Steffen grønneberg bi lecture 11 gra6036 17th march

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Steffen Grønneberg (BI) Lecture 11, GRA6036 17th March 2016 20 / 54
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An empirical example: Mental abilities The researchers’ interests were 1 to verify that the theorized structure among measurement and latent variables 2 to see how well the tests measured the abilities 3 to understand the correlation between the latent variables The tests scores were close to Normally distributed, so Maximum Likelihood Estimation was used. The researches were not interested in modeling the scale of the test scores, so they used the correlation matrix and not the covariance matrix (Note: This is uncommon ! And usually not recommended.) stata session Steffen Grønneberg (BI) Lecture 11, GRA6036 17th March 2016 21 / 54
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An empirical example: Mental abilities Parameter estimates: Steffen Grønneberg (BI) Lecture 11, GRA6036 17th March 2016 22 / 54
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An empirical example: Mental abilities The goodness-of-fit test has a p -value that is almost zero. The Goodness-of-fit test is rejected. Steffen Grønneberg (BI) Lecture 11, GRA6036 17th March 2016 23 / 54
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An empirical example: Mental abilities Let’s take a step back and consider what it means that the χ 2 Goodness-of-fit test is rejected. It means that the empirical covariance matrix is sufficiently different from the fitted model implied covariance matrix so that the difference cannot be attributed to chance variations. That is, a rejected χ 2 goodness-of-fit test means it is unlikely that our model is exactly correct (using unlikely not in a strict probabilistic sense). However, we are fitting linear models for possibly very complex phenomena – we probably only hope that the model can be a close approximation to the (possibly very complex) truth. Steffen Grønneberg (BI) Lecture 11, GRA6036 17th March 2016 24 / 54
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An empirical example: Mental abilities A similar situation is met in many statistical applications. Suppose a large pharmaceutical company would like to show that their treatment is better than their competitor’s. The difference between the old and their new product is estimated, and using statistics they can test H 0 : Improvement 0 versus H A : Improvement > 0 . These types of experiments often involve several thousands of people . This means, even if the estimated difference is positive, but very small (say, 0 . 01), we will reject H 0 . This is because the sample is so large, that even very small deviations from H 0 should be detected and with a sufficiently large sample, the p-value will become arbitrarily small. Steffen Grønneberg (BI) Lecture 11, GRA6036 17th March 2016 25 / 54
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An empirical example: Mental abilities If the pharmaceutical company simply reports that H 0 is rejected, it means very little – and would be dishonest. We get a statistically significant effect, but a practically insignificant effect . However, reporting a confidence interval of ( 0 . 0099 , 0 . 0101 ) reveals that the effect is positive but so small it’s probably practically insignificant .
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