Week 5 (Chapter 12) PDF

Chapter 12 Analysis of Variance Job of the Week https://www.justice.gov/opa/pr/us-attorney-announces-federal-charges-against-47- defendants-250-million-feeding-our-future https://www.indeed.com/jobs?q=fraud+detection&l=Cincinnati%2C+OH&from=sea rchOnDesktopSerp&vjk=2060d146b8c81315 https://www.in...

Chapter 12 Analysis of Variance Job of the Week https://www.justice.gov/opa/pr/us-attorney-announces-federal-charges-against-47- defendants-250-million-feeding-our-future https://www.indeed.com/jobs?q=fraud+detection&l=Cincinnati%2C+OH&from=sea rchOnDesktopSerp&vjk=2060d146b8c81315 https://www.indeed.com/jobs?q=fraud&l=Dayton%2C+OH&from=searchOnDeskto pSerp&vjk=0dfcd5e22d5fce2f&advn=9451740657700492 ANOVA - Analysis of Variance (ANOVA) allows statistical comparison among samples taken from many populations. - The comparison is typically the result of an experiment - e.g. trying the same test at many different locations - The factor is the major thing that differs between each experiment (e.g. location) - The specific values of a given factor are called the levels. - The levels cause the variable under study to be divided into groups. ANOVA - Examples of types of experiments that can conducted when performing ANOVA analysis: - Completely Randomized Design - an experiment with only one factor - Factorial Design - more than one factor is considered - Randomized Block Design - where groups are also divided into subgroups - The purpose of ANOVA is to reach conclusions about possible differences among the means of each group. Completely Randomized Design - Analyzes a single factor - Two step process: - Step 1: Is there a significant difference among the group means? (Null hypothesis is that there is not) - Step 2: Determine which groups contain means that are significantly different from the other group means. - For analyzing variation, the goal is to separate the total variation into variation that is due to differences among the groups and variation that is due to differences within the groups. Completely Randomized Design - One Way ANOVA - Sum of Squares Total (SST) is the total variation - Within-Group Variation (SSW) is the variation measured within each group - Among-Group Variation (SSA) is the variation measured among the groups - SST = SSA + SSW Completely Randomized Design - One Way ANOVA - The grand mean is the mean of the means of each group. - Formulas for SST, SSA, and SSW are on pages 519 and 520. - Sum of squares among groups has c-1 degrees of freedom (c = number of groups) - Sum of squares within groups has n-c degrees of freedom (n = number of items in all groups) ANOVA Video MSA / MSW MSW = Mean Square Within MSA = Mean Square Among MSW = SSW / ( n - c ) MSA = SSA / ( c - 1 ) F test for Differences Among More Than Two Means - You use the F test to determine if there is significant difference among the group means. - The F test is the ratio of MSA divided by MSW - The null hypothesis is that there is no significant difference among the means. - You reject the null hypothesis if the F test result is above the upper tail critical value. - Critical value can be looked up in table A.6 (page 877) - c - 1 degrees of freedom in the numerator - n - c degrees of freedom in the denominator - Formula on page 521 ANOVA Summary Table - Used to summarize the results of a one-way ANOVA. - Example on page 522 F test assumptions 1) Randomness and Independence a) Random samples were selected from the c groups 2) Normality a) Normality of the c groups from which the samples are selected is assumed 3) Homogeneity of variance a) The population variances of the c groups are equal Weekly Activity For this activity, we are going to survey multiple groups of students in this class and determine the “among group” and “within group” variance. - For your own group, take a sampling of the number of letters in each member’s full name (first, middle, last) - Ask a member from at least 4 other groups their values - Create a spreadsheet of the 5 group’s values (number of letters in each group members full name) - Calculate the “among group” variation and the “within group” variation. - Do you think that what group you are assigned has any relationship to the number of letters in your full name? - Write your ANOVA summary table, F critical value and conclusion on the board. - Submit to Dropbox on Pilot for a grade