Then one can decide whether or not the evidence provided should be implemented in practice or used to guide future studies. This article will help providers determine the likelihood of type I or type II errors and judge adequacy of statistical power. Like β, power can be difficult to estimate accurately, but increasing the sample size always increases power.Healthcare professionals, when determining the impact of patient interventions in clinical studies or research endeavors that provide evidence for clinical practice, must distinguish well-designed studies with valid results from studies with research design or statistical flaws. You can see from Figure 1 that power is simply 1 minus the Type II error rate (β). The Type II error rate for a given test is harder to know because it requires estimating the distribution of the alternative hypothesis, which is usually unknown.Ī related concept is power-the probability that a test will reject the null hypothesis when it is, in fact, false. The Type I, or α (alpha), error rate is usually set in advance by the researcher. Type I and Type II errors are inversely related: As one increases, the other decreases. If the alternative hypothesis is actually true, but you fail to reject the null hypothesis for all values of the test statistic falling to the left of the critical value, then the area of the curve of the alternative (true) hypothesis lying to the left of the critical value represents the percentage of times that you will have made a Type II error.įigure 1.Graphical depiction of the relation between Type I and Type II errors, and the power of the test. In order to graphically depict a Type II, or β, error, it is necessary to imagine next to the distribution for the null hypothesis a second distribution for the true alternative (see Figure 1). For this reason, the area in the region of rejection is sometimes called the alpha level because it represents the likelihood of committing a Type I error. In choosing a level of probability for a test, you are actually deciding how much you want to risk committing a Type I error-rejecting the null hypothesis when it is, in fact, true. Table 1 presents the four possible outcomes of any hypothesis test based on (1) whether the null hypothesis was accepted or rejected and (2) whether the null hypothesis was true in reality.Ī Type I error is often represented by the Greek letter alpha (α) and a Type II error by the Greek letter beta (β ). These two errors are called Type I and Type II, respectively. You can err in the opposite way, too you might fail to reject the null hypothesis when it is, in fact, incorrect. Even if you choose a probability level of 5 percent, that means there is a 5 percent chance, or 1 in 20, that you rejected the null hypothesis when it was, in fact, correct. If the likelihood of obtaining a given test statistic from the population is very small, you reject the null hypothesis and say that you have supported your hunch that the sample you are testing is different from the population.īut you could be wrong. You have been using probability to decide whether a statistical test provides evidence for or against your predictions. Quiz: Test for Comparing Two Proportions.Quiz: Test for a Single Population Proportion.Test for a Single Population Proportion.Quiz: Two-Sample t-test for Comparing Two Means.Two Sample t test for Comparing Two Means.Quiz: Two-Sample z-test for Comparing Two Means.Quiz: Introduction to Univariate Inferential Tests.Two-Sample z-test for Comparing Two Means. Quiz: Point Estimates and Confidence Intervals.Point Estimates and Confidence Intervals.Quiz: Normal Approximation to the Binomial.Quiz: Populations, Samples, Parameters, and Statistics.Populations, Samples, Parameters, and Statistics.Quiz: Introduction to Numerical Measures.
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