1 / 17

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.

brett-christensen
Download Presentation

Inferential statistics 3

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related