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Inferential statistics 3

Inferential statistics 3. Maarten Buis 16/1/2006. outline. recap computer lab significance of a correlation significance of a regression coefficient confidence interval. One, independent, or paired sample t-test.

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Inferential statistics 3

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  1. Inferential statistics 3 Maarten Buis 16/1/2006

  2. outline • recap computer lab • significance of a correlation • significance of a regression coefficient • confidence interval

  3. One, independent, or paired sample t-test • If we compare a mean in one sample to a fixed value than we do a one sample t-test. • If we compare the means of one variable between two samples, than we do a independent sample t-test • If we compare the means of two variables asked to the same persons, than we do a paired sample t-test

  4. one sample t-test

  5. independent sample t-test

  6. paired sample t-test

  7. One sided vs. two sided • Look up different critical values in Appendix B, table 2

  8. Reporting test results • Specifying H0, HA, a. • H0 is the hypothesis you want to reject • report the test statistic (in this case the t-value), the degrees of freedom if applicable, and the p-value. • report your decision (reject or not reject H0)

  9. Tests for correlation coefficients • Correlation coefficient can range between -1 and 1. • The sampling distribution can’t be symmetric if the real correlation is close to either 1 or -1. • The sampling distribution is symmetric and approximately normal if the real correlation is zero.

  10. Test for correlation coefficient • If you are testing a H0 that r is 0, than you can assume normality of the sampling distribution. Otherwise you can’t. • t only depends on observed r and N

  11. Test for correlation • You have to normalize the correlation if the H0 is not equal to 0 or when testing differences between correlations • Fishers z-transformation, see appendix 2 table D • The sampling distribution of the transformed correlation coefficient will be normally distributed with a standard error of

  12. Significance testing in regression

  13. confidence intervals • Until now we have made decisions about whether or not to except the H0 • Sometimes we are more interested in a “good guess” about the mean in the population. • The mean in the sample is our “best guess” • But we can also make an interval of “good guesses” • a small interval means a precise estimate, and a wide interval less precise estimate

  14. Confidence interval • What is a “good” interval? • A 95% confidence interval will contain the true population parameter in 95% of all the times it is computed. • We are not 95% sure that the true value lies in that interval. • The confidence we have in the confidence interval stems from the quality of the procedure we have used.

  15. Data: rents of rooms

  16. confidence interval for mean rent • N=19, so df =18 • look up the two sided critical t-value in Appendix B, table 2: 2.101 • mean is 258, s = 99, so se = • lb = 258 - 22.7*2.101 = 210 • ub = 258 + 22.7*2.101 = 306

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