Modeling and Multivariate Methods - SAS

80 Fitting Standard Least Squares Models Chapter 3
Estimates
The Least Significant Value (LSV)
After a single-degree-of-freedom hypothesis test is performed, you often want to know how sensitive the test
was. In other words, you want to know how small would a significant effect be at some p-value alpha.
The LSV provides a significant measuring stick on the scale of the parameter rather than on a probability
scale. It shows the sensitivity of the design and data. LSV also encourages proper statistical intuition
concerning the null hypothesis by highlighting how small a value would be detected as significant by the
data.
• The LSV is the value that the parameter must be greater than or equal to in absolute value, in order to
give the p-value of the significance test a value less than or equal to alpha.
• The LSV is the radius of the confidence interval for the parameter. A 1–alpha confidence interval is
derived by taking the parameter estimate plus or minus the LSV.
• The absolute value of the parameter or function of the parameters tested is equal to the LSV, if and only
if the p-value for its significance test is exactly alpha.
Compare the absolute value of the parameter estimate to the LSV. If the absolute parameter estimate is
bigger, it is significantly different from zero. If the LSV is bigger, the parameter is not significantly different
from zero.
The Least Significant Number (LSN)
The LSN or least significant number is the number of observations needed to decrease the variance of the
estimates enough to achieve a significant result with the given values of alpha, sigma, and delta (the
significance level, the standard deviation of the error, and the effect size, respectively).If you need more data
points (a larger sample size) to achieve significance, the LSN indicates how many more data points are
necessary.
Note: LSN is not a recommendation of how large a sample to take because the probability of significance
(power) is only about 0.5 at the LSN.
The LSN has these characteristics:
• If the LSN is less than the actual sample size n, then the effect is significant. This means that you have
more data than you need to detect the significance at the given alpha level.
• If the LSN is greater than n, the effect is not significant. In this case, if you believe that more data will
show the same standard errors and structural results as the current sample, the LSN suggests how much
data you would need to achieve significance.
• If the LSN is equal to n, then the p-value is equal to the significance level alpha. The test is on the border
of significance.
• Power (described next) calculated when n = LSN is always greater than or equal to 0.5.