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Unconfident Intervals

Unconfident Intervals. Why are confidence intervals so difficult to interpret?. Definitions. “An interval estimate of a population parameter” (wikipedia) “The probability that the interval will capture the true parameter value in repeated samples” (Moore)

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Unconfident Intervals

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  1. Unconfident Intervals Why are confidence intervals so difficult to interpret?

  2. Definitions • “An interval estimate of a population parameter” (wikipedia) • “The probability that the interval will capture the true parameter value in repeated samples” (Moore) • “We are 95% confident that the unknown [parameter] lies between [a] and [b] is shorthand for ‘We got these numbers using a method that gives correct results 95% of the time’” (Moore) • “When we write probability statements such as Pθ(L(X) ≤ θ ≤ U(X)), these probability statements refer to X, not θ” (Casella & Berger)

  3. Teaching CIs: Problems and Potential Solutions (Fidler & Cumming) • CIs vs. p-values, 18% vs. 44% misinterpreted • Noted common misinterpretations of CIs • Plausible values for sample mean • Range of scores • Width increases when sample size increases • A C% CI will capture about C% of replication means (about 83%). • Visual interpretations (more later)

  4. Inference by Eye (Cumming & Finch) • Stay away from probability statements about CIs! • CI calculated is just one of infinitely many possible of which 95% would contain the true population parameter • Interval estimate or “range of plausible values” • Relate CI to NHST – values outside the interval used in the null hypothesis yield a p value < .05 • Margin of error is index of precision.

  5. Inference by Eye “ ‘In all figures, include graphical representations of interval estimates whenever possible’ (Wilkinson & TFSI, 1999, p.601)” (p. 170)

  6. Rules of Eye

  7. Rules of Eye • Know where the confidence interval came from – the parameter being estimated, units of measurement, design, confidence level, etc. • “Make a substantive interpretation of the means” – i.e., understand the practical significance of the results. • Interpretation of confidence intervals (already discussed). • When graphically comparing side-by-side confidence intervals for two independent groups, 50% overlap ≈ p≤ .05 and no overlap ≈ p≤ .01. • Use confidence interval for mean of differences in paired data problems, not separate confidence intervals.

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