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Comparison of proportions 比例的比較 -Part I

Comparison of proportions 比例的比較 -Part I. Instructor: 李奕慧 yihwei@mail.tcu.edu.tw. Lecture Overview. Cross Tabulations 2 X 2 tables R XC tables Chi-square Test for Independence Chi-square Test for Trend. Cross Tabulation and Chi-square test for independence:

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Comparison of proportions 比例的比較 -Part I

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  1. Comparison of proportions 比例的比較-Part I Instructor: 李奕慧 yihwei@mail.tcu.edu.tw

  2. Lecture Overview • Cross Tabulations • 2 X 2 tables • R XC tables • Chi-square Test for Independence • Chi-square Test for Trend

  3. Cross Tabulation and Chi-square test for independence: To Explore the Association Between Two Categorical Variables, 例：機車騎士戴安全帽與否是否與發生車禍時頭部受傷的機率有關？

  4. Data Input Data Type : Measure Scale: 連續變數 Nominal/Ordinal: 類別變數 Value: 定義類別變數的項目， 0=“no”, 1=“yes”. Helmet.sav dataset

  5. Observed frequencies: O11, O12, O21, O22

  6. Under H0, Expected frequencies: E11, E12, E21, E22 E11 = 200 x P(戴安全帽) x P(頭部受傷) = 200 x (100/200) x (74/200) = 37 E12 = 200 x P(戴安全帽) x P(頭部沒受傷) = 200 x (100/200) x (126/200) = 63=100-37

  7. Expected frequencies: E11, E12, E21, E22

  8. Chi-square test (2-test) for independence

  9. 大樣本用：Pearson Chi-square Test 小樣本用：Fisher’s Exact Test

  10. Row variable: Injury Column variable: Helmet 數學上的慣例：Row *Column

  11. SPSS Menu Analyze > Descriptive Statistics > Crosstabs

  12. Another way to input data Data >Weight Cases Helmet2.sav dataset

  13. 當樣本數很小時，或E11, E12, E21, E22小於5 Chi-square 檢定不夠準確，必須使用 Yate’s continuity correction test, or Fisher’s exact test

  14. Summary results: 2-test = 3.846, P-value = 0.050 Yate’s corrected 2-test = 2.345 , P-value = 0.126 Fisher’s exact test, P-value = 0.086

  15. Table Example in Research Article Values are number of study subjects (percentage). P-value is derived from Fisher’s exact test.

  16. Helmet3.sav

  17. R x C Tables • Row variable with r levels • Column variable with c levels • Test for the independence between Row and Column variables • Using Chi-square test with df=(r-1)x(c-1)

  18. Test H0: proportions of each type of death certificates are identical in the two hospitals (There is no association between hospital type and death certificate status)

  19. Expected counts under H0: independence Erc=(nr x nc)/575

  20. Chi-square test for no association (independence) between Hospital type and death certificate status with df=(2-1)(3-1)=2, P<0.001 Reject H0 and conclude that there is an association between hospital type and death certificate status. It appears (from data) that Hospital A contains a larger proportion of death certificates that are incorrect and required recoding than Hospital B.

  21. Hospital.sav

  22. Chi-square test for trend • If one or both variables are ordinal, then chi-square test for trend is appropriate. • Chi-square test for trend also known as Mantel-Haenszel test for trend. • In R x 2 Tables, • H0: p1=p2=…=pc versus • Ha: p1<p2<…<pc (an increasing trend) or Ha:p1>p2>…>pc (a decreasing trend)

  23. Examples for chi-square test for trend H0: P65-69=P70-74=P75+ Ha: P65-69>P70-74>P75+ or P65-69<P70-74<P75+ MI之後，抽煙病人接受戒煙諮商的比例，隨著年齡增加有下降的趨勢

  24. Smoking.sav

  25. Exercise Am J Public Health. 2004 Oct;94(10):1768-74

  26. Categorical data: depression= (yes or no) • H0: proportion of subjects with depression in women = proportion of subjects with depression in men • H0: pf = pm • Ha: proportion of subjects with depression in women is different from proportion of subjects with depression in men • Ha: pf pm

  27. Depression.sav

  28. Exercise:Comparison among age groups • H0: proportions of subjects with depression are the same among the three age groups. H0: p75-79 = p80-84 = p85+ • Ha: proportions of subjects with depression are different among the three age groups. (test for independence) • Ha: depression prevalence is increasing in older age groups. (test for trend)

  29. Practice! Practice! Practice! Thank you !

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