Power & Sample Size

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Questions and Answers

Which factor directly affects the statistical power of a test?

The choice of data analysis software

Random sampling methods

The sample size (correct)

The number of hypotheses tested

What is the impact of increasing the alpha level on type I and type II errors?

Has no effect on error probabilities

Increases type II error while decreasing type I error

Decreases both type I and type II errors

Increases power but also increases type I error (correct)

How does effect size influence the power of a statistical test?

Larger effect sizes increase power (correct)

Smaller effect sizes result in higher power

Power is independent of effect size

Effect size only affects type II error

What is typically the consequence of loss to follow-up in a study?

It can lead to biased results and decreased power Signup and view all the answers

In time-to-event analysis, what is an important consideration when estimating power?

The total number of events observed in the sample Signup and view all the answers

What adjustment should be made to the sample size when the attrition rate is 20%?

Increase sample size by multiplying by 1.25 Signup and view all the answers

If a study arm is expected to have loss to follow-up, what is the recommended action?

Apply the correction to only one study arm Signup and view all the answers

Which of the following statements is true regarding post hoc power calculations?

They should be avoided as they are not informative Signup and view all the answers

What can be deduced when a study reports a p-value greater than 0.05?

A Type II error may have occurred Signup and view all the answers

What is the effect of a larger standard deviation than specified in the sample size calculation?

It may lead to an underpowered study Signup and view all the answers

What is the main consequence of loss to follow up in a clinical trial?

It reduces the power of the trial. Signup and view all the answers

How can researchers adjust for expected loss to follow up when planning a study?

Increase the initial recruitment target. Signup and view all the answers

In a study requiring 100 participants, what is the number of participants needed to recruit to account for a 20% loss to follow up?

120 participants Signup and view all the answers

What effect does specifying intraclass correlation (ICC) in hierarchical data structures typically have on sample size requirements?

It increases the sample size needed. Signup and view all the answers

What is the expected power to detect a clinically important difference if 25% of the 126 participants are lost to follow up in a study?

Less than 80% Signup and view all the answers

Study Notes

Core Principles of Mental Health Research: Power & Sample Size

Alpha Criterion & Hypothesis Test:
- Alpha (α) = 0.05 represents a 5% chance of a Type I error (rejecting a true null hypothesis).
- Type I error is rejecting the null hypothesis when it is actually true.
- The red lines in the graph represent 1.96 standard deviations above and below the mean.
- The graph is centered on 0, meaning the null hypothesis is true.

Alternative Hypothesis:

The purple line in the graph represents the sampling distribution for a mean difference in the case where the null hypothesis is true, but the alternative hypothesis could also be true.
The true difference between groups in the alternative hypothes is 6 points (the value is assumed, not necessarily a fixed value).
The alternative hypothesis is centered around the point estimate of 6 points.

Power:

Power is the probability of correctly rejecting a false null hypothesis.
Pink area = test power.
Green area = previous Type I error area, now contributes to power
Yellow area = Type II error (50% chance in a study).
Factors affecting power:
- Significance level (alpha): Higher alpha increases power but also increases the risk of a Type I error.
- Effect size: Larger differences between groups are easier to detect.
- Standard deviation (SD): A smaller SD allows detection of smaller effects.
- Sample size: Larger samples provide more power.

Continuous Outcomes – Comparison of Two Means

Power is calculated to determine the required sample size, not the other way around.
The sample size per group calculation is: n=(Z1-a/2+21-β)²×(2σ²)/(μ₂-μ₁)²
- μ₂-μ₁ = true difference in means
- σ = standard deviation
- a = significance level
- 1 - β = power
- Z = Z score from a normal distribution

Binary Outcomes – Comparison of two proportions

Sample size calculation for comparing proportions: n=(Z1-a/2+21-β)² X (p1(1-p1)+p2(1-p2))/(p2-p1)²
- p₁ = true proportion in control
- p₂ = true proportion in treatment

More Complicated Scenarios

Loss to Follow Up: Follow-up loss needs to be accounted for during sample size planning; 25% loss to follow up is a common scenario.
Unequal Treatment Group Sizes: Different group sizes may impact the required sample size.
Baseline Adjustment: Baseline characteristics may impact the required sample size (often reducing it in correlations.)
Hierarchical Data Structures: More complex data structures require adjustments to the sample size calculation that account for intraclass correlation.

Avoiding Post-Hoc Power Calculations

Post-hoc power calculations are generally not meaningful; it doesn't determine why the study had a higher/lower than expected power.
A well-planned approach should include the expected effect/group sizes/SD in power calculations before launching a study.

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Description

This quiz covers the fundamental elements of mental health research, focusing on concepts such as the alpha criterion, hypothesis testing, power, and sample size. Explore how Type I errors impact research outcomes and the significance of power in hypothesis testing. Perfect for students delving into research methodologies in psychology.