Statistical Principles: Errors in Hypothesis Testing Page 1/3
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Q1. Which of the following statement(s) about Type II errors for a hypothesis test is False?
False statements are c) and d). c) A Type II error represents a false negative. One way to remember this is that II is similar to N, a \ has been added to II get an N, whereas a Type I error is similar to P, a ⊃ has been added to I to get P. d) A type II error (β) is typically set at 0.1 or 0.2 (occasionally quoted as a percentage 10% or 20%). Power is typically quoted as 80% or 90% and is 1 - β.
Q2. Which of the following statement(s) about Type I errors for a hypothesis test is True?
True statement is d). a) Probabilities for Type II error are called α (alpha). b) Type I error is often set at 5% or 0.05 but sometimes we use other values, for example 1% or 0.01. This corresponds to 95% confidence. c) A Type I error represents a false positive. So we conclude a significant effect even though no true effect exists. One way to remember this is that I is similar to P, a ⊃ has been added to I get a P, whereas a Type II error is similar to N, a \ has been added to II to get N.
Q3. A Pregnancy test gave a negative result for a woman who is in fact pregnant. This is an example of a:
The answer is b). This is an example of a False Negative which is a Type II error.
Q4. What does the expression 1- β (beta) represent?
The answer is c). 1- β (beta) represents the Power of the study. It is 1 minus the probability of the Type II error (β) which is usually set at 0.02 or 0.01 (20% or 10%). Thus Power is typically 80% or 90%.
Q5. Which of the following statement(s) would be True when trying to reduce the chance of making a Type II error in a situation where the primary outcome variable is a continuous measure?
The answers are b) and c). a) If the standard deviation is increased it means the amount of variation (size of error) is greater. We want the minimum amount of variation so the smaller the standard deviation the better. Remember the variance is the standard deviation squared. b) Increasing the size of the sample will reduce the amount of variation and improve the Power of the study. c) If you increase the probability of making one type of error (Type I or II), the probability of making the other type of error (Type I or II) decreases, assuming everything else stays the same. So if alpha is increased from 0.05 to 0.1, the probability of making a Type I error increases, an consequently the probability of making a Type II error decreases. d) If you increase the size of β (beta) from 0.10 to 0.20 you are increasing the chance of a False Negative and reducing the Power of the Study which is 1- β*100%. In an ideal world you choose have 100% power so β would be 0. If you would like to explore the topic further, you can use the CurveApplet from the Amazing Applications of Probability and Statistics by Tom Rogers.
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