# There is always a spot left for the p value that

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values (with MSE always in the denominator) gives us the test statistics necessary for testing. There is always a spot left for the p-value that corresponds to the test statistic. The test is always upper tail, even though the hypotheses might suggest otherwise. Source df SS MS F P Treatments ? 457.3 ? ? ? Error 36 ? 26.9 Total 39 ? Source df SS MS F P Treatments 3 457.3 152.4 5.67 0.003 Error 36 968.4 26.9 Total 39 1425.7 This ANOVA table is testing the hypotheses of equal means vs. at least two being different. Therefore, this step in the analysis only tells the researcher if a difference exists, not the location, which could be more useful. b.Tukey-Kramer If a difference is detected, the next step is post-hoc tests, such as Tukey-Kramer. Tukey-Kramer locates which means are different using pairwise testing. Performing this manually, the critical range needs to be calculated and the absolute value of all paired differences is compared against it. If the difference exceeds the range, those individual means are statistically different. When using software, there are three different methods available: grouping data, confidence intervals, and pairwise tests. 39-36 SSE/df = MSE 26.9*36 457.3 / 3 F0= MSA/MSE = 152.4 / 26.9 457.3 + 1425.7
Stat2610 Final Exam Study Guide (Including Test 3 Concepts) One-Way Completely Randomized Design, Manual Tukey Test (example 9a) A sporting goods manufacturing company wanted to compare the distance traveled by golf balls produced by each of three different design molds. Five balls were manufactured with each design and were brought to the local golf course for testing by the club professional. The order in which the balls were hit from the first tee with a driver was randomized, so that the pro did not know which design was being hit. All 15 balls were hit during a short period of time in which the environmental conditions were essentially the same. Use 5% significance. Part 1) Do the assumptions hold? According to the graph, it can be argued that they do. ResidualPercent100-10999050101Fitted ValueResidual2362352342331050-5-10ResidualFrequency7.55.02.50.0-2.5-5.0-7.5-10.03210Observation OrderResidual1514131211109876543211050-5-10Normal Probability Plot of the ResidualsResiduals Versus the Fitted ValuesHistogram of the ResidualsResiduals Versus the Order of the DataResidual Plots for Distance_1Part 2) Does a difference exist? Normality Equal Variances P-Value Method: 0.002 < 0.05 Reject HCritical Value Method: g1832g3030g3404g1832g3080,g3030g2879g2869,g3041g2879g3030g3404g1832g2868.g2868g2873,g2870,g2869g2870g34043.89; g1832g2868g3408g1832g3080g1525g1844g1857g1862g1857g1855g1872 g1834g2868Part 3) Location of differences g1846g3080g3404g1869g3048g3495g1839g1845g18312g3415 g34351g1866g2869g3415 g33971g1866g2870g3415 g3439If samples are not equal, a new range must be calculated for each pairwise comparison. The MSE factor comes from the ANOVA table detecting differences. The “qu” is determined according to α, the number of treatments and df for error. g1869g3048g3404g1869g3048,g2868.g2868g2873,g2871,g2869g2870g34043.77, g1846g3080g34043.77g349599.62g3415 g467215g3415 g339715g3415 g4673g340416.82|g1876g1191g2869g3398g1876g1191g2870|g340419.4g340816.82|g1876g1191g2869g3398g1876g1191g2871|g340410.2g340716.82|g1876g1191g2870g3398g1876g1191g2871|g340429.6g340816.82g1876g1191g2869g3405g1876g1191g2870;g1876g1191g2870g3405g1876g1191g2871g1845g1861g1859g1866g1861g1858g1861g1855g1853g1866g1872g1864g1877 g1856g1861g1858g1858g1857g1870g1857g1866g1872 g1859g1870g1867g1873g1868g1871:g46661,3g4667g46662g4667At 5% significance, we can conclude that the average distance traveled by design 2 is significantly different from designs 1 and 3.
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