How important is it to define the nested design in a within subject ANOVA?

Question

I am asking to find out why a factor may become non significant after I define the nested design. The following are the two aov analysis in R.

Obs (subject #) is the within subject factor and stim3 & label (1st & 2n stimuli manipulations) are the nested within subject. stim3 & label are nested within obs. The analysis shows that 'label' is only significant when the analysis is done without defining the nested design. I wanted to ask why this is the case and how sound is the choice to define the nested design.

 > summary(aov(resp2 ~ stim3*label+Error(obs/(stim3*label)), tl ) )

    Error: obs
              Df Sum Sq Mean Sq F value Pr(>F)
    Residuals 11   5.25   0.478               

    Error: obs:stim3
              Df Sum Sq Mean Sq F value  Pr(>F)    
    stim3      1  165.4   165.4     425 3.8e-10 ***
    Residuals 11    4.3     0.4                    
    ---
    Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

    Error: obs:label
              Df Sum Sq Mean Sq F value Pr(>F)  
    label      1   6.77    6.77    4.77  0.051 .
    Residuals 11  15.61    1.42                 
    ---
    Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

    Error: obs:stim3:label
                Df Sum Sq Mean Sq F value Pr(>F)
    stim3:label  1  0.026  0.0255    0.15   0.71
    Residuals   11  1.893  0.1721               

    Error: Within
                Df Sum Sq Mean Sq F value Pr(>F)
    Residuals 1872    279   0.149               

    > summary(aov(resp2 ~ stim3*label+Error(obs), tl ) )

    Error: obs
              Df Sum Sq Mean Sq F value Pr(>F)
    Residuals 11   5.25   0.478               

    Error: Within
                  Df Sum Sq Mean Sq F value  Pr(>F)    
    stim3          1  165.4   165.4 1048.60 < 2e-16 ***
    label          1    6.8     6.8   42.95 7.2e-11 ***
    stim3:label    1    0.0     0.0    0.16    0.69    
    Residuals   1905  300.4     0.2                    
    ---
    Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Thanks for reading!

Answer 1

The nesting is essential because without it the subject is not connected to its repeated observations in the model. Not nesting is treating correlated observations like they are not correlated. Since one method si right and the other wrong I think all four possiblities can happen depending on the data. Significant nested to not significant unnested, significant nested to significant unnested, insignificant nested to significant nested and insignificant nested to insignificant un nested.