By B. J. Winer
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Additional info for Statistical Principles in Experimental Design
The numerical value for SSmethnds computed f r o m (5) and (6) involves more rounding errors than does the computational formula (7). The variation due to experimental error is, by definition, the pooled within-method variation, (8) SSerror = SSw=SSS,. This statistic measures the sum of the variation w i t h i n each of the subgroups. Its computational formula is given by (4). The total variation, or total sum of squares, is (9) SS,otai = SS(A'„ - C)2, the sum of the squared deviation o f each observation in the experiment about the grand mean.
Hence Hx w i l l also be rejected when the proper number of degrees of freedom is used in determining the critical value. 20. 6-1. c'll3 is given b y rv> \-'J t - "'"'•• ~ u ' ^ 'critical — , "'<• — wb where na = 4lna,w„ = 4/nb, ta = h ^ . ,l(nh - 1). 51. ,ritical computed in this manner will differ only slightly from the critical value obtained by means of the Welch approximation. Formula (3) is actually a modified version of (4). 90. 69. 35 Use of (4) is to be preferred to (3). Testing Hypotheses about the Difference between Two Means— Correlated Observations In Sees.
However, the degrees of freedom for the estimate i n (9) are n — 1, whereas the degrees of freedom for the estimate in (10) are I n — 2. 868 considered more efficient than a design which does not have repeated measures, the decrease i n the experimental error must be sufficient to offset the reduction i n degrees of freedom. I n areas o f research i n which the variance associated w i t h the term -n-, i n the model i n (2) is likely to be large, the control on this source of variation provided by a repeated-measures design w i l l greatly increase the sensitivity o f the experiment.