell it to treat the lowest level as the reference category? Or should I just manually create a new variable that switches those levels. > > I hope these questions make sense. I am new to Stata and have never encountered a situation where ANOVA and regression don't agree. > > Many thanks for your help. > Jess * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: My ANOVA and regression results don't agree***From:*"Pepper, Jessica" <[email protected]>

**Re: st: My ANOVA and regression results don't agree***From:*Phil Schumm <[email protected]>

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