/****************************************************************/ /* 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! */ /* */ /*--------------------------------------------------------------*/