Is a Type I or Type II error more likely if a 0.05 level is used? Explain.

Question

Quizplus · Accepted Answer

The Answer is The likelihood of committing a Type I or Type II error depends on the significance level (alpha) chosen for a statistical test, as well as the effect size, sample size, and the true state of the population being tested.

A Type I error, also known as a false positive, occurs when the null hypothesis is true, but we incorrectly reject it. This means we are seeing an effect or difference when there is none. A Type II error, also known as a false negative, occurs when the null hypothesis is false, but we fail to reject it, meaning we are not seeing an effect or difference when there is one.

When a 0.05 level (alpha = 0.05) is used, it means that there is a 5% chance of committing a Type I error if the null hypothesis is true. This is because the 0.05 level is the threshold for statistical significance; if the p-value obtained from the test is less than 0.05, we reject the null hypothesis.

Whether a Type I or Type II error is more likely cannot be determined solely by the alpha level. However, setting a lower alpha level (such as 0.01) would reduce the likelihood of committing a Type I error but increase the likelihood of a Type II error, assuming all other factors are constant. Conversely, setting a higher alpha level (such as 0.10) would increase the likelihood of committing a Type I error but decrease the likelihood of a Type II error.

The probability of committing a Type II error is denoted by beta (β), and the power of the test (1 - β) is the probability of correctly rejecting a false null hypothesis. To reduce the likelihood of a Type II error, researchers can increase the sample size, which increases the power of the test, or choose a larger effect size as the threshold for detecting a difference.

In summary, using a 0.05 level means that there is a 5% chance of committing a Type I error if the null hypothesis is true. Whether a Type I or Type II error is more likely also depends on other factors such as sample size, effect size, and the true state of the population. A balance between the risks of Type I and Type II errors must be considered when designing experiments and choosing significance levels.

Is a Type I or Type II Error More Likely