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I am running an experiment testing reaction times under different conditions. I have a data sample located here and I have added a graphical plot of my data below in order to ease your understanding:

enter image description here

I would like to check whether weak emotion recognition has significantly higher error rates than all other conditions. I was told that the proper way to do this was a repeated measurement ANOVA. I have found out that this can be done via R's stats::aov() function.

I am interfacing with R via RPy and you may see my exact code under this notebook.

I am getting the following resulting summary:

Error: ID
          Df Sum Sq  Mean Sq F value Pr(>F)
Residuals  6  0.022 0.003666               

Error: Within
          Df  Sum Sq  Mean Sq F value Pr(>F)   
COI        6 0.02628 0.004379   3.468 0.0083 **
Residuals 36 0.04547 0.001263                  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

How does this help me address my issue?

Additionally, in a discussion resulting from this other question I have been told that while anova is acceptable in some cases (such as this one) linear models such as the one generated by nlme::lme() are preferable.

I have used that function in this other notebook, and the output reads as follows:

Fixed effects: ER ~ COI 
                 Value  Std.Error DF  t-value p-value
(Intercept) 0.01928571 0.01514819 36 1.273137  0.2111
COIem-hard  0.07028571 0.01899579 36 3.700069  0.0007
COIsc-11    0.00403687 0.01899579 36 0.212514  0.8329
COIsc-15    0.01700000 0.01899579 36 0.894935  0.3768
COIsc-19    0.00417857 0.01899579 36 0.219974  0.8271
COIsc-23    0.00432488 0.01899579 36 0.227676  0.8212
COIsc-27    0.00417857 0.01899579 36 0.219974  0.8271

how am I to interpret those p-values in the context of the point I'm trying to make? Also, why is my first COI (COIem-easy) absent from the list?

As a general point I would also be very happy to hear which of these 2 approaches you advise I should use.

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COIem-easy is absent because the effect is 0. What R is doing is setting that as the reference value that all other COI's are compared to. The p-value for the t-test is the test that the effect of that level is equal to 0 or not. In other words is that level of COI equal to COIem-easy.

The ANOVA is testing if there is some difference between the levels. It will not tell you which levels are different. The p-value indicates that there is one.

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  • $\begingroup$ the p value also does not tell me whether one or two categories are very far away from the others - right? Also, why is the effect of COIem-easy zero? $\endgroup$ – TheChymera Nov 14 '13 at 22:13
  • $\begingroup$ Correct, the ANOVA p-value does not include that information. The hypothesis for ANOVA is just that there is a difference. COIem-easy is zero because R is defining the effects of the other levels relative to COIem-easy. $\endgroup$ – Christopher Louden Nov 15 '13 at 14:09
  • $\begingroup$ so COIem-easy is in this case set equal to the base intercept? how does the function choose which category ID it assigns this role to? $\endgroup$ – TheChymera Nov 15 '13 at 15:34
  • $\begingroup$ It uses the first level in the factor. $\endgroup$ – Christopher Louden Nov 15 '13 at 15:35
  • $\begingroup$ so simply the one which happens to be the first in my list? $\endgroup$ – TheChymera Nov 15 '13 at 16:07

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