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Short answer: It is not posible to have "significant factor effect while there is no significant difference between the two factor level means." If the equations 'exactly equivalent,' which they are, then when you reject the null hypothesis with one of them, you will reject it with the other, as well.
Try some sample data, and see how it comes out.
Cheers, Jay
Gang Chen wrote:
================================================================== The gateway between this list and the sci.stat.edu newsgroup will be disabled on June 9. This list will be discontinued on June 21. Subscribe to the new list EDSTAT-L at Penn State using the web interface at http://lists.psu.edu/archives/edstat-l.html. ================================================================== . Suppose there is one factor with two levels. I could either run one-way ANOVA or unpaired t test. I always thought that the unpaired t-test would be the same as one-way ANOVA in the following sense: the F test in ANOVA for two factor level means being equal (or factor effect) would be equivalent to the unpaired t test for the difference betwen the two factor level means since F = t^2 holds in this case.
After I took a close look of the formulas, I now realize that unpaired t test is exactly equivalent to a one-way ANOVA when the latter is used to test for a difference in means between two factor levels. Then I have problem understanding the subtle difference: It seems that it is possible to have significant factor effect while there is no significant difference between the two factor level means. My question is: How is this possible?
Thanks, Gang Chen
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