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Chapter12

# Chapter12 - Chapter 12 Inference for One-Way ANOVA and...

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1 Chapter 12 Inference for One-Way ANOVA and Comparing the Means Learning goals for this chapter: Know how one-way ANOVA and 2-sample comparison of means techniques are related. Test the standard deviations to see if it is appropriate to pool the variances. Understand why it is important to pool the variances in one-way ANOVA. Explain and check the assumptions for doing one-way ANOVA. Calculate 2 R and the estimate for . Write the correct hypotheses (includ ing the words “population mean”) for one - way ANOVA. Use the F test statistic and P-value from SPSS to perform the one-way ANOVA test. State the conclusion to a one-way ANOVA test in terms of the story. Know when to use a Bonferroni multiple comparisons test. Use SPSS to perform the Bonferroni multiple comparisons test and interpret the output (both P-values and confidence intervals). State the conclusions to a Bonferroni multiple comparisons test in terms of the story. Interpret side-by-side boxplots and means plots in terms of the story. Recognize the response variable, factors, number of levels for each factor, and the total number of observations for a story. Identify from reading a story whether the scenario is one-way ANOVA. Use One-Way ANOVA when you have one categorical and one quantitative variable and you want to compare the means. If the categorical variable has 2 groups (gender = male or female, for example), use Ch. 7 two-sample comparison of means t-test. If the categorical variable has more than 2 groups (eye color = blue, brown, black, green, hazel, other), then use Ch 12 one-way ANOVA. ANOVA : ANalysis Of Variance: the method for comparing several means One-way ANOVA: F test for H 0 : 1 = 2 =. . . = I (all the population means are equal) H a : not all the population means are equal (at least one is different)

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2 Is there at least one population mean that is statistically significantly different from the others? When you first approach a problem which involves comparing more than 2 groups, here is what you should do: 1. Find the size ( n ), sample mean, and sample standard deviation of each group. You can then plot the means on a graph. Do histograms of each group to look for outliers and overall shape. 2. Find the 5-number summary (Min, Q1, Median, Q3, Max) for each group, and do side-by-side box plots to see how much overlap there is between the groups.
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