BUS 308 Week 3 Lecture 1 Examining Differences - Continued Expected Outcomes After reading this lecture, the student should be familiar with: 1. Issues around multiple testing 2. The basics of the Analysis of Variance test 3. Determining significant differences between group means 4. The basics of the Chi Square Distribution. Overview Last week, we found out ways to examine differences between a measure taken on two groups (two-sample test situation) as well as comparing that measure to a standard (a one-sample test situation). We looked at the F test which let us test for variance equality. We also looked at the t-test which focused on testing for mean equality. We noted that the t-test had three distinct versions, one for groups that had equal variances, one for groups that had unequal variances, and one for data that was paired (two measures on the same subject, such as salary and midpoint for each employee). We also looked at how the 2-sample unequal t-test could be used to use Excel to perform a one-sample mean test against a standard or constant value. This week we expand our tool kit to let us compare multiple groups for similar mean values. A second tool will let us look at how data values are distributed – if graphed, would they look the same? Different shapes or patterns often means the data sets differ in significant ways that can help explain results. Multiple Groups As interesting as comparing two groups is, often it is a bit limiting as to what it tells us. One obvious issue that we are missing in the comparisons made last week was equal work. This idea is still somewhat hard to get a clear handle on. Typically, as we look at this issue, questions arise about things such as performance appraisal ratings, education distribution, seniority impact, etc. Some of these can be tested with the tools introduced last week. We can see, for example, if the performance rating average is the same for each gender. What we couldn’t do, at this point however, is see if performance ratings differ by grade, do the more senior workers perform relatively better? Is there a difference between ratings for each gender by grade level? The same questions can be asked about seniority impact. This week will give us tools to expand how we look at the clues hidden within the data set about equal pay for equal work. ANOVA So, let’s start taking a look at these questions. The first tool for this week is the Analysis of Variance – ANOVA for short. ANOVA is often confusing for students; it says it analyzes variance (which it does) but the purpose of an ANOVA test is to determine if the means of different groups are the same! Now, so far, we have considered means and variance to be two distinct characteristics of data sets; characteristics that are not related, yet here we are saying that looking at one will give us insight into the other. The reason is due to the way the variance is an.