Podcast
Questions and Answers
If we reject the null hypothesis when it is actually true, we commit a Type 1 ____
If we reject the null hypothesis when it is actually true, we commit a Type 1 ____
error
What is the probability that a significance test will reject the null when a particular alternative value of the parameter is true?
What is the probability that a significance test will reject the null when a particular alternative value of the parameter is true?
power
If we calculate a very small P value, we have evidence to ___ the null
If we calculate a very small P value, we have evidence to ___ the null
reject
Hypotheses always refer to the ____
Hypotheses always refer to the ____
The ___ hypothesis is the claim about the population for which we are finding evidence for
The ___ hypothesis is the claim about the population for which we are finding evidence for
The test ____ is a standardized value that assesses how far the estimate is from the hypothesized parameter
The test ____ is a standardized value that assesses how far the estimate is from the hypothesized parameter
Reject the null hypothesis if the P value is ___ than the significance level
Reject the null hypothesis if the P value is ___ than the significance level
What is the probability that we would observe a statistic at least as extreme as the one observed, assuming the null is true?
What is the probability that we would observe a statistic at least as extreme as the one observed, assuming the null is true?
We can use a ___ test to compare observed data with a hypothesis about a population
We can use a ___ test to compare observed data with a hypothesis about a population
If our calculated P value is not small enough to provide convincing evidence, we ___ to reject the null
If our calculated P value is not small enough to provide convincing evidence, we ___ to reject the null
Conclusions should always be written in ____
Conclusions should always be written in ____
What is the Greek letter used to designate the significance level?
What is the Greek letter used to designate the significance level?
A ___ test allows us to analyze differences in responses within pairs
A ___ test allows us to analyze differences in responses within pairs
The ___ hypothesis is the claim for which we are seeking evidence against
The ___ hypothesis is the claim for which we are seeking evidence against
An observed difference that is too small to have occurred due to chance alone is considered statistically ____
An observed difference that is too small to have occurred due to chance alone is considered statistically ____
What are the statements a statistical test is designed to compare?
What are the statements a statistical test is designed to compare?
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Study Notes
Key Concepts in Hypothesis Testing
- Type 1 Error: Occurs when the null hypothesis is rejected while it is actually true.
- Power of a Test: The likelihood that a significance test will correctly reject the null hypothesis for a specific alternative value.
- Rejecting the Null: A very small P value provides evidence to reject the null hypothesis.
- Population: All hypotheses refer to this overarching group considered in statistical analysis.
Hypothesis Definitions
- Alternative Hypothesis: Represents the claim about the population for which evidence is being sought.
- Test Statistic: A standardized measure that evaluates how far an estimate deviates from the hypothesized parameter.
- P Value: Reflects the probability of observing a statistic as extreme as the one found, assuming the null hypothesis is true.
Decision Making in Hypothesis Testing
- Significance Level (Alpha): The threshold for rejecting the null hypothesis, often denoted by the Greek letter alpha.
- Comparison of P Value and Alpha: Reject the null hypothesis if the P value is less than the significance level.
- Fail to Reject the Null: If the P value is not sufficiently small, there is not enough evidence to reject the null hypothesis.
Reporting Results
- Contextual Conclusions: It's crucial to present conclusions within the appropriate context of the research.
- Statistical Significance: An observed difference that is unlikely to be due to random chance is labeled as statistically significant.
- Paired Tests: Designed to analyze differences in responses within defined pairs of observations.
Conclusion
- Hypotheses: The competing statements that a statistical test is structured to evaluate.
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