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Infant mortality and economics

Infant mortality and economics. Is there any relationship?. Testing linear relationships. We are interesting in establishing a relationship between economic variables and an important measure of health: infant mortality

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Infant mortality and economics

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  1. Infant mortality and economics Is there any relationship?

  2. Testing linear relationships • We are interesting in establishing a relationship between economic variables and an important measure of health: infant mortality • We have data at the county level for North Carolina; we want to know how the mean infant mortality may change as, say, income increases

  3. Test hypothesis • So the usual approach is to test the hypothesis that the coefficient of income (slope) is equal to zero • To improve power, we want to do a one-sided test, and reject the hypothesis of zero slope in favor of a negative slope, if the t-statistic is sufficiently negative

  4. And if we fail to reject? • Either the slope is really zero (or not far enough away for us to care) • Or the situation is really noisy: • Noise variance is large • Sample size is small • Not much spread in explanatory variable

  5. To show that the slope is small • We need to show that if the slope were big enough to care, we could have found it – Pr(reject H | Hypothesis true) = level = .05 (say) Pr(reject H | Alternative true) = power Power will be a function of variance, sample size, spread, and slope. If we keep the first three as in our study, and show that the power is LARGE for small values of slope, ….

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