Introductory Statistics

Inference for Several Means (ANOVA) Intro to ANOVA Hypothesis Testing Checking Requirements and Descriptive Statistics

Quantitative Procedures Tree Quantitative Procedures One SampleTwo Samples2+ Samples σ Known (1)σ Unknown (2) σ Unknown, Paired Samples (3) σ Unknown, Independent Samples (4) ?

Quantitative Procedures Tree Quantitative Procedures One SampleTwo Samples2+ Samples σ Known (1)σ Unknown (2) σ Unknown, Paired Samples (3) σ Unknown, Independent Samples (4) ANOVA (5)

Analysis of Variance (ANOVA) ANOVA – Analysis of Variance Compares Sample Means – HUH??!!! ANOVA compares 1) the variation between each of the sample means and 2) the variation within each of the samples. ANOVA tests whether several populations have the same mean by comparing how far apart the sample means are with how much variation there is within the samples. Group 1=X Group 2=O Example 1. XXXXXXX OOOOOOO MinMax Variation Between Sample is larger than variation within Samples, so the means appear to be different Example 2. XOXX OXOX OXXO XXOO OOXX MinMax Variation Between Sample is similar to variation within Samples, so the means appear to be similar

F distribution Here is a brief summary of the characteristics of the F-distribution: It is right skewed. The values of F are never negative. The P-value for the ANOVA test is the area in the right tail. We will never divide the area in the tail.

Analysis of Variance (ANOVA) The Analysis of Variance F statistic for testing equality of several means has this form: F = variation among the sample means ∕ variation among individuals in the same sample Similar to other Test Statistics (e.g. Z-Score, t statistic), as F gets further away from zero, the greater likelihood that the value becomes an “unusual result” Variation among sample means Variation among individuals in the same sample

Inference for Several Means (ANOVA) Intro to ANOVA Hypothesis Testing Checking Requirements and Descriptive Statistics

Steps to Hypothesis Testing – Independent Samples

Steps to Hypothesis Testing – ANOVA

Hypothesis Testing – ANOVA (Example)

Inference for Several Means (ANOVA) Intro to ANOVA Hypothesis Testing Checking Requirements and Descriptive Statistics

Requirements to Check and Descriptive Statistics Before Doing ANOVA Requirements to Check for ANOVA procedure The all samples are from Simple Random Sampling The samples are independent The populations have the same variances (check if largest standard deviation is no more than two times the smallest standard deviation ) The data are normally distributed for each group (use Q-Q Plots) Descriptive Statistics to Use with Data Numerical – Sample Size, Sample Mean and Standard Deviation from all samples Graphical – Histogram or boxplots from all groups