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example_oneway - Stat 2225 Handout One-Way ANOVA Example...

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Stat 2225 Handout One-Way ANOVA Example Q15.65 on p. 522. Want to see if the burning time (response variable) is different among four brands (explanatory variable) of road flares. ANOVA Table Analysis of Variance ----------------------------------------------------------------------------- Source Sum of Squares Df Mean Square F-Ratio P-Value ----------------------------------------------------------------------------- Between groups 662.675 3 220.892 3.56 0.0236 Within groups 2235.7 36 62.1028 ----------------------------------------------------------------------------- Total (Corr.) 2898.38 39 Summary Statistics Count Average Variance IQR ------------------------------------------------------------------------------------ Flare A 10 61.6 80.4889 18.0 Flare B 10 57.3 70.4556 14.0 Flare C 10 61.8 22.1778 5.0 Flare D 10 51.8 75.2889 11.0 ------------------------------------------------------------------------------------ Total 40 58.125 74.3173 10.5 Box-and-Whisker Plot response Flare A Flare B Flare C Flare D 35 45 55 65 75 85 Step 0: interval data types; from boxplot, the normality is not really good due to Flare C (as shown); the equal variance assumption is not very good either (80 is bigger than twice of 22). But we’ll go on, just as an illustration of the procedure. Step 1: H0: 1 µ = 2 µ = 3 µ = 4 µ vs. Ha: at least one pair of the average burning times is different. Step 2: TS = 3.56 (from output); it has an F distribution with 3 and 36 degrees of freedom. Step 3: p-value = 0.0236 (the critical value from table is F 3,36,0.05 = 2.86647), we conclude that we have enough evidence to infer that the burning time of road flares are significantly different among those 4 brands.
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