Statistical Power and Hypothesis Testing
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What does statistical power refer to in hypothesis testing?

  • The likelihood of detecting a true effect (correct)
  • The chance of rejecting a true null hypothesis
  • The ability to produce false negatives
  • The probability of obtaining a p-value greater than 0.05

    • Which of the following is an example of statistical significance?

  • A p-value of 0.10
  • A p-value of 0.06
  • A p-value of 0.20
  • A p-value of 0.03 (correct)

    • What is the purpose of a power analysis?

  • To calculate the likelihood of a Type I error
  • To analyze the validity of the research question
  • To determine the minimum sample size for a study (correct)
  • To find the statistical significance of the results

    • How can statistical power be improved in a study?

    <p>By using a larger sample size</p> Signup and view all the answers

    What is typically the most common threshold for statistical significance?

    <p>p &lt; 0.05</p> Signup and view all the answers

    What does high statistical power indicate?

    <p>There is a large chance of detecting a true effect.</p> Signup and view all the answers

    What is the main factor influencing statistical power?

    <p>Sample size, effect size, and significance level.</p> Signup and view all the answers

    What happens if a study lacks sufficient power?

    <p>It may miss detecting true effects entirely.</p> Signup and view all the answers

    What type of error is a power analysis designed to minimize?

    <p>Type II error.</p> Signup and view all the answers

    If the statistical power is set at 80%, how many studies would likely detect true effects out of 100 studies?

    <p>80 studies.</p> Signup and view all the answers

    Which of the following correctly describes a power analysis?

    <p>A calculation to determine the minimum sample size.</p> Signup and view all the answers

    What could be a consequence of having too much statistical power?

    <p>Leading to significant results with little real-world usefulness.</p> Signup and view all the answers

    Which of the following statements about hypothesis testing is accurate?

    <p>The primary goal is to collect data to reject the null hypothesis when appropriate.</p> Signup and view all the answers

    What is the significance level of a study typically set to?

    <p>5%</p> Signup and view all the answers

    How does sample size affect the power of a study?

    <p>Increasing sample size enhances power up to a point.</p> Signup and view all the answers

    What does a higher significance level increase the risk of?

    <p>Type I error</p> Signup and view all the answers

    What might indicate the practical significance of a finding in a study?

    <p>Effect size</p> Signup and view all the answers

    Which design is generally more powerful and requires fewer participants?

    <p>Within-subjects design</p> Signup and view all the answers

    Which factor does NOT contribute to increasing the power of a statistical test?

    <p>Using a two-tailed test</p> Signup and view all the answers

    What complicates the interpretation of observed effect sizes in low-powered studies?

    <p>High measurement error</p> Signup and view all the answers

    What is a consequence of high population variance on statistical tests?

    <p>Reduces power</p> Signup and view all the answers

    What is the relationship between effect size and sample size in a study?

    <p>Higher sample sizes can detect smaller effect sizes.</p> Signup and view all the answers

    What strategy can improve power by reducing variability in your measurements?

    <p>Triangulation of measurements.</p> Signup and view all the answers

    Which approach should only be used when there is a strong theoretical reason to expect a directional effect?

    <p>One-tailed test</p> Signup and view all the answers

    What could potentially inflate the observed effect size in low-powered studies?

    <p>Systematic measurement error</p> Signup and view all the answers

    What is generally the consequence of utilizing a conservative significance level?

    <p>Reduced sensitivity to detecting true effects.</p> Signup and view all the answers

    What is the main purpose of sample size calculations in a study?

    <p>To estimate treatment effects precisely if they exist</p> Signup and view all the answers

    Which of the following factors does NOT determine the required sample size for a study?

    <p>Availability of study resources</p> Signup and view all the answers

    Which of the following best describes a Type I error?

    <p>Detecting an effect that does not exist</p> Signup and view all the answers

    What consequence can arise from conducting small studies?

    <p>Increased likelihood of publication bias</p> Signup and view all the answers

    What does the term 'confidence interval' (CI) refer to in the context of sample size?

    <p>A range of values that likely contain the true population parameter</p> Signup and view all the answers

    How can loss to follow-up impact the required sample size for a study?

    <p>It decreases the precision of estimates</p> Signup and view all the answers

    Why is it considered unethical to conduct a study with a very small sample size?

    <p>Participants may not receive reliable treatment evaluation</p> Signup and view all the answers

    What is a potential drawback of conducting a study with a large sample size?

    <p>It may uncover trivial or unimportant effects</p> Signup and view all the answers

    Which of the following describes a Type II error?

    <p>Failing to reject a false null hypothesis</p> Signup and view all the answers

    What key factor does NOT determine the required sample size for a study?

    <p>Study duration</p> Signup and view all the answers

    What is a potential consequence of conducting small studies?

    <p>Increased likelihood of publication bias</p> Signup and view all the answers

    Which statement best explains imprecision in estimates from small studies?

    <p>They result in wide confidence intervals.</p> Signup and view all the answers

    What approach to sample size considers the number of available patients?

    <p>Economic / pragmatic</p> Signup and view all the answers

    What is the main ethical consideration in determining sample size?

    <p>Ensuring participants receive appropriate treatment</p> Signup and view all the answers

    Why might a very small study be considered unreliable?

    <p>It may not detect meaningful treatment effects.</p> Signup and view all the answers

    What is likely to happen if a sample size is too small?

    <p>Findings that are inconclusive and misleading.</p> Signup and view all the answers

    What minimum difference in BDI-II score between groups is considered significant enough to recommend CBT?

    <p>6 points</p> Signup and view all the answers

    Which factor is NOT likely to affect the power of the study?

    <p>Duration of intervention</p> Signup and view all the answers

    What is the standard deviation of BDI-II scores estimated for cancer patients in this study?

    <p>12 points</p> Signup and view all the answers

    What is the primary outcome measure used to assess depression in this clinical trial?

    <p>Beck Depression Inventory II</p> Signup and view all the answers

    How can power be increased in the study described?

    <p>By reducing the standard deviation</p> Signup and view all the answers

    What is the primary outcome measure in the cognitive behavioural therapy study?

    <p>Beck Depression Inventory II</p> Signup and view all the answers

    What degree of certainty is expected for detecting a treatment difference in the study?

    <p>80% power</p> Signup and view all the answers

    What minimum difference in BDI-II scores needs to be detected to recommend CBT for clinical practice?

    <p>6 points</p> Signup and view all the answers

    What is the expected mean BDI-II score for the control group in the study?

    <p>20 points</p> Signup and view all the answers

    Which statistical test will be used to compare the mean scores at the 12-week follow-up?

    <p>T-test</p> Signup and view all the answers

    What is the expected standard deviation of BDI-II scores in cancer patients participating in the trial?

    <p>12 points</p> Signup and view all the answers

    What type of treatment will the control group receive in the study?

    <p>Treatment as usual</p> Signup and view all the answers

    What is the maximum score on the Beck Depression Inventory II indicating severe depressive symptoms?

    <p>63</p> Signup and view all the answers

    What percentage of participants remain after 20% attrition from a sample size of 125?

    <p>105</p> Signup and view all the answers

    What is the adjusted sample size if the original sample size is 100 and the attrition is 20%?

    <p>125</p> Signup and view all the answers

    Which of the following reasons could lead to a p-value greater than 0.05?

    <p>No true difference exists in the population</p> Signup and view all the answers

    Why is it advised to avoid post hoc power calculations?

    <p>They are not meaningful after results are known</p> Signup and view all the answers

    How is the adjusted sample size affected by a higher attrition rate of 25% compared to 20%?

    <p>It increases</p> Signup and view all the answers

    What effect does a Type II error have on research findings?

    <p>It fails to detect a true difference when it exists</p> Signup and view all the answers

    When is it necessary to adjust sample sizes for loss to follow-up?

    <p>Regardless of the sample size</p> Signup and view all the answers

    For which situation is performing a power analysis most crucial?

    <p>When specifying the expected effect size</p> Signup and view all the answers

    What effect does a smaller detectable difference have on the required sample size?

    <p>It increases the sample size needed</p> Signup and view all the answers

    How does increased variability in an outcome affect the sample size requirement?

    <p>It requires a larger sample size</p> Signup and view all the answers

    What is a consequence of expecting a loss to follow-up of 25% in a study with an initial required sample size of 126?

    <p>At least 94 participants will remain for analysis</p> Signup and view all the answers

    In calculating sample size, what does a significance level of 5% imply?

    <p>There is a 5% risk of a Type I error</p> Signup and view all the answers

    What happens to the sample size requirement when using a 1% significance level instead of a 5% significance level?

    <p>Sample size increases</p> Signup and view all the answers

    How does adjustment for baseline measurements typically affect required sample size?

    <p>It reduces the required sample size</p> Signup and view all the answers

    What can be concluded about hierarchical data structures in relation to sample size?

    <p>They typically increase the required sample size</p> Signup and view all the answers

    What is the impact of a 20% loss to follow-up on the sample size recruitment process?

    <p>More participants need to be recruited initially</p> Signup and view all the answers

    What is the effect of adjusting for a high intraclass correlation in clustered samples?

    <p>It requires larger sample sizes</p> Signup and view all the answers

    Which factor directly increases the required sample size to detect a specified effect size?

    <p>Smaller effect sizes</p> Signup and view all the answers

    What must typically be determined from prior studies or consultations when assessing sample size?

    <p>Clinically important effect</p> Signup and view all the answers

    In the formula for sample size comparison of two means, what does $σ$ represent?

    <p>Standard deviation of the outcome</p> Signup and view all the answers

    Which of the following factors is typically NOT specified when determining sample size?

    <p>Climactic conditions during testing</p> Signup and view all the answers

    What is the typical significance level set in studies when calculating required sample size?

    <p>5%</p> Signup and view all the answers

    What does a higher Z score indicate in the context of determining sample size?

    <p>Greater statistical significance</p> Signup and view all the answers

    Which formula is used for calculating required sample size for binary outcomes?

    <p>𝑛=( 𝑧 1 − 𝛼/2 + 𝑧 1 − 𝛽 ) × $𝑝_{1} imes (1 − 𝑝_{1})$ + $𝑝_{2} imes (1 − 𝑝_{2})$ / $ (𝑝_{2} − 𝑝_{1})^{2}$</p> Signup and view all the answers

    When assessing sample size, which of the following is true about statistical power?

    <p>It commonly suggested to be set at 80% or 90%.</p> Signup and view all the answers

    What is one of the main characteristics shared between the formula for comparing two means and two proportions?

    <p>Both formulas use the Z score in their calculations.</p> Signup and view all the answers

    Study Notes

    Statistical Power and Significance

    • Statistical power (sensitivity) is the probability of detecting a true effect if one exists in a study
    • A true effect is a real, non-zero relationship or difference between variables in a population
    • High power increases the chance of detecting a true effect
    • Low power means a small chance of detecting a true effect, often due to random or systematic errors
    • Power depends on sample size, effect size, and significance level
    • Power analysis determines necessary sample size for a study
    • Adequate power is crucial for accurate population conclusions from sample data

    Hypothesis Testing

    • Hypothesis testing involves null (no effect) and alternative (true effect) hypotheses
    • The goal is to gather sufficient data to potentially reject the null hypothesis in favor of the alternative

    Type I and Type II Errors

    • A Type II error is failing to detect a true effect
    • High power reduces the risk of a Type II error
    • Power is usually set at 80%
    • This means in 80 out of 100 studies with true effects, an effect will be detected

    Power Analysis Components

    • Power analysis involves four main components:
      • Sample size
      • Effect size
      • Significance level
      • Statistical power
    • Knowing any three allows calculation of the fourth
    • Traditional values for significance level and power are 5% and 80%.

    Sample Size and Power

    • Sample size is positively correlated with power
    • Small samples (under 30) typically have low power; large samples have high power
    • Increasing sample size enhances power, but marginal gains occur with very large samples
    • Within-subjects designs are more powerful than between-subjects designs, requiring fewer participants

    Significance Level

    • Significance level is the probability of a Type I error (false positive)
    • This is typically set at 5% (p<0.05)
    • Increasing significance level (e.g., to 10%) increases power but increases Type I error risk
    • Decreasing significance level (e.g., to 1%) increases the conservativeness of the test and reduces power

    Effect Size

    • Effect size is the magnitude of difference or relationship between variables.
    • It indicates practical significance
    • High-powered studies detect medium and large effects, low-powered studies typically, large ones less likely

    Determining Effect Size

    • Estimating effect size involves systematic literature reviews.
    • Mean effect size from similar studies with similar manipulations and measures is utilized

    Factors Affecting Power

    • Population variability: high variability reduces power
    • Measurement error: higher error reduces power
    • Research design also influences power
    • Sample size and variability influence the results
    • An example is the different results of two studies using the drug streptokinase after a heart attack. The first Australian trial with a small sample size (517 participants) found no significant effect, while the ISIS-2 trial (17,187 participants) found a statistically significant effect. Different sample sizes can lead to conflicting conclusions.

    Improving Power

    • Increase effect size (e.g., stronger manipulations)
    • Increase sample size (but diminishing returns)
    • Increase significance level
    • Reduce measurement error (improve precision and accuracy)
    • Use a one-tailed test (if appropriate)

    Statistical Significance

    • Statistical significance means the observation is unlikely under the null hypothesis
    • Significance is indicated by a p-value (probability value)
    • Common threshold is p < 0.05

    Additional Considerations

    • Sampling error exists between observed and true effect sizes
    • Observed effects in low-powered studies may be exaggerated by unrelated factors
    • Various other research aspects influence power
    • Too small of a sample size can lead to a lack of precision with results
    • Ethical considerations need to be included when deciding how big the sample size should be for a study, and potential waste of resources (time and funding should be taken into account).
    • Small studies with p<0.05 are more likely accepted for publication than small studies with p>0.05
    • Sample size that is too large can lead to wasted resources.
    • Different approaches to sample size determination exist, including statistical/scientific, economic, and ethical considerations for establishing sample size, along with credibility factors. Small studies may not yield reliable results, as they are more likely to result in publication bias.

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    Description

    This quiz covers key concepts related to statistical power, hypothesis testing, and types of errors in research studies. Understand how power influences the detection of true effects and the implications of Type I and Type II errors. Test your knowledge on the importance of adequate sample size and power analysis in drawing accurate conclusions.

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