Fall 2023 HDFS 5349 Quantitative Methods I

Welcome to QM I, the department's introductory statistics class. I'm a bit unusual in using a blog to organize class materials, but I think it's worked well over the years. Also, for those of you who haven't been in school here, 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:

• Histograms (overview). Your textbook authors King and colleagues (2018) offer some advice on interval widths and the appearance of histograms, noting that "it is customary to make the height of the distribution about  three-quarters of the width" (pp. 32-33). To adjust the width of the columns, click on histogram in your output, then go to "Options," "Un-bin Element," and "Bin Element," then in small square in upper-right of screen, under "X Axis," select "Custom," and then enter desired interval width.
• Frequency tables 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

Writing Up Statistical Results in APA Style

Formula for a Paired t-Test

A paired t-test incorporates the possibility that the two variables whose means are being compared may also be correlated. In the following example, participating back-pain patients receive actual medication for one stretch of, say, six weeks and placebo (sugar pills) for a different stretch of six weeks. Ideally, the patients and medical staff who directly provide the pills to the patients would not know what kind of pill was being provided (i.e., a double-blind design) and the order of delivery -- medication then placebo or placebo then medication -- would be varied at random.

The focus of the paired t-test is, of course, whether participants' average reported pain while taking actual medication differs from their average reported pain under placebo. However, because patients with the most severe initial pain might report relatively high pain under medication and even higher pain under placebo, whereas patients with the mildest initial pain might report relatively low pain under placebo and even lower pain while receiving medication, patients' pain reports under medication and placebo could be positively correlated (see following graphic).

As shown in the following screenshot from this University of Georgia webpage, the correlation r between the two variables X and Y (highlighted) enters the paired t-test formula for comparing means.

Another document goes into additional depth regarding the paired/correlatedt-test, including implications of the correlation "r" being included in the formulation. As it notes, a larger correlation between the two variables will increase the size of the (absolute) t.

I've also created a graphic to interpret the SPSS output of a paired t-test, emphasizing the t-test comparison of means but also showing where the correlation between the two variables appears.