Basic Analysis and Graphing - SAS

Chapter 5 Performing Oneway Analysis 181
Statistical Details for the Oneway Platform
• nc = n(CSS)/σ 2 is the non-centrality parameter.
r
CSS = ( μ g
– μ) is the corrected sum of squares.
g = 1
• μ g is the mean of the g th group.
• μ is the overall mean.
• σ 2 is estimated by the mean squared error (MSE).
Statistical Details for the Summary of Fit Report
Rsquare
Using quantities from the Analysis of Variance report for the model, the R 2 for any continuous response fit
is always calculated as follows:
----------------------------------------------------------
Sum of Squares (Model)
Sum of Squares (C Total)
Adj Rsquare
Adj Rsquare is a ratio of mean squares instead of sums of squares and is calculated as follows:
1 – -----------------------------------------------------
Mean Square (Error)
Mean Square (C Total)
The mean square for Error is found in the Analysis of Variance report and the mean square for C. Total can
be computed as the C. Total Sum of Squares divided by its respective degrees of freedom. See “The Analysis
of Variance Report” on page 141.
Statistical Details for the Tests That the Variances Are Equal Report
F Ratio
O’Brien’s test constructs a dependent variable so that the group means of the new variable equal the group
sample variances of the original response. The O’Brien variable is computed as follows:
( n ij
– 1.5)n ij
( y ijk
– y ) 2 2
– 0.5s i··j ij
( nij – 1)
r ijk
= --------------------------------------------------------------------------------------------------
( n ij
– 1) ( n ij
– 2)
where n represents the number of y ijk observations.
Brown-Forsythe is the model F statistic from an ANOVA on z ij
= y ij
– ỹ i where ỹ i
is the median response
for the ith level. If any z ij is zero, then it is replaced with the next smallest z ij in the same level. This corrects
for the artificial zeros occurring in levels with odd numbers of observations.