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

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