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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 SenseMaking NumbersMaking Significance Ulf H. Olsson Professor of Statistics
Making Sense True Process Empirical Domain Theoretical Domain Ulf H. Olsson
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
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
Making Numbers (Estimator) si : sample element : parameter vector : model implied element (parameter function) Ulf H. Olsson
Making Numbers (Cov. Estimator) S: sample covariance : parameter vector : model implied covariance Ulf H. Olsson
Econometric Model • Klein’s Model (1950) Ulf H. Olsson
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
Making Significance • “ Weak Test” Ulf H. Olsson
Making Significance • ”Strong Test” Ulf H. Olsson
Making Significance Ulf H. Olsson
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
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
Making Sense A strong theory will give precise predictions! Ulf H. Olsson
Making sense is more important than making numbers, it is even more important than making significance? Ulf H. Olsson