* (The sample size program can also be used to determine appropriate sample sizes in
a standard [non-predictor sort] experiment simply by setting the
correlation value to 0. Here is a
link to the web version
of the program.)*

For
example, one might be interested in the effects of three fire retardants on
the mean bending strength of a sample of boards. One could simply randomly
assign the boards to the three treatments. However, a researcher could
significantly *reduce sample sizes* (or increase power) by
non-destructively measuring the modulus of elasticity (MOE)
of the boards prior to
treatment. The researcher could then perform a randomized block
experiment in which the
blocks were composed of boards with similar MOEs. Since MOE is well
correlated with bending strength, the experiment would be
more sensitive to the differences that are due to the fire retardant
treatments. Knowing the correlation between MOE and bending strength,
one could quantify this increase in experimental sensitivity and identify
an appropriate sample size.

The work consists of nine papers and related computer programs:

- Verrill, S. (1993), "Predictor
Sort Sampling, Tight T's, and the Analysis of
Covariance,"
*Journal of the American Statistical Association*,**88**, No. 421, 119-124. This paper focuses on hypothesis testing theory. It is available in pdf form. - Verrill, S. and Green, D. (1996). Predictor
Sort Sampling, Tight
*t*'s, and the Analysis of Covariance: Theory, Tables, and Examples. Research Paper FPL-RP-558. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 105 pages. This paper is more expository in nature. It is available in pdf form. - Verrill, S., Green, D., and Herian, V. (1997). TT: A Program that Implements Predictor Sort Design and Analysis. General Technical Report FPL-GTR-101. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 21 pages. This paper helps a user run the program. It is available in pdf form.
- Verrill, S. (1999), "When Good Confidence Intervals Go Bad: Predictor Sort
Experiments
and ANOVA,"
*The American Statistician*,**53**, 38-42. This paper focuses on confidence intervals on treatment means. It is available in pdf form. Note that this paper makes an incorrect statement about the suitability of an unmodified analysis of covariance approach. This statement is corrected in Verrill and Kretschmann (2017a). Please see below. - Verrill, S. (2001), "Rolling Your Own: Linear Model Hypothesis Testing
and Power Calculations via the Singular Value Decomposition,"
*Statistical Computing and Graphics Newsletter*,**12**, No. 1, 15-18. This paper is available in pdf form. - Verrill, S. (2000), "Power Calculations in the Predictor Sort Computer Program." This unpublished note and the preceding paper discuss some of the numerical methods behind the power calculations that are implemented in the predictor sort power calculation program. This paper is available in pdf form.
- Verrill,S., Herian, V., and Green, D. (2004). Predictor Sort Sampling and Confidence Bounds on Quantiles I: Asymptotic Theory. Research Paper FPL-RP-623, Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 67 pages. This paper is available in pdf form. An American Statistical Association conference proceedings version of this paper is also available in pdf form.
- Verrill, S. and Kretschmann, D. (2017a). A Reminder about
Potentially Serious Problems with a Type of Blocked ANOVA Analysis.
Research Paper FPL-RP-683, Madison, WI: U.S. Department of
Agriculture, Forest Service, Forest Products Laboratory.
This paper summarizes the preceding research, corrects a flaw in the
1999 paper (analysis of covariance confidence intervals on treatment
means
*do*need to be modified), extends predictor sort results to multiple comparison procedures, provides links to updated computer programs, and presents the results from extensive new power and confidence interval coverage simulations. As of 1/12/17, the current version of the paper (in editing) is available in pdf form. - Verrill, S. and Kretschmann, D. (2017b). Simulations of Nonparametric Analyses of Predictor Sort (Matched Specimens) Data. Draft research paper, Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. This paper reports simulations that investigate the performance of nonparametric tests, and nonparametric confidence bounds on quantiles given predictor sort data. The simulations also investigate situations in which the predictor/response data is not bivariate normal. As of 1/12/17, the current version of the paper (under review) is available in pdf form.
- Web based and R programs to perform power calculations, specimen allocation, and hypothesis testing, and to calculate confidence intervals on treatment means are available here.

- Simpson, W.T. (1996), "Evaluation of a Method for Estimating Kiln Schedules and Species Groupings for Drying Tropical and Temperate Hardwoods," FPL-RP-548, USDA Forest Service, Forest Products Lab, Madison, WI.
- Simpson and Verrill (1997), "Estimating Kiln Schedules for
Tropical and Temperate Hardwoods Using Specific Gravity,"
*Forest Products Journal*,**47**, 64-68.

The Drying Schedule program implements the techniques described in the
second paper.
FORTRAN source code is
available under a GNU copyright.
Binary code is available for the
DOS
and Solaris 2.x
operating
systems. *The Drying Schedule program may also be run over the
Web*.

For further information, please contact Steve Verrill at

Last modified on 3/5/18.