Statistical testing, ANOVA, Kruskall-Wallis, p-vaue The data below refer to thre

Question

Statistical testing, ANOVA, Kruskall-Wallis, p-vaue

The data below refer to three suppliers of the Levi-Strauss clothing manufacturing plant in Albuquerque. The firm's quality control department collects weekly data on percent-age waste (run-up) relative to what can be achieved by computer layouts of patterns on cloth. It is possible to have negative values, which indicate that the plant employees beat the computer in controlling waste. Under question are differences among the supplier plants. (a) Formulate the question into a hypothesis testing problem about the waste means at the various plants. (Be sure to define any parameter you introduce.) (b) Show how to compute the ANOVA F-ratio. (c) How is a p-value traditionally computed? What assumptions does that rely on? How would you check for that using plots? (d) Compute the Kruskal-Wallis statistic without the normalizing constants. Show your work (use the data table above). What is the null hypothesis that the test is testing?

Explanation / Answer

(A) Hypothesis:

Null hypothesis H0: there is no difference between any of plants' waste i.e.X1=X2=X3 (where Xi is mean waste of ith plant)

Alternative hypothesis Ha: there is difference between at least 1 pair.

(B) 1 way ANOVA with 1 factor of 3 levels using excel add in:

F-value= MSBetween/ MSWithin = 79.4/88.1 = 0.9

(c) P-value = =F.DIST.RT(0.902,2,6) = 0.45>0.05

so cant reject H0 at 5% level; so no difference between plants.

Assumptions:

1) samples are Normally distributed

2) samples are iid

3) samples are homoskedastic (equal variance)

Anova: Single Factor SUMMARY Groups Count Sum Average Variance PT1 3 9.3 3.1 39.31 PT2 3 -1.2 -0.4 219.52 PT3 3 29.2 9.733333 5.523333 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 158.9356 2 79.46778 0.901836 0.454524 5.143253 Within Groups 528.7067 6 88.11778 Total 687.6422 8

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