Statistical Methods

Review.

Prof. Johnson — Fri, 10 Dec 2010 20:09:46 +0000

Today gave a quick overview of the final examination and distributed a study sheet (downloadable from Blackboard).

Inference with regression.

Prof. Johnson — Wed, 08 Dec 2010 21:32:16 +0000

Today we focused on statistical inference with regression. As in other scenarios, we can estimate parameters, make confidence intervals for parameters, and conduct tests concerning parameters. Another kind of prediction that is new however is prediction. A regression model can be used to predict the unknown value of a response variable. A confidence interval for this prediction is called a prediction interval.

Introduction to regression.

Prof. Johnson — Mon, 06 Dec 2010 21:09:02 +0000

This week we’ll be doing a quick overview of regression. I talked the idea of a statistical relationship between variables, by expressing the mean of a response variable as a mathematical function of the value of an explanatory variable. Linear regression uses a line as this function. We started talking about how to estimate the parameters of the regression line using the data and the concept of least squares.

ANOVA with more than one factor: main effects, interactions, and block designs.

Prof. Johnson — Fri, 03 Dec 2010 20:48:37 +0000

Today we considered that ANOVA can be generalized to consider relatively complicated designs with two or more factors. In a two-way design, we can make inferences concerning the main effects of each factor, as well as their interaction. This partitions the between-groups variability into three distinct sources. If a factor is made from a preexisting characteristic of the units, then it can be used as a a blocking variable in what is sometimes known as a block design. The intention of a blocking variable is to control for an important source of variability.

Multiple comparisons.

Prof. Johnson — Wed, 01 Dec 2010 20:49:45 +0000

Today after reviewing the three assumptions underlying inferences from ANOVA, I introduced the technique of multiple comparisons — namely the so-called Fisher’s method. I also discussed the issue of the familywise error rate in the context of multiple comparisons.

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

Prof. Johnson — Mon, 29 Nov 2010 20:49:14 +0000

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.

Prof. Johnson — Fri, 19 Nov 2010 20:26:49 +0000

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.

Prof. Johnson — Mon, 15 Nov 2010 23:26:48 +0000

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.

Prof. Johnson — Fri, 12 Nov 2010 19:06:08 +0000

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.

Prof. Johnson — Wed, 10 Nov 2010 19:03:05 +0000

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.