Hypothesis Testing: Fisher & Neyman-Pearson Approaches

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Questions and Answers

Explain the fundamental difference in how Ronald Fisher and the Neyman-Pearson approach treat the p-value in hypothesis testing. How does each use the p-value to draw conclusions?

Fisher views the p-value as a continuous measure of evidence against the null hypothesis, but not a definitive decision-making tool. The Neyman-Pearson approach uses the p-value in a decision-making framework, to either reject or fail to reject the null hypothesis based on a pre-defined significance level.

Describe a scenario where a statistically significant result (low p-value) might not be practically significant. What other information is needed to determine the importance of the result?

A statistically significant result could occur with a very large sample size, even if the actual effect size is small and has little real-world impact. The effect size (e.g., Cohen's d) alongside confidence intervals are needed to evaluate practical importance.

Explain how increasing the sample size in a study can affect statistical power and the likelihood of committing a Type II error. What are the implications for study design?

Increasing the sample size generally increases statistical power (1 - β), which reduces the likelihood of committing a Type II error (failing to reject a false null hypothesis). This implies that larger sample sizes are better at detecting true effects, but researchers must consider the trade-off between sample size, cost, and the minimum effect size of interest.

What is publication bias, and how does it potentially distort our understanding of research findings? Suggest a strategy to mitigate the impact of publication bias.

<p>Publication bias is the tendency for journals to disproportionately publish statistically significant results, leading to an overestimation of the evidence supporting certain hypotheses. One way to mitigate this impact is by pre-registering studies, which ensures that all research, regardless of the outcome, is documented.</p> Signup and view all the answers

How can the use of confidence intervals alongside p-values provide a more complete picture of the results of a hypothesis test? What specific information does a confidence interval offer that a p-value does not?

<p>Confidence intervals provide a range of plausible values for the true population parameter, offering information about the precision and magnitude of the effect. Unlike p-values, confidence intervals show the direction and size of the effect, facilitating a more nuanced interpretation of the results.</p> Signup and view all the answers

Flashcards

Null Hypothesis Significance Testing (NHST)

A statistical method using p-values to assess evidence against a null hypothesis.

P-value

The probability of observing data as extreme as, or more extreme than, the data actually observed, assuming the null hypothesis is true.

Type I Error (α)

Rejecting a true null hypothesis; a 'false positive'.

Type II Error (β)

Failing to reject a false null hypothesis; a 'false negative'.

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Power (1 - β)

The probability of correctly rejecting a false null hypothesis.

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Study Notes

General inference theory and related distributions have shifted to testing approaches and interpretation.

Key Focus Areas

Understanding Null Hypothesis Significance Testing (NHST).
Evaluating effect sizes and power in statistical tests.
Recognizing errors and limitations in hypothesis testing.

Fisher's Approach: P-Values as Evidence

Ronald Fisher (1890-1962) introduced p-values to measure how well observed data aligns with the null hypothesis (Ho).
A small p-value suggests evidence against (Ho), but does not prove it false.
A p-value is NOT the probability that (Ho) is true.
A p-value does NOT indicate effect size or practical importance.
Fisher treated p-values as continuous measures of evidence, not strict decision rules.

Neyman-Pearson Approach: Decision-Making & Error Control

Jerzy Neyman & Egon Pearson developed a decision-making framework.
Type I error (α): False positive (rejecting a true (Ho)).
Type II error (β): False negative (failing to reject a false (Ho)).
Power (1 - β): The probability of detecting a true effect.
Neyman-Pearson requires determining to reject or accept (Ho).
Emphasizes long-term error control through repeated testing.

NHST in Practice: Strengths

Provides a standardized way to test hypotheses.
Helps quantify uncertainty in research.

NHST in Practice: Pitfalls

Over-reliance on p-values (without considering effect sizes).
Misinterpretation of "non-significance" as evidence of no effect.
Publication bias favoring "significant" results over null findings.

NHST in Practice: Best Practices

Use confidence intervals alongside p-values.
Report effect sizes to show practical importance.
Consider Bayesian approaches for better uncertainty estimation.

Effect Size & Power: What NHST Misses

Effect Size: The magnitude of an association (e.g., Cohen's d, correlation coefficients).
Power Analysis: Ensures a study has a large enough sample size to detect meaningful effects.
Power should be at least 80% to minimize Type II errors.
A non-significant p-value might mean a true effect exists but is too small to detect with the given sample size.

One-Sided Vs. Two-Sided Tests

Two-sided test: Tests for an effect in either direction (e.g., does a drug increase OR decrease blood pressure?).
One-sided test: Tests for an effect in a specific direction (e.g., does a drug only increase blood pressure?).
Most NHST tests are two-sided unless a strong rationale exists for a directional hypothesis.

Choosing The Right Approach

Fisher's Approach is flexible and for exploratory research.
Fisher views p-values as evidence.
Fisher's Approach is best for one-time studies.
Neyman-Pearson's Approach is for decision-making and industrial testing.
Neyman-Pearson uses an an accept/reject framework with error control.
Neyman-Pearson Approach is best for repeated experiments.

Takeaways

Statistical significance ≠ Scientific significance, considering effect sizes.
NHST is a tool, not a final answer.
Interpret results in context.
Low power can hide real effects.
Misuse of NHST leads to bad science
Avoid mechanical "p < 0.05" thinking.

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Description

Explore the basics of hypothesis testing, contrasting Fisher's P-values with the Neyman-Pearson approach to decision-making. Understand Type I and Type II errors, statistical power, and effect sizes. Learn the limitations of Null Hypothesis Significance Testing.