Analysis of variance and the F-test for the equality of means.

Today I demonstrated the calculation of the between- and within-groups mean squares, the summary of the ANOVA in a table, and introduced the F-test for the equality of two or more means. This test is essentially an extension of the test for the equality of two means that we covered earlier.

The last take-home quiz was distributed today. You can download it from Blackboard as well. I also have a few spare copies that are in the pocket on my office door (Brink 417).

Introduction to ANOVA.

Today I introduced the statistical technique of the analysis of variance (ANOVA). ANOVA concerns the measurement of the sources of variability in a study where there are two or more groups of observations of a quantitative variable. We discussed the concepts of between-groups and within-groups variability, and the measurement of each using mean squares.

Read: 14.1, 14.2 (skip the section titled “ANOVA and Regression” starting on page 706), 14.3 (skip the section titled “Regression Models with Indicator Variables for Two-Way ANOVA” starting on page 715).

Simpson’s paradox and the ecological fallacy.

We reviewed Simpson’s paradox with another example, and then looked at what is sometimes called the ecological fallacy which is a related phenomenon. I discussed that the underlying problem in both cases is ignoring lurking/confounding variables, and I discussed ways to deal with lurking/confounding variables and some advantages and disadvantages to each.

Analysis of two-way tables of counts — continued, and Simpson’s paradox.

Today we considered a somewhat different design where there isn’t a clear explanatory or response variable, but we want to investigate if there is a significant relationship between two categorical variables where we have one sample of observations that we’ve classified on those variables. For this test of independence, I showed that we can estimate the expected counts in the same way as we did for the test of homogeneity.

We also discussed Simpson’s paradox in the context of the analysis of the relationship between categorical variables.

Read: 10.5, and pages 138-140.

Analysis of two-way tables of counts.

Today we focused on the analysis of the relationship between two categorical variables. Here we considered an application of the goodness-of-fit test to determine if two or more conditional distributions are the same (i.e., the test of homogeneity). By assuming that the populations conditional distributions are the same, we can estimate the expected counts from the data and use the test to determine if apparent differences among two or more sample conditional distributions are statistically significant.

Review of goodness-of-fit tests and an introduction to the analysis of the association between categorical variables.

Today we looked at another example of the use of a goodness-of-fit test to test for Hardy-Weinberg Equilibrium. I then introduced how we can use the same idea to determine if there is a statistical relationship between two categorical variables using an experiment that investigated the efficacy of four different therapies for treating clinical depression.

Homework: 11.1, 11.4, 11.9, 11.11, 11.13, 11.15, 11.17, 11.18.

Goodness-of-fit tests.

Today I introduced the idea of a goodness-of-fit test where a scientific hypothesis implies a statistical null hypothesis which can then be evaluated using a statistical test in the usual way. For the kind of data we are looking at now, I introduced the chi-square test statistic and sampling distribution.

Read: 11.1, 11.2.

Review of two-group inference.

Today we reviewed inference for the difference between two sample means. We considered statistical tests with and without the assumption that the population variances are (nearly) equal, and we considered how to deal with two dependent samples where the observations can be matched between samples as in a matched pairs design.