A Chemical Reaction Study
/****************************************************************/
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: ADXEG1 */
/* TITLE: A Chemical Reaction Study */
/* PRODUCT: QC */
/* SYSTEM: ALL */
/* KEYS: Design of Experiments,Fractional Factorial Designs */
/* PROCS: */
/* DATA: */
/* REF: Box, G.E.P., Hunter, W.G., and Hunter, J.S. (1978). */
/* Statistics for Experimenters. New York: John */
/* Wiley & Sons, pp. 375-380. */
/* MISC: ADX Macros are stored in the AUTOCALL library */
/* */
/* A fractional factorial design was used to study a chemical */
/* reaction to find out what percentage of the chemicals */
/* responded in the reactor. The researchers identified five */
/* treatment factors which were thought to influence the */
/* percentage of reaction, */
/* */
/* * the feed rate of the chemicals (FEED), which range from */
/* 10 to 15 liters/min, */
/* * the percentage of a catalyst (CAT) that is added, */
/* ranging from 1% to 2%, */
/* * the agitation rate of the reactor (AGIT), ranging from */
/* 100 to 120 rpm, */
/* * the temperature (TEMP), ranging from 140 to 180 degrees */
/* C, and */
/* * the concentration (CON), ranging from 3% to 6%. */
/* */
/****************************************************************/
/*--------------------------------------------------------------*/
/* EXAMPLE 1: A DESIGN FOR A CHEMICAL REACTION STUDY. */
/* SOURCE: BOX, HUNTER, AND HUNTER (1978). */
/*--------------------------------------------------------------*/
/*
/ For this example, we need only the fractional factorial macros:
/ if we haven't already included them, we do so now.
/---------------------------------------------------------------*/
%adxgen;
%adxff;
%adxinit /* Initialize ADX environment. */
/*
/ First, find out which designs are available for the five
/ treatment factors.
/---------------------------------------------------------------*/
%adxpff((ntmts=5))
/*
/ Box, Hunter, and Hunter choose a half-fractional factorial
/ design of resolution 5, which has 16 runs and no blocking.
/---------------------------------------------------------------*/
%adxffd(reactor,5,16)
/*
/ We now have a data set that contains 5 treatment variables and
/ 16 observations. We want to decode the data into factors and
/ levels which the experimenter will understand. NOTE: The
/ factors must be separated by a slash when typing in this
/ statement.
/---------------------------------------------------------------*/
%adxdcode(reactor,t1 feed 10 15 /t2 cat 1 2 /t3 agit 100 120
/t4 temp 140 180 /t5 con 3 6)
/*
/ Normally, we would want to write a report which will print the
/ runs in the design in a randomized order and provide space for
/ a researcher to fill in the values of a response: use the
/ following to do this:
/ %adxrprt(reactor,response)
/ Assuming this has been done, we add the data to the design with
/ the following DATA step: the numbers can be found in Box,
/ Hunter, and Hunter (1978), p. 379.
/---------------------------------------------------------------*/
data reactor;
set reactor;
input @@ response;
cards;
56 69 53 49 63 78 67 95 53 45 55 60 65 93 61 82
;
run;
/*
/ We need to recode this data so that we can analyze it.
/---------------------------------------------------------------*/
%adxcode(reactor,reactor,feed cat agit temp con)
/*
/ Now analyze the coded data.
/---------------------------------------------------------------*/
%adxffa(resp=response,res=5)
/*--------------------------------------------------------------*/
/* */
/* The output contains the results of the analysis of variance */
/* as well as a normal plot of the estimated effects. A normal */
/* plot is a scatterplot of the quantiles of univariate data */
/* against the expected quantiles of a random normal sample. */
/* Under the null hypothesis that all effects are zero, the */
/* estimates should behave like a random sample from such a */
/* distribution, and should fall pretty much along the */
/* reference line which is also plotted. The reference line */
/* corresponds to the normal distribution with zero mean and */
/* standard deviation given by */
/* */
/* - the estimated standard error of the effects estimates, */
/* if an estimate of error is available; or */
/* - the standard deviation of all the effects, if no */
/* estimate of error is available. */
/* */
/* Typically most of the effects will indeed be zero and their */
/* estimates will fall on this line: a few will be significant */
/* and will not line up with the rest. In this example, the */
/* analysis of variance indicates that the largest effects are */
/* due to catalyst, temperature, concentration, and their */
/* interactions, and the normal plot confirms this. The results */
/* produced by the fractional factorial design are not very */
/* different from those obtained from a complete factorial */
/* design---but, of course, it was obtained with only half the */
/* effort! */
/* */
/*--------------------------------------------------------------*/
