9_13_11_Ftest_Traff_Data_v1

9_13_11_Ftest_Traff_Data_v1 - F-Test The F-test is designed...

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CE4001 Transportation Safety 1 F-Test The F-test is designed to test if two population variances are equal. Recall the Chi-squared Test Compares ratio of two variances. If the variances are equal, the ratio of the variances will be 1.
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CE4001 Transportation Safety 2 F-Test What are the possible null and alternate hypotheses? ° 2 ± 2 ± 1 ° 1
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CE4001 Transportation Safety 3 Hypotheses H0: Ha: ° 1 = ° 2 ° 1 < ° 2 ° 1 ≠ ° 2 ° 1 > ° 2
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CE4001 Transportation Safety 4 F statistic 2 2 2 1 S S F rejected for if   1 , 1 , 2 1 N N F F 2 1  N 1 and N 2 are the samples sizes for the 2 samples. The degrees of freedom for using the table refers to the significance level, and samples sizes of the two samples
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CE4001 Transportation Safety 5 F statistic 2 2 2 1 S S F rejected for if   1 , 1 , 1 2 1 N N F F 2 1  The other direction
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CE4001 Transportation Safety 6 Quick note about hypothesis testing H a : for a lower one tailed test for an upper one tailed test for a two tailed test The hypothesis that the two standard deviations are equal is rejected if for an upper one-tailed test for a lower one-tailed test for a two-tailed test or
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CE4001 Transportation Safety 7 F tables There is a different table for each significance level So should we carry around a bunch of F tables? Or how else could we obtain F values?
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CE4001 Transportation Safety 8 F tables Use the Excel function finv to obtain F values finv(probability, dof 1, dof 2) E.g. finv(0.05, 5, 5) = 5.05 df2/df1 1 2 3 4 5 1 161.4476 199.5000 215.7073 224.5832 230.1619 2 18.5128 19.0000 19.1643 19.2468 19.2964 3 10.1280 9.5521 9.2766 9.1172 9.0135 4 7.7086 6.9443 6.5914 6.3882 6.2561 5 6.6079 5.7861 5.4095 5.1922 5.0503
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CE4001 Transportation Safety 9 F vs. T Compare the F distribution with T distribution (symmetric about 0) For T we use negative values on the left side, while for F we use 1-
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CE4001 Transportation Safety 10 Miscellaneous Statistics Notes Regression to the mean (not applicable to Albert Pujols) Problem with using rates
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CE4001 Transportation Safety 11 Regression to the Mean (RTM) Anyone heard of this problem?
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CE4001 Transportation Safety 12 Regression to the Mean (RTM) Problematic if sites are identified for
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This note was uploaded on 10/26/2011 for the course ECON 101 taught by Professor Dr.siam during the Spring '11 term at American University of Kuwait.

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9_13_11_Ftest_Traff_Data_v1 - F-Test The F-test is designed...

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