Clinical vs statistical significance

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P-Values - Numbers Have Significance

  • P-value: The probability of observing data as extreme (or more extreme) than the current results, assuming the null hypothesis (H₀) is true.

    • Null Hypothesis (H₀): Assumes no difference or effect (e.g., a new drug is no better than a placebo).
    • Alternative Hypothesis (H₁): Assumes a difference or effect exists.
  • Significance Threshold (α): Typically set at 0.05.

    • If $p < 0.05$, the results are statistically significant.
    • This allows for the rejection of the null hypothesis (H₀).

Normal distribution with rejection regions

⭐ Statistical significance is not the same as clinical significance. A very large study might find a statistically significant result that is too small to be clinically meaningful (e.g., a drug that lowers blood pressure by only 1 mmHg).

Confidence Intervals - Guessing with Precision

  • Confidence Interval (CI): An estimated range of values that is likely to contain the true population parameter. It quantifies the uncertainty around an estimate.
  • A 95% CI implies that if a study were repeated many times, 95% of the calculated CIs would contain the true population value.
  • Relationship to p-value:
    • If the 95% CI for an effect size does NOT cross the null value, the result is statistically significant (p < 0.05).
    • Null values: 1 for ratios (Odds Ratio, Relative Risk), 0 for differences (means).
  • Precision & CI Width:
    • Narrow CI: ↑ precision (less random error).
    • Wide CI: ↓ precision (more random error).

Average TV hours per week with 95% confidence interval

⭐ If the CIs for two different groups do not overlap, their difference is statistically significant. However, if they do overlap, the difference may or may not be statistically significant-you must calculate the CI for the difference itself.

Clinical vs. Statistical - Real World vs. Research

  • Statistical Significance: Is the observed effect likely due to chance? Governed by the $p$-value.
  • Clinical Significance: Is the effect large enough to be meaningful for patients and change clinical practice? Governed by effect size.

Hypothesis Testing with Distribution and Rejection Regions

FeatureStatistical SignificanceClinical Significance
Question AnsweredIs the effect real (not by chance)?Does the effect matter in practice?
Key Metric$p$-valueEffect size (e.g., NNT, odds ratio)
Key InfluencerSample sizeMagnitude of benefit, patient values
InterpretationIf p < 0.05, result is unlikely randomA small effect may be statistically significant but clinically irrelevant
  • Statistical significance (p < 0.05) just means a finding is unlikely to be due to chance; it does not automatically imply clinical importance.
  • Clinical significance is the practical relevance of a treatment effect-whether it makes a real difference to patients.
  • Very large sample sizes can make tiny, clinically irrelevant effects statistically significant.
  • Conversely, a small study may be underpowered and fail to find statistical significance for a clinically important effect.
  • Evaluate the effect size (e.g., relative risk) and the confidence interval to gauge clinical relevance.

Practice Questions: Clinical vs statistical significance

Test your understanding with these related questions

A study is funded by the tobacco industry to examine the association between smoking and lung cancer. They design a study with a prospective cohort of 1,000 smokers between the ages of 20-30. The length of the study is five years. After the study period ends, they conclude that there is no relationship between smoking and lung cancer. Which of the following study features is the most likely reason for the failure of the study to note an association between tobacco use and cancer?

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Flashcards: Clinical vs statistical significance

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The power of a study is increased with _____ sample size

TAP TO REVEAL ANSWER

The power of a study is increased with _____ sample size

increased

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