Duncan’s Multiple Range Test - Detroit, MI Arts - Business 邓肯的多个范围测试-底特律，MI艺术业务

Duncan’s Multiple Range Test - Detroit, MI Arts - Business 邓肯的多个范围测试-底特律，MI艺术业务 Duncan’s Multiple Range Test USE THIS AFTER A SINGLE ANOVA, You know one of the tau’s [set of readings] is out of line, so now FIND IT!!! Purpose: The plain vanilla ANOVA will test to see if one [but we don’t know which one] of the factor segments matters. There are a number of methods to test WHICH factors matter. Duncan’s Multiple Range test is convenient, because it combines the ease of hypothesis testing with the power of testing each mean to each mean. Arrangement: we will do hypothesis testing, on each mean pair: Ho: ui = uj Alternatives to this method : Many other methods will accomplish similar items: regression, graphical comparison, contrasts, orthogonal contrasts, Scheffe’s method, least significant difference method, Newman-Keul’s method, Tukey’s test. Your book even says [page 107]: ‘Which method do I use?’ …Unfortunately, there is no clear cut answer to this question, and professional statisticians often disagree of the utility of the various procedures’!!!! In Chapter 3 of Montgomery has the Duncan’s multiple range method on pp. 103-105. BRIEF STEPS: 1. Do the Single Factor Anova first, to make sure this is worth doing. 2. Rank the treatment averages: Yi. [smallest to largest value] 3. You already have the overall Standard Deviation, St 4. Look up in the r table [Appendix 7] for the r value. It depends on the degrees of freedom of the number of treatments and the number in each treatment, and the alphs 5. Now, CALCULATE THE STATISTIC R. R = r[from table] * St 6. Now, compare each of the treatment R’s [for example… 1 versus 2, 2 versus 4…] by subtracting. 7. Compare the the look up R values. If bigger… REJECT!! ------------------------------- Detailed. Method: 1. come up with hypotheses: Ho: ui = uj [all taus are zero] H1: one of the means differ, or is different enough from the rest to say tau is not zero 2. Calculate a value, compare to table value. The table values are so WONDERFUL, Duncan has his own set of Appendix tables: Table 7 on page 675. You will need alpha, p= range [when you rank the means], and f = degrees of freedom for error. 3. The calculated statistic is known as Rp. Rp = Sy * r(p,f) STEPS for calculating Rp [and finding p and f] 1. calculate each factor level mean and rank them: 1 is smallest, n is highest. 2. calculate an overall standard error for the averages, n is the number in each factor: SMSEn,/ y Where MSE is the mean square for error, or SSE/df. The f value is the total number of samples - 1; and this will be the same for all the r(p,f) The p values will be calculated as the range differences….. for example: sample 1 and sample 2 then p=2, sample 2 and sample 4 then p = 3….. In other words, subtract the mean ranks and add one. So if you are comparing mean 1 and mean 2, alpha is .05 and df=10: r(p,f) = r(2,10) = 3.15 3. Once you have calculated all the Rp’s for all the pairs [1/2, 1/3, ?, 1/5, 2/3, 2/4, 2/5, ?, 3/5, 4/5], then you compare this value to the difference in the means for the factors. 4. if the calculated subtraction is greater than the table value, then there is a significant difference between the mean pairs. You will note that there are only alpha = 0.05 and 0.01 given in the table. If you want better values: A. obtain better tables B. interpolate BUT ask yourself…. Does this matter?? [in a statistical sense]. For example, if Z = 1.95, and t = 2.12; yet your calculated value = 15.5; your assumption won’t ‘matter’