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

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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.

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.