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Unformatted text preview: COMPARING TWO OR MORE POPULATION/PROCESS MEANS WITH INDEPENDENT SAMPLES The manager of a property appraisal service suspects differences between individual appraisers are causing variation in appraisal amounts he wants to know if he is correct so that he can correct any differences through a training program to standardize the outputs of the appraisers. The 3 appraisers (A, B, &amp; C) have been assigned 5 randomly selected properties: A B C 4 Basic Assumptions of ANOVA : 90 93 92-samples are independent from one another 94 96 88-distribution of samples represented by a normal distribution 91 92 84-normal distributions of samples have equal variances: a = b = c = . 85 88 83-processes are stable and are free from assignable causes of variation 88 90 87 Treatments : the populations/processes being studied the effect of a factor on the response variable at Xa = 89.6 Xb = 91.8 Xc = 86.8 different levels (those levels are the treatments) treatments in the above example are the 3 appraisers Sa = 11.3 Sb = 9.2 Sc = 12.7 Degrees of Freedom: are additive, just like SSTR &amp; SSE = SST, (n-1) = (k-1) + (n-k) na = 5 nb = 5 nc = 5 *Create the Null &amp; Alternative Hypothesis: (step 1) - Ho: a = b = c; &amp; Ha: at least one of the is different from the rest (there will always be differences among the sample means because of random sampling variation our goal is to find the variation that is not random) *Examine Potential Sources of Variation in Sample: (step 2) In our example, one source is the appraisers, the treatments (differences among their process means would cause differences among the sample means) this is precisely what we want to detect . Another sources is the differences among property values, which is caused by randomly selecting the 15 properties and assigning them at random to the appraisers. Appraiser inconsistency could be another source (one appraiser is more consistent with his output than another). *Graph the Data: (step 3) Enter the data into stacked format let the subscripts indicate the treatment (1-appraiser A, 2-appraiser B, etc) in C1, and enter the observations into the C2 as they correspond to their respective treatment. GRAPH, SCATTERPLOT, SIMPLE, enter observations from C2 as the Y axis &amp; the treatments from C1 into the X axis, OK. ( if you find the midpoint, or center, of each group of observations and draw a horizontal line connecting the dots if the line is parallel to the X axis or fairly straight, it is reasonable to assume the null hypothesis is correct) *Analysis of Variance: (step 4) need 2 statistics: amount of variation among the samples, and amount of variation within the samples: among is SSTR &amp; within is SSE. SSTR : accounts for differences among sample means for the treatments (3 appraisers): SSTR = na(Xa X) + nb(Xb X) + nc(Xc X): in our example SSTR = 5(89.6 89.4) + 5(91.8 89.4) + 5(86.8 89.4) = 62.8: the larger the value of SSTR, the greater the...
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This note was uploaded on 12/07/2009 for the course MGMT 302 taught by Professor Canavos during the Spring '09 term at VCU.
- Spring '09