Stat-403/Stat-650 : Intermediate Sampling and Experimental Design ...

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2Type I error in the data exceeds what he/she is willing to tolerate. That is, the test is significant at5% level but not significant at 1%. In fact, p-value measures the amount of statistical evidenceagainst the null hypothesis in favor of the alternative hypothesis: the smaller the p-value thestronger the evidence against the null hypothesis. When drawing a conclusion, the weight ofevidence indicated by the computed p-value should be reported. This weight of evidence may beindicated in words according to the following table:Weight of evidence againstp-value = pthe null hypothesissssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssp ≤ 0.01very strong0.01 and 2) are available and one is interested intesting if there is a difference in performance between them. Two samples of trees are randomlyselected and each is treated with one of the two fertilizers and the growth rate (Y) is measured.This test can be carried out using PROC ANOVA or PROC GLM with class variable A indicatingthe type of fertilizer (1 or 2) applied. The required model statement is MODEL Y = A . The SASoutput consists of an ANOVA table with the p-value of the test. If a p-value of 0.35 was obtained,the conclusion would be: "There is no evidence (p = 0.35) that the two fertilizers performdifferently."Example 2: Suppose further that an experiment had treatments with the following levels: acontrol (no fertilizer), a standard fertilizer, and a new fertilizer applied at two different amounts.The experimenter might have the following questions:1. Is the control different from the other treatments?2. Is the standard fertilizer different from the new fertilizer?3. Are the two different levels for the new fertilizer producing different responses?These questions could be answered with the following contrasts:Contrasts Coefficientsfor QuestionTreatmentssssssssssssssss1 2 3ssssssssssssssssssssssssssssssssssssssControl -3 0 0Standard 1 -2 0New: level 1 1 1 -1New: level 2 1 1 149
3 Pamphlet #30rrrrrrrrrrrrrrrrrrrrrPROC GLM with the appropriate contrast statements could be used to test the contrasts. Thep-values for the contrasts are computed and reported as part of the SAS output. If the p-value forquestion 1 was 0.015, then the conclusion would be: "There is strong evidence (p = 0.015) that thecontrol is different from the other treatments."Example 3: Suppose it is believed that the growth rate (Y) is linearly dependent on theamount of fertilizer applied (X). To test this claim, fit a regression line Y = β 0 + β 1 X and testthe hypotheses H o : β 1 = 0 vs H a : β 1 ≠ 0 . This can be accomplished using PROG REGwith the model statement MODEL Y = X . SAS will compute the estimated values of β 0 and β 1 ,perform an F-test and report the p-value under the column "PROB > F". If a p-value of 0.023 wasobtained, the conclusion could be stated as follows: "There is strong evidence (p = 0.023) that theamount of fertilizer applied affects the growth rate."Example 4: Suppose one is interested in testing if there is a relationship between tree speciesand success in seed germination. Count data of the number of germinated seeds from each treespecies is available for analysis by a contingency table. SAS has 2 procedures to do this:PROC FREQ can be used for two dimensional tables only while PROC CATMOD is suitable forany dimensional table. If PROC FREQ was used, the statementTABLE SPECIES*SEED/CELLCHI2 CHISQwould produce a two-way frequency table of species by seed with the χ 2 statistics due to eachcell printed. The total χ 2 statistic and the corresponding p-value would also be reported. If ap-value of 0.084 was obtained, then the conclusion would be: "There is moderate evidence(p = 0.084) that success in seed germination is different for the different tree species."In short, p-values convey information about the strength of evidence against the nullhypothesis and allow an individual to draw a conclusion at any specific level α. Nevertheless, αshould not be the only criteria for decision making. When the null hypothesis is not rejected, β ,the size of the Type II error should also be reported. A false H o could have been missed if β islarge in the experiment due to a small sample size or large sampling variability. This topic ofPower Analysis will be explored in future pamphlets.References:Devore, J.L., 1987. Probability and Statistics for Engineering and the Science. 2nd ed. Brooks/ColePublishing Company.Stafford, S.G., A Statistics Primer for Foresters, Journal of Forestry, March 1985, p 148-157.50CONTACT: Vera Sit or Wendy Bergerud356-0435 387-5676
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