Review Question - QID 217718

The probability that an effect is detected given that an effect truly exists is known as the statistical power, or the true positive rate. The statistical power is calculated by: power = 1-beta; therefore, the researchers should maximize this quantity in order to maximize the probability that they detect the intervention's effect.

Given that the null hypothesis is false, the probability that a statistical test correctly rejects the null hypothesis is called the test’s statistical power. It is calculated as: power = 1-beta, where beta denotes the probability of a type 2 error, or false-negative rate. Before studies are conducted, a sample size estimation is often performed to determine the minimum number of participants required to achieve a certain (usually 80%) statistical power. Statistical power increases with sample size and effect size. Statistical power also varies with sample standard deviations. The smaller the standard deviation, the greater the statistical power.

Incorrect Answers:
Answer 1: 1-alpha is not typically calculated as a statistical quantity, but maximizing this value would minimize alpha. This would then decrease the false positive rate and increase the true negative rate. This is not related to the true positive rate (power).

Answer 3: Alpha is the probability of a type 1 error, or false-positive rate. Alpha is also known as the significance level and is determined prior to statistical testing. It is typically set to 0.05, denoting the highest tolerable false positive rate. Maximizing alpha would increase the false positive rate.

Answer 4: Beta is the probability of a type 2 error, or false-negative rate. It is related to the statistical power by the following equation: power = 1-beta. Maximizing beta would increase the false-negative rate and decrease power such that the test would be less likely to detect an effect if an effect truly exists.

Answer 5: Standard deviation (SD) is a quantity that is determined by the characteristics of the sample being studied. It is a measure of the spread of the data around the mean and can be calculated for any data set given the mean and number of observations: SD = sqrt(sum[x-mean]/n), where sum[x-mean] represents the summation of this quantity across all values of x in the data. As the SD of the variable being measured increases, statistical power would decrease.

Bullet Summary:
Statistical power is defined as the true positive rate, defined as power = 1-beta.