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Making Sense Making Numbers Making Significance

Making Sense Making Numbers Making Significance. Ulf H. Olsson Professor of Statistics. Making Sense. True Process. Empirical Domain. Theoretical Domain. Making Numbers. Estimation. Theoretical Domain. Empirical Domain. (Error of) Estimation.

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Making Sense Making Numbers Making Significance

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  1. Making SenseMaking NumbersMaking Significance Ulf H. Olsson Professor of Statistics

  2. Making Sense True Process Empirical Domain Theoretical Domain Ulf H. Olsson

  3. Making Numbers • Estimation Theoretical Domain Empirical Domain (Error of) Estimation If the model is correctly specified, different estimators should have similar values asymptotically (White, 1994) Ulf H. Olsson

  4. Making Numbers • 1) Structural Errors • 2) Incorrect functional form • 3) Distributional assumptions • => Different estimators will produce different results • => The empirical domain is among other things a function of the chosen estimator Ulf H. Olsson

  5. Making Numbers (Estimator) si : sample element : parameter vector : model implied element (parameter function) Ulf H. Olsson

  6. Making Numbers (Cov. Estimator) S: sample covariance : parameter vector : model implied covariance Ulf H. Olsson

  7. Econometric Model • Klein’s Model (1950) Ulf H. Olsson

  8. Making Numbers (OLS and TSLS) • CT = 16.237+0.193*PT+0.0899*PT_1+0.796*WT, R² = 0.981 • (1.303) (0.0912) (0.0906) (0.0399) • 12.464 2.115 0.992 19.933 • CT = 15.324+0.0763*PT+0.186*PT_1+0.828*WT, R² = 0.979 • (1.453) (0.138) (0.146) (0.0439) • 10.546 0.553 1.275 18.844 Ulf H. Olsson

  9. Making Significance • “ Weak Test” Ulf H. Olsson

  10. Making Significance • ”Strong Test” Ulf H. Olsson

  11. Making Significance Ulf H. Olsson

  12. Making SignificanceReject-Support (RS) • The researcher wants to reject H0 • Society wants to control Type I error • The researcher must be very concerned about Type II error • High sample size works for the researcher • If there is too much power, trivial effects become highly significant. Ulf H. Olsson

  13. Making SignificanceAccept-Support (AS) • The researcher wants to accept H0 • Society should be worrying about controlling Type II error • The researcher must be very careful to control Type I error • High sample size works against the researcher • If there is too much power, the researcher’s theory can be rejected by a significance test even though it fits the data almost perfectly Ulf H. Olsson

  14. Making Sense A strong theory will give precise predictions! Ulf H. Olsson

  15. Making sense is more important than making numbers, it is even more important than making significance? Ulf H. Olsson

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