Chapter 8 Review of Concepts

Confidence Intervals

A summary statistic, such as a mean, is a point estimate of the population mean. A more useful estimate is an interval estimate, a range of plausible numbers for the population mean. The most commonly used interval estimate is the confidence interval, which can be created around a mean using a z distribution. The confidence interval provides the same information as a hypothesis test but also gives us a range of values.

Effect Size

Knowing that a difference is statistically significant does not provide information about the size of the effect. A study with a large sample might find a small effect to be statistically significant, whereas a study with a small sample might fail to detect a large effect. To understand the importance of a finding, we must calculate an effect size. Effect sizes are independent of sample size because they are based on distributions of scores rather than distributions of means. One common effect-size measure is Cohen’s d, which can be used when a z test has been conducted.

A meta-analysis is a study of studies in which the researcher chooses a topic, decides on guidelines for a study’s inclusion, tracks down every study on a given topic, and calculates an effect size for each. A mean effect size is calculated and reported, often along with a standard deviation, median, hypothesis testing, confidence interval, and appropriate graphs. A file drawer analysis can be performed to determine how many unpublished studies that failed to reject the null hypothesis must exist for the effect size to be rendered nonsignificantly different from zero.

Statistical Power

Statistical power is a measure of the likelihood that we will correctly reject the null hypothesis; that is, the chance that we will not commit a Type II error when the research hypothesis is true. Statistical power is affected most directly by sample size, but it is also affected by other factors. Researchers often use a computerized statistical power calculator to determine the appropriate sample size to achieve 0.80 statistical power.