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.
Which of the following describes a Type II error? You make a Type II error when the null hypothesis is false but you fail to reject it because your data couldn't detect it, just by chance.
probability of a type II error equals beta. the probability of NOT making a type II error is 1.00 - beta.
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.
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. A p-value of 0.05 indicates that you are willing to accept a 5% chance that you are wrong when you reject the null hypothesis.
If your test statistic is positive, first find the probability that Z is greater than your test statistic (look up your test statistic on the Z-table, find its corresponding probability, and subtract it from one). Then double this result to get the p-value.
The power of the test is the sum of these probabilities: 0.942 + 0.0 = 0.942. This means that if the true average run time of the new engine were 290 minutes, we would correctly reject the hypothesis that the run time was 300 minutes 94.2 percent of the time.
The probability of error is similarly distinguished.
- For a Type I error, it is shown as α (alpha) and is known as the size of the test and is 1 minus the specificity of the test.
- For a Type II error, it is shown as β (beta) and is 1 minus the power or 1 minus the sensitivity of the test.
Type 1 errors have a probability of “α†correlated to the level of confidence that you set. A test with a 95% confidence level means that there is a 5% chance of getting a type 1 error.
The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. As the formula shows, the z-score is simply the raw score minus the population mean, divided by the population standard deviation.
If your statistical test was significant, you would have then committed a Type I error, as the null hypothesis is actually true. In other words, you found a significant result merely due to chance. The flipside of this issue is committing a Type II error: failing to reject a false null hypothesis.
There is a way, however, to minimize both type I and type II errors. All that is needed is simply to abandon significance testing. If one does not impose an artificial and potentially misleading dichotomous interpretation upon the data, one can reduce all type I and type II errors to zero.
A Type II error is rejecting the null when it is actually true.
A type I error occurs when the null hypothesis is valid but rejected. A type II error occurs when the null hypothesis is false, but fails to be rejected. Because the null hypothesis was true, but rejected, they made a Type I error.
What happens to the probability of making a Type II error, β, as the level of significance, α, decreases? Why? the probability increases. Type I and Type II errors are inversely related.
Considering this nature of statistics science, all statistical hypothesis tests have a probability of making type I and type II errors. Usually, the significance level is set to 0.05 (5%), implying that it is acceptable to have a 5% probability of incorrectly rejecting the true null hypothesis.
Of course you wouldn't want to let a guilty person off the hook, but most people would say that sentencing an innocent person to such punishment is a worse consequence. Hence, many textbooks and instructors will say that the Type 1 (false positive) is worse than a Type 2 (false negative) error.
β = probability of a Type II error = P(Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false. (1 − β) is called the Power of the Test. α and β should be as small as possible because they are probabilities of errors.
