Chapter 9 Review of Concepts

The t Distributions

The t distributions are similar to the z distribution, except that in the former, we must estimate the standard deviation from the sample. When estimating the standard deviation, we make a mathematical correction to adjust for the increased likelihood of error. After estimating the standard deviation, the t statistic is calculated like the z statistic for a distribution of means. The t distributions can be used to compare the mean of a sample to a population mean when we don’t know the population standard deviation (single-sample t test), to compare two samples with a within-groups design (paired-samples t test—introduced in Chapter 10), and to compare two samples with a between-groups design (independent-samples t test—introduced in Chapter 11).

The Single-Sample t Test

Like z tests, single-sample t tests are conducted in the rare cases in which we have one sample that we’re comparing to a known population. The difference is that we only have to know the mean of the population to conduct a single-sample t test. There are many t distributions, one for every possible sample size. We look up the appropriate critical values on the t table based on degrees of freedom, a number calculated from the sample size. We can calculate a confidence interval and an effect size (Cohen’s d), for a single-sample t test. Dot plots are graphs that depict the shape of a sample’s distribution while also displaying every single data point in the sample. With dot plots, we can also include the scores of two or more samples directly above one another, which allows for comparisons of distributions.