16 Categorical Data - Categorical Data Devore and Berk Chp....

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Unformatted text preview: Categorical Data Devore and Berk Chp. 13 Population Proportion Chi-Square Goodness of Fit Contingency Tables Single Slide Review z Are populations the same or different? z Check means z Check variances z Analyze mean squared error under different models for means z Use normal, t, F distributions to quantify how different things are Suppose you wish to compute a proportion? z Proportion of Females to Total Population z Not Ratio of Females to Males z Proportion Heads to Total Tosses z Proportion Surviving Out of Total z Proportion of Hemlocks to Total Trees TREE X Y CANOPY SPECIES DBH90 1 58.96 5.11 CD TSCA 27.0 2 58.58 5.40 S TSCA 12.6 3 58.08 5.89 D TSCA 25.3 4 56.25 6.16 S TSCA 12.7 5 56.21 7.26 I TSCA 16.1 6 54.24 6.34 S TSCA 16.2 7 53.21 7.31 S TSCA 16.5 8 53.51 7.63 CD TSCA 42.5 9 52.93 8.93 S TSCA 15.1 10 51.95 9.90 S TSCA 12.5 11 49.31 4.79 D ACRU 25.7 12 49.76 3.13 I ACRU 16.3 13 48.57 1.09 I PIRU 13.0 14 52.44 2.50 PIRU 9.2 15 53.71 3.27 CD TSCA 19.6 Harvard's Hemlock Woodlot Easting Northing 10 20 30 40 50 60 20 40 60 80 100 120 TREE X Y CANOPY SPECIES DBH90 HEMTRUE 1 58.96 5.11 CD TSCA 27.0 1 2 58.58 5.40 S TSCA 12.6 1 3 58.08 5.89 D TSCA 25.3 1 4 56.25 6.16 S TSCA 12.7 1 5 56.21 7.26 I TSCA 16.1 1 6 54.24 6.34 S TSCA 16.2 1 7 53.21 7.31 S TSCA 16.5 1 8 53.51 7.63 CD TSCA 42.5 1 9 52.93 8.93 S TSCA 15.1 1 10 51.95 9.90 S TSCA 12.5 1 11 49.31 4.79 D ACRU 25.7 12 49.76 3.13 I ACRU 16.3 13 48.57 1.09 I PIRU 13.0 14 52.44 2.50 PIRU 9.2 15 53.71 3.27 CD TSCA 19.6 1 Mean Mean Proportion = = = = = = n i i N i i y n y p Y N Y p 1 1 1 1 Mean Variance of Proportion ( ) ( ) = = = = = = = + = + = = N i i N i i N i i N i i N i i N i i i N i i Y Y N Y Y N Y N Y Y Y Y N Y Y N Y V 1 1 2 1 1 2 1 2 1 2 2 1 2 1 1 2 1 2 1 1 ) ( Mean Variance of Proportion ( ) pq p p p p Y Y N Y N Y Y N Y N Y Y N Y V N i i N i i N i i N i i N i i N i i N i i = = = = = = = = = = = = = ) 1 ( 1 1 1 1 1 ) ( 2 1 1 2 1 1 1 2 1 2 1 2 Mean Variance of Estimated Proportion ( ) q p n y y n n y V n y n V y V p V n i i n i i n i i 1 1 1 1 1 ) ( 1 1 ) ( ) ( 1 2 1 2 1 = = = = = = = = Mean Variance of Estimated Proportion with Finite Population Correction (fpc) = 1 1 1 ) ( N n N q p n p V Mean Confidence Interval of Estimated Proportion with fpc = 1 1 2 ) ( 2 N n N n q p p p V p Setup the 0:1 Column Take a Sample...
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16 Categorical Data - Categorical Data Devore and Berk Chp....

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