Modeling and Multivariate Methods - SAS

78 Fitting Standard Least Squares Models Chapter 3
Estimates
Table 3.9 Description of the Power Details Window (Continued)
Adjusted Power and
Confidence Interval
To look at power retrospectively, you use estimates of the standard error and
the test parameters. Adjusted power is the power calculated from a more
unbiased estimate of the noncentrality parameter.
The confidence interval for the adjusted power is based on the confidence
interval for the noncentrality estimate. Adjusted power and confidence
limits are computed only for the original δ where the random variation is.
Effect Size
The power is the probability that an F achieves its α-critical value given a noncentrality parameter related to
the hypothesis. The noncentrality parameter is zero when the null hypothesis is true (that is, when the effect
size is zero). The noncentrality parameter λ can be factored into the three components that you specify in
the JMP Power window as
λ =(nδ 2 )/σ 2 .
Power increases with λ. This means that the power increases with sample size n and raw effect size δ, and
decreases with error variance σ 2 . Some books (Cohen 1977) use standardized rather than raw Effect Size,
Δ = δ/σ, which factors the noncentrality into two components: λ = nΔ 2 .
Delta (δ) is initially set to the value implied by the estimate given by the square root of SSH/n, where SSH
is the sum of squares for the hypothesis. If you use this estimate for delta, you might want to correct for bias
by asking for the Adjusted Power.
In the special case for a balanced one-way layout with k levels:
δ 2 ( α i
– α
= ----------------------------
)2
k
Because JMP uses parameters of the following form:
β i
= ( α i
– α)
withβ k
= – α m
m = 1
the delta for a two-level balanced layout appears as follows:
2
δ 2 β 1
+ (–β 1
) 2
2
= ----------------------------- = β
2 1
Text Reports for Power Analysis
k – 1
The Power Analysis option calculates power as a function of every combination of α, σ, δ, and n values that
you specify in the Power Details window.
• For every combination of α, σ, and δ, the least significant number is calculated.