Podcast
Questions and Answers
In hypothesis testing, what characterizes a Type I error?
In hypothesis testing, what characterizes a Type I error?
- Failing to reject a true null hypothesis.
- Correctly rejecting a true null hypothesis.
- Rejecting a true null hypothesis. (correct)
- Failing to reject a false null hypothesis.
Which of the following actions would increase the power of a statistical test?
Which of the following actions would increase the power of a statistical test?
- Decreasing the sample size.
- Increasing the standard deviation.
- Increasing the sample size. (correct)
- Decreasing the alpha level.
What does Cohen's d measure?
What does Cohen's d measure?
- The correlation between two variables.
- The statistical significance of a result.
- The probability of making a Type II error.
- The magnitude of the difference between two means in standard deviation units. (correct)
If a researcher sets their alpha level to 0.01, what is the probability of committing a Type I error?
If a researcher sets their alpha level to 0.01, what is the probability of committing a Type I error?
In the context of hypothesis testing, what does 'power' refer to?
In the context of hypothesis testing, what does 'power' refer to?
How is beta ($\beta$) related to the power of a test?
How is beta ($\beta$) related to the power of a test?
What is the interpretation of Cohen’s d = 0?
What is the interpretation of Cohen’s d = 0?
Which of the following is a strategy to reduce the likelihood of a Type II error?
Which of the following is a strategy to reduce the likelihood of a Type II error?
What is the primary reason for calculating Cohen's d after finding a statistically significant result?
What is the primary reason for calculating Cohen's d after finding a statistically significant result?
If increasing the sample size leads to a statistically significant result, what else is needed to determine if the result is meaningful?
If increasing the sample size leads to a statistically significant result, what else is needed to determine if the result is meaningful?
A researcher is testing whether a new drug reduces blood pressure. The null hypothesis is that the drug has no effect. If they commit a Type II error, what is the most accurate interpretation?
A researcher is testing whether a new drug reduces blood pressure. The null hypothesis is that the drug has no effect. If they commit a Type II error, what is the most accurate interpretation?
Which of the following values of Cohen's d represents the largest effect size?
Which of the following values of Cohen's d represents the largest effect size?
In a clinical trial for a new medication, the researchers want to minimize the chance of falsely concluding that the drug is effective. Which type of error are they most concerned about minimizing?
In a clinical trial for a new medication, the researchers want to minimize the chance of falsely concluding that the drug is effective. Which type of error are they most concerned about minimizing?
A study with low statistical power is most likely to:
A study with low statistical power is most likely to:
How does increasing the sample size affect the width of a confidence interval, assuming all other factors remain constant?
How does increasing the sample size affect the width of a confidence interval, assuming all other factors remain constant?
What is the relationship between alpha level and the critical region in hypothesis testing?
What is the relationship between alpha level and the critical region in hypothesis testing?
In the context of effect size, what does practical significance refer to?
In the context of effect size, what does practical significance refer to?
A statistically significant result with a small Cohen's d indicates:
A statistically significant result with a small Cohen's d indicates:
What is the impact of conducting multiple hypothesis tests on the same dataset without adjusting the alpha level?
What is the impact of conducting multiple hypothesis tests on the same dataset without adjusting the alpha level?
For the Prebunking Workshop, the average number of articles detected with misinformation is 3.2 (σ = 1.45). Report the 95% confidence interval around the sample mean and explain what the confidence interval means.
For the Prebunking Workshop, the average number of articles detected with misinformation is 3.2 (σ = 1.45). Report the 95% confidence interval around the sample mean and explain what the confidence interval means.
Flashcards
Type I error
Type I error
Incorrectly rejecting the null hypothesis when it is actually true (false positive).
Type II error
Type II error
Failing to reject the null hypothesis when it is actually false (false negative).
Power
Power
The probability of correctly rejecting a false null hypothesis (1 - beta).
Beta (β)
Beta (β)
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What is a Type I error?
What is a Type I error?
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What is a Type II error?
What is a Type II error?
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Cohen's d
Cohen's d
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What does Cohen's d measure?
What does Cohen's d measure?
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What is alpha (α)?
What is alpha (α)?
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Study Notes
- Main topics include errors and power in hypothesis testing, and effect size as measured by Cohen's d, and how to visualize these concepts.
Rejecting the Null Hypothesis
- When rejecting the null hypothesis (Hâ‚€), two possibilities exist: the decision to reject was either correct or incorrect.
- An incorrect rejection means the sample was an unlikely one drawn from the population (e.g., μ = 65).
- A correct rejection indicates the sample came from a different population with a different mean.
- It might not be definitively be known if the decision was correct, but there are methods to reduce mistakes. Minimize errors besides sampling errors.
Errors in Hypothesis Testing
- Type I error has a true null hypothesis that is rejected. This is known as a false positive.
- Type II error means the researcher fails to reject a false null hypothesis. This is a false negative.
- α (alpha) represents the probability of making a Type I error.
- β (beta) represents the probability of making a Type II error.
- Power is the probability of correctly rejecting a false null hypothesis (1-β).
- Correct decision (1-alpha) is when you fail to reject a true null hypothesis.
Understanding Errors with Basketball Example
- The Null hypothesis(H₀) is that the population mean μ = 65 . Target is rejecting this.
- True State of Affairs: The null hypothesis can be either true or false.
- Decision Scenarios include:
- Reject null hypothesis and Hâ‚€ is True: Erroneous. Population of 67" female basketball players are not taller than women in the general population but the null hypothesis was rejected.
- Fail to reject null hypothesis and Hâ‚€ is True: Correct Decision. Population of 67" female basketball players are not taller than women in the general population and you fail to reject the null hypothesis.
- Reject null hypothesis and Hâ‚€ is False: Correct Decision. Population of 67" female basketball players are taller than women in the general population, and the null hypothesis is rejected.
- Fail to reject null hypothesis and Hâ‚€ is False: Erroneous. Population of 67" female basketball players are taller than women in the general population, yet you fail to reject the null hypothesis.
Visualizing Power, Alpha, and Beta
- Every hypothesis test with an alpha level of 0.05 has a 5% chance of a Type I error (false positive). Alpha is set by the experimenter.
- To find "I-beta" (power), locate where alpha ends and draw a line straight up through alternative distribution. The area under the alternative distribution curve indicates POWER. Scientists want this region to be LARGE.
- The remaining area under the alternative distribution curve is BETA. Scientists want this region to be SMALL (reduce likelihood of type 11 error).
- How to maximize the AUC(Area Under the Curve) related to power and minimize the AUC related to type I and type II errors: Consider the mean, variability, alpha, sample size, whether non-directional or one directional.
- The probability of correctly rejecting Hâ‚€ is increased by maximizing POWER.
Cohen's d: Measuring Effect Size
- Cohen's d quantifies the size of the difference between sample mean and population mean in standard deviation units.
- Cohen's d = (X - μ) / σ, where X is the sample mean, μ is the population mean, and σ is the population standard deviation.
- Cohen's d calculated only for significant effects.
- For the basketballs example: d = (67-65)/3.5 = 0.57
- Average tallness in population of women basketball players is significantly greater than average height of women in the population.
- Test statistic formula during one-sample z-test hypothesis test (SAMPLING DISTRIBUTION SD): Zobs = (X - μ) / σX
- If a statistically significant effect is found (p < 0.05), calculate Cohen's d to find the size of the found statistically significant effect (POPULATION SD).
Interpreting Cohen's d
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Cohen's d measures the magnitude of an effect, the distance from 0.
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Cohen's d is 0.56 this is a medium effect.
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Cohen’s Effect Size Conventions:
- Small effect: |d| ≈ 0.2
- Medium effect: 0.2 < |d| < 0.8
- Large effect: |d| > 0.8
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Positive d = effect shifted above the population mean.
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Negative d = effect shifted below the population mean.
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Description
Understand errors in hypothesis testing, including Type I and Type II errors. Learn about statistical power and the factors that influence it. Explore effect size, specifically Cohen's d, to quantify the magnitude of an effect.
