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

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