Using summary measures to compute 2x2 ANOVA comprising two within subject factors each having 2 levels
We can also compute repeated measures ANOVAs with summary information involving two within subject factors but we need more information than in the BB or BW cases. In particular if we denote W1 and W2 as the two levels of the within subjects factors and Wij as the ijth combination with W1=i and W2=j then we need the means and standard deviations given in the table below together with the number of subjects (n) and correlations r(W11,W12), r(W21,W22), r(W11,W21), r(W12,W22), r(W11+W12,W21+W22), r(W11+W21,W12+W22), r(W11W12,W21W22).

W1 
W2 
W1 
mean1, sd1 (cell W11) 
mean2, sd2 (cell W12) 
W2 
mean3, sd3 (cell W21) 
mean4, sd4 (cell W22) 
These can then be inputted into this spreadsheet which will then compute the F ratios for the W1 and W2 main effects and the W1 x W2 interaction. Note: we cannot use summary inputs to test ANOVA model assumptions.
The spreadsheet computes both type II (recommended) and type III sums of squares (SPSS default) for the main effects which respectively ignore and adjust for the W1 x W2 interaction.