A type 1 error is also known as a false positive and occurs when a researcher incorrectly rejects a true null hypothesis. The probability of making a type I error is represented by your alpha level (α), which is the p-value below which you reject the null hypothesis.
The probability of making a Type II error. 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. And the probability of making a Type II error gets smaller, not bigger, as sample size increases.
A type I error (false-positive) occurs if an investigator rejects a null hypothesis that is actually true in the population; a type II error (false-negative) occurs if the investigator fails to reject a null hypothesis that is actually false in the population.
As the sample size gets larger, the z value increases therefore we will more likely to reject the null hypothesis; less likely to fail to reject the null hypothesis, thus the power of the test increases.
The probability of committing a type II error is equal to one minus the power of the test, also known as beta. The power of the test could be increased by increasing the sample size, which decreases the risk of committing a type II error.
A type I error is a kind of fault that occurs during the hypothesis testing process when a null hypothesis is rejected, even though it is accurate and should not be rejected. In hypothesis testing, a null hypothesis is established before the onset of a test. These false positives are called type I errors.
However, smaller alpha levels result in larger sample sizes. But the revserse is also true: larger alpha levels lead to smaller sample sizes. For example, an alpha level of 10% will need a much smaller sample than a test using α = 1%.
The relationship between margin of error and sample size is simple: As the sample size increases, the margin of error decreases. If you think about it, it makes sense that the more information you have, the more accurate your results are going to be (in other words, the smaller your margin of error will get).
Unlike significance tests, effect size is independent of sample size. Statistical significance, on the other hand, depends upon both sample size and effect size. Sometimes a statistically significant result means only that a huge sample size was used.
Caution: The larger the sample size, the more likely a hypothesis test will detect a small difference. So the probability of rejecting the null hypothesis when it is true is the probability that t > tα, which we saw above is α. In other words, the probability of Type I error is α.
A Type I error is when we reject a true null hypothesis. Lower values of α make it harder to reject the null hypothesis, so choosing lower values for α can reduce the probability of a Type I error. So using lower values of α can increase the probability of a Type II error.
The probability of a type 1 error (rejecting a true null hypothesis) can be minimized by picking a smaller level of significance α before doing a test (requiring a smaller p -value for rejecting H0 ).
A type II error occurs when the null hypothesis is false, but erroneously fails to be rejected. Let me say this again, a type II error occurs when the null hypothesis is actually false, but was accepted as true by the testing. A Type II error is committed when we fail to believe a true condition.
While it is impossible to completely avoid type 2 errors, it is possible to reduce the chance that they will occur by increasing your sample size. This means running an experiment for longer and gathering more data to help you make the correct decision with your test results.
How to Avoid the Type II Error?
- Increase the sample size. One of the simplest methods to increase the power of the test is to increase the sample size used in a test.
- Increase the significance level. Another method is to choose a higher level of significance.
