Monday, August 25, 2014

Welcome to QM I for Fall 2014, and, for those of you who haven't been in school here in the past, welcome to Texas Tech! You'll be visiting this welcoming page a lot, as it contains the links for our lecture notes.

I'll do my best to provide a lot of practical, real-world exercises in analyzing data, and I'll try to keep things fun. This passage from a book I read several years ago, Coincidences, Chaos, and All That Math Jazz, by Edward B. Burger and Michael Starbird, provides a concise overview of what statistics can offer:

Statistics can help us understand the world. It is a powerful and effective tool for placing economic, social welfare, sports, and health issues into perspective. It molds data into digestible morsels and shows us a measured way to look at situations that have either random or unknown features. But we must use common sense when applying statistics or other tools that draw on our experience of the world to shape data into meaningful conclusions (p. 60).

In addition, the following article sets forth some goals for what you should learn in this class (and other classes). We can access this article via the Texas Tech Library website or Google Scholar.

Utts, J. (2003). What educated citizens should know about statistics and probability. American Statistician, 57(2), 74-79.

LECTURE NOTES (asterisked [*] pages are from my undergraduate research-methods class).

Units of analysis*

Sampling*

Types of Measures*

Visual depictions of a data distribution (examples):
  • Histograms (overview; determining interval/bin widths; SPSS instructions here and here). UPDATE 9/10/14: King and Minium (2003) offer some advice on interval widths and the appearance of histograms, citing the "convention that the height of the figure should be about three-quarters of the width." Also, "When we have relatively few cases and wish to see if a pattern exists, we can often reduce irregularity due to chance fluctuation by using fewer class intervals than usual" (pp. 56-57).
  • Frequency tables (click here and then select output), which contain similar information to histograms; the cumulative percentages also are roughly similar to percentiles (for a given score, you can see what percent of the sample falls below it)
  • Shapes of distributions
  • As a class exercise, we will attempt to reproduce via SPSS this histogram of U.S. Presidents' ages upon assuming office (note that Grover Cleveland, who served two non-consecutive terms is counted as being "two presidents," the 22nd and 24th)
Descriptive statistics:* Central tendency (mean, median, and mode) and spread (standard deviation); moments of a distribution; and z-scores (here, here, here, and here)

Probability (here and here)

Correlation and significance-testing

t-tests

Chi-square

Non-parametric statistics

Statistical power

Confidence intervals