Basic Analysis and Graphing - SAS

Chapter 4 Performing Bivariate Analysis 125
Statistical Details for the Bivariate Platform
The most common use of this technique is in comparing two measurement systems that both have errors in
measuring the same value. Thus, the Y response error and the X measurement error are both the same type
of measurement error. Where do you get the measurement error variances? You cannot get them from
bivariate data because you cannot tell which measurement system produces what proportion of the error. So,
you either must blindly assume some ratio like 1, or you must rely on separate repeated measurements of the
same unit by the two measurement systems.
An advantage to this approach is that the computations give you predicted values for both Y and X; the
predicted values are the point on the line that is closest to the data point, where closeness is relative to the
variance ratio.
Confidence limits are calculated as described in Tan and Iglewicz (1999).
Statistical Details for the Summary of Fit Report
Rsquare
Using quantities from the corresponding analysis of variance table, the Rsquare for any continuous response
fit is calculated as follows:
Sum of Squares for Model
----------------------------------------------------------------
Sum of Squares for C. Total
RSquare Adj
The RSquare Adj is a ratio of mean squares instead of sums of squares and is calculated as follows:
Mean Square for Error
1 – -----------------------------------------------------------
Mean Square for C. Total
The mean square for Error is in the Analysis of Variance report. See Figure 4.12. You can compute the mean
square for C. Total as the Sum of Squares for C. Total divided by its respective degrees of freedom.
Statistical Details for the Lack of Fit Report
Pure Error DF
For the Pure Error DF, consider the multiple instances in the Big Class.jmp sample data table where more
than one subject has the same value of height. In general, if there are g groups having multiple rows with
identical values for each effect, the pooled DF, denoted DF p , is as follows:
g
DF p
= ( n i
– 1)
i = 1
n i is the number of subjects in the ith group.