Effect size and statistical power notes
This study set covers the essential concepts of effect size and statistical power in statistics, providing explanations and real-world examples to enhance understanding.
Quiz(32 questions)
1. What does statistical power primarily measure?
Terms in this Study Set(32)
Effect Size Concepts(16)
Effect Size
A quantitative measure of the magnitude of a phenomenon. It helps to understand the strength of a relationship between two variables.
Cohen's d definition
A measure of effect size that indicates the standardized difference between two means. Example: If two store sales averages differ by 50, Cohen's d can quantify this difference.
True or False: Effect size is only about statistical significance.
False - Effect size measures the strength of a relationship, not just whether it is significant.
What does a Cohen's d of 0.5 mean?
It indicates a medium effect size, suggesting that the difference between the two groups is noticeable but not large.
Difference between Cohen's d and Pearson's r
Cohen's d measures mean differences, while Pearson's r measures the strength and direction of a linear relationship between two variables.
Formula for Cohen's d
- where and are group means, and is the standard deviation.
What does a negative Cohen's d indicate?
It suggests that the first group's mean is lower than the second group's mean.
Example of Effect Size in Sales
If a new marketing strategy increases average sales from 1,500, with a standard deviation of $200, the effect size can be calculated to show impact.
Eta-squared (η²) definition
A measure of effect size that indicates the proportion of variance accounted for by a factor. Example: If η² = 0.14, 14% of the variance in sales is due to the marketing strategy.
Fill in the blank: A larger effect size indicates _____.
a stronger relationship between variables.
What is the purpose of effect size in hypothesis testing?
To provide context beyond p-values, helping to understand how meaningful the results are in practical terms.
True or False: Smaller sample sizes always lead to smaller effect sizes.
False - Effect size can be large regardless of sample size; however, small samples may yield less reliable estimates.
Difference between standardized and unstandardized effect sizes
Standardized effect sizes (like Cohen's d) allow for comparison across studies, while unstandardized effect sizes are specific to the units of measurement.
What does a large effect size imply?
It suggests a substantial difference or relationship may exist, which can influence decisions. E.g., a new product significantly increases average customer spend.
Partial eta-squared (ηp²) definition
A measure of effect size used in the context of ANOVA that reflects the proportion of total variance attributable to a factor, controlling for other factors.
Calculate Cohen's d: M1=60, M2=50, SD=10.
Cohen's d = (60-50)/10 = 1.0. This indicates a large effect size.
Statistical Power Fundamentals(16)
What is statistical power?
Statistical power is the probability that a test will correctly reject a false null hypothesis. It reflects the test's ability to detect an effect when there is one.
True or false: Higher sample sizes increase statistical power.
True. Larger sample sizes reduce variability and increase the likelihood of detecting a true effect.
Fill in the blank: Statistical power is influenced by sample size, effect size, and _____ .
significance level.
How is power calculated?
Power can be calculated using the formula: Power = 1 - β, where β is the probability of a Type II error. The power increases with larger sample sizes or effect sizes.
What happens when power is too low?
When power is low, there's a higher risk of failing to detect a true effect, leading to Type II errors.
Question: Why is power important in research?
Power ensures that a study can detect meaningful effects, preventing wasted resources and time on inconclusive results.
Compare high power vs. low power.
High power: greater likelihood of detecting effects. Low power: increased risk of Type II errors and missed opportunities.
Example: A store tests a new discount strategy.
If the power is 0.80, there's an 80% chance of detecting a significant increase in sales due to the discount.
What is a common power level used in studies?
A common power level used is 0.80, indicating an 80% chance of detecting an effect if one exists.
True or false: Increasing effect size increases statistical power.
True. Larger effect sizes make it easier to detect differences, thus increasing power.
Calculate the power with effect size 0.5, sample size 30.
With an effect size of 0.5 and sample size of 30, typically power can be estimated using software or power tables.
Fill in the blank: The significance level (alpha) often used is _____ .
0.05.
Question: How do researchers increase power?
Researchers can increase power by increasing sample size, increasing effect size, or decreasing the significance level.
Effect of Type I error on power?
A stricter significance level (lower alpha) can decrease power because it becomes harder to reject the null hypothesis.
What does a power analysis do?
A power analysis determines the necessary sample size to achieve a desired power level before conducting a study.
Example: A psychologist tests a therapy's impact.
If they aim for 90% power with a small effect size, they may need a larger sample compared to aiming for 80% power.
Questions in this Study Set(32)
1. What does statistical power primarily measure?
2. What is effect size primarily used for in research?
3. True or false: A larger sample size generally leads to lower statistical power.
4. If Cohen's d is measured at 0.8, what does this indicate?
5. Fill in the blank: Sample size, effect size, and _____ influence statistical power.
6. Which of the following is NOT a measure of effect size?
7. What is the relationship between effect size and statistical power?
8. What does a negative Cohen's d value imply?
9. What happens if a study has low power?
10. How is Cohen's d calculated?
11. Why is high statistical power desirable in research?
12. Which effect size measure indicates the proportion of variance explained by a factor?
13. What is a common threshold for statistical power in research?
14. True or False: A larger effect size always indicates statistical significance.
15. If the effect size is small, what must researchers typically do to achieve adequate power?
16. In a marketing study, if the average sales increase from 800 with a standard deviation of $150, what effect size can be calculated?
17. Which statement about Type I error and statistical power is true?
18. What does a Cohen's d of 0.2 typically indicate?
19. What does a power analysis help researchers determine?
20. True or False: Effect size can vary depending on the sample size used.
21. Which of the following is NOT a factor affecting statistical power?
22. Which of the following best describes partial eta-squared?
23. How can researchers increase the power of their study?
24. How does Cohen's d differ from Pearson's r?
25. In a study testing a new product, a power of 0.90 means what?
26. In a scenario where two rental properties are compared, one has a monthly rent of 1,000, what does a calculated Cohen's d signify?
27. What typically happens if a study uses a very small sample size?
28. What does a small effect size imply about the relationship between two variables?
29. In a research study, if the significance level (alpha) is set at 0.01 instead of 0.05, how does this affect the statistical power?
30. Which of the following scenarios best illustrates a large effect size?
31. If a researcher increases the sample size from 50 to 100 while keeping the effect size constant, what is the expected effect on statistical power?
32. If two different advertising campaigns show average sales of 1,000 with a standard deviation of $100, what is the Cohen's d indicating the effect size of the difference in sales?
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