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Analyzing Non-Normal Data: Binomial Proportions and Median Testing in SPSS

This lecture focuses on statistical methods for analyzing non-normal data, particularly binomial data. It explores whether the proportions of Turks in Aalborg and Århus are significantly different, using sample data and expected values. The course covers how to compute proportions, confidence intervals, and perform hypothesis testing with SPSS. Additionally, it discusses handling highly skewed distributions, exemplified by Kiama Blowhole eruption data, and testing if the median equals a specific value. Participants will learn practical techniques for data analysis and comparison of means.

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Analyzing Non-Normal Data: Binomial Proportions and Median Testing in SPSS

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  1. Tables and Non Parametric Tests Lecture 5

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

  3. Binomial Data Are the proportions of Turks in Aalborg and Århus the same?

  4. Are the proportions significantly different? 7.0% 10.5% Compare 3.5% (10.5 – 7.0%) with suitable SE.

  5. Another Approach Observed Expected In total 77 turks in a 900 sample, i.e. 8.6% We expect 34 turks in Århus (8.6% of 400)

  6. Same proprotion in Aalborg and Århus? Observed Expected Observed and expected should be close

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

  8. Cross-Tabs

  9. Tricks

  10. Output Expected values Proportions Test Statistic P-value

  11. 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 • Calculate proportion and 95% CI • Is 10% in the CI? Cross-Tabs handles two or more cities (categories) …or use SPSS as I will show later

  12. One-Sample (Symmetry or Location) Normal distributed ? • 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?

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

  14. Median equal to 40 sec?

  15. Output NPar Tests Median equal to 40 sec? NOPE!

  16. Only above 100 sec in 1% of the eruptions?

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