OCTOBER 23
CONCEPTUALIZING PROBABILITY THORY

Schmidt, Ch. 8, "Probability: Measuring Uncertainty," 217-231.

Statistics courses in mathematics departments devote great attention to probability theory. Unfortunately, they often pay little attention to measuring variables and measuring relationships between variables, which we emphasize. Some knowledge of probability theory, however, is crucial to statistics, especially to statistical inference, which enables us to make predictions to populations based on data from samples of the population. This chapter will require close reading. Be sure you understand the addition and multiplication rules of probability.

OCTOBER 24

No optional session scheduled

OCTOBER 25
PROBABILITY DISTRIBUTIONS

Schmidt, Ch. 8, "Probability: Measuring Uncertainty," 231-243.
Schmidt, "Standard Scores," a selection from Chapter 4, "Variability," pp. 108-114

This chapter explains how to draw a random sample using a table of random numbers, which you've already done. In discussing what's a "random variable," Schmidt distinguishes between "discrete" and "continuous" variables, which you also have encountered. Learn what's meant by the "expected" value of a discrete random variable and a continuous one.

OCTOBER 26
SAMPLES AND POPULATIONS

NOTE: This is an
important session.
BE THERE!

Schmidt, Ch. 9, "Sampling: Choosing Some to Represent All," 250-267.

This reading is very important: Be sure to distinguish between the distribution of a variable in the population and the distribution as observed in a sample. That's easy enough to grasp, but you may have to work at imagining the (hypothetical) sampling distribution of means observed in an infinite number of samples. If you are a normal human being, you will find this notion of a "sampling distribution" difficult to understand at first, but you will grow to believe in it.

Assignment: At the beginning of the course, you created the file mystates. for your original sample of ten cases. Under Analyze in the SPSS Menu Bar, choose Descriptive Statistics (as before) but this time select Descriptives. Designed for what SPSS calls scale (continuous) variables, it gives measures of central tendency and dispersion without producing the unwanted frequency table.

• Run Desciptives on the % vote for G.W. Bush in 2000, requesting only these statistics under the Options: mean and standard deviation.
• BRING THIS OUTPUT TO CLASS ON THIS DAY. Because each of you had a sample of 10 cases from the universe of states, we will be able to generate a sampling distribution from your individual sample means as you call them out and as I record them on the blackboard.

OCTOBER 29
INFERRING FROM
SAMPLES TO
POPULATIONS

Schmidt, Ch. 12, "Parameter Estimation: Educated Guessing," 326-333.

I'll discuss different types of sampling and then explain the material covered in the Schmidt chapter: How to estimate to population parameters from sample statistics.