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发件人: MCLAREN, Donald <[log in to unmask]> 主题: Re: [SPM] a simple question about one-way within-subjects ANOVA 收件人: [log in to unmask] 日期: 2011年4月7日,周四,上午2:03
Alexa,
My statement about the error term being wrong only applies to within-subject designs or mixed-designs. If you look at any other statistica program (SAS, SPSS, STATA, etc.) anytime that they compute the effect of an individual condition, they use a different error term. The reason for this is that comparing a condition against 0 is a test of a between-subject effect, while comparing condition 1 versus condition 2 is a test of a within-subject effect. The test of each effect has its own error term. However, in SPM (FSL, FAST, etc.) only 1 error term is generated. For within-subject or mixed-designs, the error term in SPM, etc. is the within-subject error term. One cannot partition this error term to derive the between-subject error term because the between-subject error term is based on the between subject variance not the within-subject variance.
Here is a good example, of heights of people:
condition 1: height [ 61 62 59 63] condition 2: height + 2 inch board [63 64 61 65]
condition 1 versus 60 is not significant (p=.25) condition 2 versus 60 is significant (p=.024)
Now, if we build a big model and ask if condition 1 is different than 0, we get p=0, t-stastic=Inf. In other words, by measuring people's height with a board, their height without the board becomes significantly taller than 60 inches. To me, this demonstrates that SPM's error term is wrong in make conclusions about individual conditions within a repeated measures design.
If one were to change condition 2: height +2 inch board to [63 64 61 64] (I guess the board shrunk before being used on the last person. condition 1 versus 60 is not significant (p=.25) condition 2 versus 60 is significant (p=.022)
Condition 1, using a paired test (e.g. a one-way ANOVA with 2 condition), is now still significant with a p-value of 0.005986. Thus, we would [incorrectly] conclude that these people are significant taller than 60 inches. This is a result of making a second measurement that doesn't change the first measurement. Also, we want to make a inference about the between-subject effect, which should not be influenced by other measurements of the same subjects as it is asking about the population behavior.
In conclusion, asking about the effect of 1 condition within SPM is invalid because it doesn't represent the between-subject effect because it is not using the between subject error term as that error term is not currently provided by SPM.
Hopefully this clears up my original statement on the validity of asking the significance of a single condition or group of condition in a within-subject or mixed-design model.
Please feel free to ask any question or suggest comments on the approach or statistics.
Best Regards, Donald [log in to unmask] |