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Tables and Non Parametric Tests Lecture 5

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Compare Means Menu

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Compare Means Output ”Service package” ”Important package”

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Non-normal Data Log-normal data Transform Data Compare the means of the transformed (normal) data Binomial data Really non-normal data

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Binomial Data Are the proportions of Turks in Aalborg and Århus the same? Non- Turks Turks Aalborg46535 Århus35842

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Are the proportions significantly different? Non- Turks Turks Aalborg46535 Århus35842 7.0% 10.5% Compare 3.5% (= 10.5 – 7.0%) with suitable SE. Compare 3.5% (= 10.5 – 7.0%) with suitable SE.

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Another Approach Non- Turks Turks Aalborg46535 Århus35842 Non- Turks Turks Aalborg45743 Århus36634 Observed Expected In total 77 turks in a 900 sample, i.e. 8.6% In total 77 turks in a 900 sample, i.e. 8.6% We expect 34 turks in Århus (8.6% of 400) We expect 34 turks in Århus (8.6% of 400)

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Same proportion in Aalborg and Århus? Non- Turks Turks Aalborg46535 Århus35842 Non- Turks Turks Aalborg45743 Århus36634 Observed Expected Observed and expected should be close

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How to do it in SPSS …or data could be organized in 900 rows

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Cross-Tabs

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Tricks

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Output Expected values Proportions P-value Test Statistic

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Binomial One-Sample Two-Sample K-Sample Is proportion equal to 10% Proportions in Aalborg and Århus are equal Proportions in Aalborg, Randers, Vester Hjermislev and Århus are equal Cross-Tabs handles two or more cities (categories) 1.Calculate proportion and 95% CI 2.Is 10% in the CI? 1.Calculate proportion and 95% CI 2.Is 10% in the CI? …or use SPSS as I will show later

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Non-Normal Data Observations Ranks

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Statistics on Ranks Rank 14 26 37 510 812 913 1116 1417 1519 1820 Mean Ranks should be close if the two distributions are located similarly 8.6 12.4

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How to do it in SPSS

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Output Mann-Whitney Test ”Service package” ”Interesting package” ”Important package”

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One-Sample (Symmetry or Location) Kiama Blowhole Data Highly skew distribution Average approx 40 sec Rarely above 100 sec Median equal to 40 sec? Only above 100 sec in 1% of the eruptions? Normal distributed ?

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Output Data are Not Normal Not Uniform But QQ-plots are better!!

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Location of median Median equal to 40 sec? Only above 100 sec in 1% of the eruptions?

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Median equal to 40 sec?

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Output NPar Tests NOPE! Median equal to 40 sec?

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Only above 100 sec in 1% of the eruptions?

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K samples test

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Output Kruskal-Wallis Test ”Important package” ”Service package”

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Overview (normal samples) One sample Two samples (paired) K samples Two samples (unpaired)

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Overview (binomial samples) One sample Two samples (paired) K samples Two samples (unpaired)

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Overview (non normal samples) One sample Two samples (paired) K samples Two samples (unpaired)

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Copyright © 2013 Pearson Education, Inc. All rights reserved Chapter 9 Inferences Based on Two Samples Confidence Intervals and Tests of Hypotheses.

Copyright © 2013 Pearson Education, Inc. All rights reserved Chapter 9 Inferences Based on Two Samples Confidence Intervals and Tests of Hypotheses.

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