Chapter 9

The Single-Sample t Test

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The Distributions

  • Estimating Population Standard Deviation from a Sample
  • Calculating Standard Error for the t Statistic
  • Using Standard Error to Calculate the t Statistic

The Single-Sample Test

  • The t Table and Degrees of Freedom
  • The Six Steps of the Single-Sample t Test
  • Calculating a Confidence Interval for a Single-Sample t Test
  • Calculating Effect Size for a Single-Sample t Test

Next Steps: Dot Plots

BEFORE YOU GO ON

  • You should know the six steps of hypothesis testing (Chapter 7).
  • You should know how to determine a confidence interval for a z statistic (Chapter 8).
  • You should understand the concept of effect size and know how to calculate Cohen’s d for a z test (Chapter 8).

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A Statistical Test for Almost Any Topic The single-sample t test allows you to compare data about one relatively small group to what is already known about a larger group. Single-sample t tests have been used to study how many items we can remember, the frequency of migraine headaches, and the spelling skills of Braille readers.
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Try to figure out what these three studies have in common: (1) Mary Richardson and Diann Reischman (2011) at Grand Valley State University in Michigan compared their students’ short-term memory to the normal limitation on everyone’s short-term memory that George Miller reported in 1956: Most people can only remember seven unrelated items, plus or minus two; (2) public health researchers in Milan, Italy (Raggi et al., 2011), were worried about the disabling migraine headaches in women showing up in their clinic, so they compared the effects of headaches from their sample to national norms; (3) Christine Clark and Julia Stoner (2008), who both work in special education at Illinois State University, wanted to compare the spelling skills of a sample of blind Braille readers to a normative sample of readers whose spelling abilities had already been measured using the Test of Written Spelling (TWS-4).

What these studies do not have in common is what was studied: memory, migraines, and spelling ability. That diversity of topics should get you pretty excited because it suggests that the statistical test you are about to learn empowers you to study almost anything! What are you interested in? You may be able to discover something new by using the statistical test you learn about in this chapter. What each of these studies has in common is how each topic was studied. They all compared their smaller sample with normative data from a much larger population–using the single-sample t test.

MASTERING THE CONCEPT

9.1: We use a t distribution instead of the z distribution when sampling requires us to estimate the population standard deviation from the sample standard deviation.

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