501_Lecture_12

# 501_Lecture_12 - Section 12.1 One-Way Analysis of Variance...

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Section 12.1 One-Way Analysis of Variance (ANOVA)

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Inference for One-Way ANOVA Comparing means for several groups Format of data An analogy: two sample t-statistic ANOVA hypotheses and model Understanding two types of variation Estimates of population parameters Testing hypotheses for one-way ANOVA The ANOVA table and the F-test
Inference for One-Way ANOVA Values of a quantitative random variable are of interest score, cholesterol level, etc. We will compare several groups described or labeled by values of one (typically) categorical random variable gender, age group, etc. This is One-Way ANOVA Compare means of several groups Question: The difference between the group means, are they statistically significant?

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Typical data (Compare…) : Example 1 : Numbers of days for healing a standard wound (in an animal) for several treatments Example 2 : Wages of different ethnic groups in a company Example 3 : Lifetimes of different brands of tires If comparing means of two groups, ANOVA is equivalent to a 2-sample (two-sided) pooled t- test ANOVA allows for 3 or more groups
Recall: Two Populations, Unknown Population Standard Deviations Goal: test H 0 : μ 1 = μ 2 against H a : μ 1 ≠ μ 2 σ 1 , σ 2 are unknown but assumed to be equal The pooled t test statistic is given in 7.2 (p. 499) Then the ANOVA test statistic (denoted by an F) is the square of the t -statistic.

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Comparing groups’ means here:
To understand variability within and between groups: Graphical investigation: side-by-side box plots multiple histograms Whether the differences between the groups are significant depends on the difference in the means the standard deviations of each group the sample sizes

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Boxplots for groups: Are the means significantly different?
Reduced variability within each group Difference in means more plausible. (Still depends on sample sizes.)

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One-Way ANOVA hypotheses ANOVA tests the following hypotheses: H 0 : μ 1 = μ 2 = μ 3 = … = μ I (the means of all the groups are equal) H a : Not all the means are equal Does not say how or which ones differ
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## This note was uploaded on 02/20/2012 for the course STAT 501 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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501_Lecture_12 - Section 12.1 One-Way Analysis of Variance...

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