Analyst Application Survival Analysis
Sample Size and Power Calculations
The power of a hypothesis test is the probability of rejecting the null hypothesis when the null hypothesis is false. Ideally, you want the highest power attainable with the smallest sample size. Power and sample size calculations are crucial during the design phase of an experiment. With these preliminary computations, researchers can ensure a sample size sufficient enough to obtain significant conclusions.
The sample size tasks available in the Analyst Application enable you to determine the power of a test given the sample size or determine the sample size required to obtain a specified power. In addition to computing the power or sample size, you can produce plots of power versus sample size and add reference lines to these plots corresponding to specific values of power or sample size. These calculations can be made for a variety of situations, including t-tests, confidence intervals, studies of equivalence, and one-way ANOVA.
Confidence Intervals
The concept of power of a confidence interval is different from the power of a hypothesis test. First, you define the "precision" to be half the length of a two-sided confidence interval (or the distance between the endpoint and the parameter estimate in a one-sided interval). The power is achieved if the length of the two-sided interval is no more than twice the desired precision. However, a slight modification of the concept is used with confidence intervals. The power is considered to be the conditional probability that the desired precision is achieved, given that the interval includes the true value of the parameter of interest. The reason for the modification is that there is no reason for the interval to be particularly small if it does not contain the true value of the parameter.
Equivalence Testing
In the case of equivalence testing, a researcher is seeking to determine whether there exists significant evidence that two treatments are the same (equivalent). This is the opposite of traditional hypothesis testing, intended to determine if there is enough evidence to ascertain whether two treatments are significantly different. In a test of equivalence, equivalence is taken to be the alternative hypothesis, and the null hypothesis is nonequivalence. The power is the probability of accepting equivalence when the treatments are in fact equivalent.
One-Way ANOVA
Finally, in a one-way analysis of variance, the aim is to determine whether there is a signficant difference between more than two groups.
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