P-Value

1. P-Value

2. Review Answers • Dr. Klucksky chose p0 = 50% because if his chickens have no predictive powers, he should expect their predictions to be accurate 50% of the time. • Because the p-value of 0.014 is low, he rejects the null hypothesis and accepts the alternate hypothesis that the chickens’ predictions are accurate more than 50% of the time. • Dr. Klucksky is 95% confident that between 51.1% and 67.4% of his chickens’ predictions are accurate. • 95% of samples will produce confidence intervals containing the true proportion of chicken predictions that are accurate.

3. P-Values Guide Our Decisions • If the p-value is low, • Reject the null hypothesis • Accept the alternate hypothesis • If the p-value is not low, • Fail to reject the null hypothesis But what does a p-value actually mean?

4. Assume the Null is True • Assume the population proportion really is p0. Many samples will have p-hats very close to the true p0. Some samples will have p-hats a little further away from the true p0. A few samples will have p-hats far away from the true p0. p0

5. Out of Every Possible Sample… • What is the probability of getting exactly your p-hat? • Technically, it’s zero. • What is the probability of getting your p-hat or weirder? • What is the probability of getting your p-hat ormore extreme? • The Normal model can tell you that! My sample p-hat is right here! That’s only 1.4% of all possible p-hats! p0

6. Don’t Forget! • All of this is based on an assumption: We assumed the null hypothesis is true. • If we don’t state that, • We don’t have a p0… • We don’t have a Normal model… • We can’t have any probabilities! That’s only 1.4% of all possible p-hats! p0

7. That’s a p-Value! The probability of collecting a sample p-hat with the same value as ours, or more extreme, assuming the null hypothesis is true. The probability The probability of collecting a sample p-hat with the same value as ours, The probability of collecting a sample p-hat with the same value as ours, or more extreme,

8. Be Specific • State the p-value • State the p-hat obtained. • “More extreme” is a generic term. • Use “more” or “less” if possible. • Reserve “more extreme” for two-sided hypothesis tests. • State the null hypothesis in words. • Include context.

9. Possible Example Answers • There is a 1.4% probability of collecting a sample of Dr. Klucksky’s chickens’ predictions where 59.25% or more are accurate, assuming the true accuracy rate is 50%. • If it is true that 50% of Dr. Klucksky’s chickens’ predictions are accurate, then the probability of collecting a sample in which 59.25% or more are accurate is 1.4%. • If Dr. Klucksky’s chickens have no predictive power, then there is a 1.4% probability of collecting a sample of their predictions in which 59.25% or more are accurate.