Understanding Type II errors, or false negatives, in hypothesis testing is essential for accurate statistical analysis. These errors occur when a true effect exists but the test fails to detect it, leading to the incorrect acceptance of the null hypothesis. The probability of a Type II error is represented by eta, and reducing this error increases the test's power. Factors like sample size and test sensitivity play crucial roles in minimizing the risk of Type II errors and ensuring reliable results.
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Type II errors occur when the null hypothesis is incorrectly accepted as true
Formula for Probability of Type II Errors
The probability of a Type II error is the chance that the test statistic will not fall into the rejection region even though the null hypothesis is false
Power of the Test
The power of the test is the probability of correctly rejecting a false null hypothesis
Sample Size
Larger sample sizes reduce the likelihood of Type II errors and increase the power of the test
Test Design
The balance between Type I and Type II errors is a critical consideration in the design of hypothesis tests
Power is the probability of correctly rejecting a false null hypothesis
Sample Size
Larger sample sizes increase the power of the test
Test Design
The sensitivity of measurements and the significance level can also affect the power of a test
Power is a critical aspect of test design as it determines the likelihood of detecting true effects
Larger sample sizes reduce the likelihood of Type II errors
Sample size must be carefully considered in relation to the desired power of the test and practical constraints of the study
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A ______ error, or false negative, happens when a statistical test doesn't identify an actual difference that exists.
Type II
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Determinants of Type II error probability
Influenced by true population parameter, unknown in practice
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Type II error in hypothesis testing
Failing to reject null hypothesis when it is actually false
