Video Transcript
and the question to say that to how the sample variance simply the likelihood of rejecting the null hypothesis and major in the value of corn. See, Alright, so here is the sequel to the meaning of the sample, minus the mean of the population divided by the standard deviation. Alright, so here, increasing though obedience of the sample, it will degrees the with the idea of the right. So when we increase the sample size, there is a degrees in the standard error or increase in the difference between the sample statistics and hypothesized parameter that is the p value reduces. That's making it more likely that we rejected the hypothesis. So when we increase the alpha, there is larger range for the p values of which we could reject the null hypothesis. Right? So which means in this case the correct option is option D. That is large variances degrees, both likelihood of rejecting the null and the value of the cones. Right? He writes that the answer for the question of this helps you. Thank you for watching.
The probability of not committing a Type II error is called the power of a hypothesis test.
Effect Size
To compute the power of the test, one offers an alternative view about the "true" value of the population parameter, assuming that the null hypothesis is false. The effect size is the difference between the true value and the value specified in the null hypothesis.
Effect size = True value - Hypothesized value
For example, suppose the null hypothesis states that a population mean is equal to 100. A researcher might ask: What is the probability of rejecting the null hypothesis if the true population mean is equal to 90? In this example, the effect size would be 90 - 100, which equals -10.
Factors That Affect Power
The power of a hypothesis test is affected by three factors.
- Sample size (n). Other things being equal, the greater the sample size, the greater the power of the test.
- Significance level (α). The lower the significance level, the lower the power of the test. If you reduce the significance level (e.g., from 0.05 to 0.01), the region of acceptance gets bigger. As a result, you are less likely to reject the null hypothesis. This means you are less likely to reject the null hypothesis when it is false, so you are more likely to make a Type II error. In short, the power of the test is reduced when you reduce the significance level; and vice versa.
- The "true" value of the parameter being tested. The greater the difference between the "true" value of a parameter and the value specified in the null hypothesis, the greater the power of the test. That is, the greater the effect size, the greater the power of the test.
Test Your Understanding
Problem 1
Other things being equal, which of the following actions will reduce the power of a hypothesis test?
I. Increasing sample size.
II. Changing the significance level from 0.01 to 0.05.
III. Increasing beta, the probability of a Type II error.
(A) I only
(B) II only
(C) III only
(D) All of the above
(E) None of the above
Solution
The correct answer is (C). Increasing sample size makes the hypothesis test more sensitive - more likely to reject the null hypothesis when it is, in fact, false. Changing the significance level from 0.01 to 0.05 makes the region of acceptance smaller, which makes the hypothesis test more likely to reject the null hypothesis, thus increasing the power of the test. Since, by definition, power is equal to one minus beta, the power of a test will get smaller as beta gets bigger.
Problem 2
Suppose a researcher conducts an experiment to test a hypothesis. If she doubles her sample size, which of the following will increase?
I. The power of the hypothesis test.
II. The effect size of the hypothesis test.
III. The probability of making a Type II error.
(A) I only
(B) II only
(C) III only
(D) All of the
above
(E) None of the above
Solution
The correct answer is (A). Increasing sample size makes the hypothesis test more sensitive - more likely to reject the null hypothesis when it is, in fact, false. Thus, it increases the power of the test. The effect size is not affected by sample size. And the probability of making a Type II error gets smaller, not bigger, as sample size increases.
Power analysis is important in experimental design. It is to determine a sample size required to discover an effect size, a measure of a change or a difference that are being tested, with a given degree of confidence. That means that the power (1- a type II error) of a statistical test involves with a sample size, a type I error, and an effect size. In my previous article, I explained how type I and type II errors are related: as a type I error (α )
increases corresponding type II error (β) decreases; thus the power increases. In…