Outline for Our Day with Statistics
Today, we’re going to spend the entire day talking about statistics. We’ll learn how to apply various statistical procedures to different musical problems.
We’ll start off by talking about measurement. Recall that there are two reasons for measuring: (1) To allow us to recognize when we are wrong (i.e., “We recognize failure by drawing a line in the sand.”) (2) To discover new phenomena that are otherwise invisible.
We’ll define what is meant by measurement. We’ll discuss some limitations of measurement and consider the main criticisms against measurement. We’ll see that there is broad value in measuring things that at first might seem impossible, or at least highly questionable.
The field of statistics is broadly divided into two: (1) descriptive statistics, and (2) inferential statistics. As you might imagine, descriptive statistics allow us to describe things. Inferential statistics is used to test hypotheses. Both descriptive and inferential statistics are used in exploratory research. But hypothesis testing relies exclusively on inferential statistics.
Inferential statistics is itself divided into two: (1) frequentist inference, and (2) Bayesian inference. Frequentist statistics are by far the most commonly used statistics in research—and that will be our exclusive focus in this workshop. However, Bayesian statistics have become increasingly important, and you should at least be aware that there are other approaches to statistics than what we will cover here.
We’ll cover the basics of descriptive statistics, including familiar concepts (such as an “average”), and related concepts like median and mode. Other descriptive concepts will include measures of variation such as range and standard deviation.
Yesterday, we saw that that there are four different kinds of measurement scales — nominal, ordinal, interval, and ratio scales. Today, we’ll see that, depending on the measurement scale, it may be necessarily to use different statistical methods.
We’ll describe in detail the logic behind a statistical test.
We’ll define the concept of statistical significance, and show you one way of calculating it.
We’ll teach you how to perform a chi-square test, and we’ll give you a good number of exercises so that you can feel confident doing this inferential test.
When you read an empirical research paper, you often see a statement followed in parentheses by a string of numbers and funny Greek letters: today we’ll teach you the basics of how to interpret the meaning of these things.
This afternoon, we’ll hear a guest lecture by Professor Josh Albrecht from Mary Hardin Baylor University in Texas. Josh will lead us through some advanced statistical methods, notably multiple regression, cluster analysis, factor analysis, multi-dimensional scaling. and modeling. Josh will walk you through some sample research projects in music that make use of these methods. The purpose will be to show you some of the musical things you can do with statistics rather than teaching you how to do them.
Finally, we’ll review the homework reading.
Our aim today is two-fold: One is to get your feet wet and to teach you how to perform a specific statistical test. The test you’ll learn is one of the most robust tests — a test that can be performed in a wide variety of circumstances with lots of different data. Moreover, it is a test that you can calculate with pen-and-paper, without having to use a computer.
Our second aim is to give you the lay-of-the-land: to introduce you to the broad sweep of what’s possible with statistics.