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1 Chi-Square Test(one) Chapter 8

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2 Content test of fourfold data test of RC table Multiple comparison of sample rates test of paired fourfold data Fisher probabilities in fourfold data test of goodness of fit

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objection to deduce if there is any discrimination of the ratio or structure ratio between two populations or among more than two populations multiple comparison of the ratio of multi-samples to deduce if there is any correlation between two class variables test of goodness of fit fit for :qualitative data

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4 Section one test of fourfold data

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5 objective to judge if there is any discrimination of the rate or structure ratio between two populations equal to the u- test demand the number of individuals from the two samples classified into two categories should be transformed into a fourfold data

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6 1 distribution is a continuous distribution 2 one of the basic characters is that it can be plus to others 1 The basic idea of test distribution

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8 2. The basic idea of test eg 8-1 one hospital want to compare the curative effect of drug A Omeprazole and drug B (Ranitidine in treating the peptic ulcer. They devided 169 patients with peptic ulcer into two groups at random the results are as follows (table 8-1). According to the data, whether the effective ratio is different ?

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9 Table 8-1 the comparison of the healing ratio between two groups in healing peptic ulcer H 0 1 = 2 H 1 1 2

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10 chart 8-2 the basic form of fourfold table data

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11 The respected frequencies can be calculated by the following formula T RC refers to the expected frequencies in Row R and Line C n R refers to the frequency sum of a certain row n C refers to the frequency sum of a certain column

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12 Table 8-1 the comparison of the healing ratio between two groups in healing peptic ulcer

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13 Basic idea can be showed with the basic formula of test A means actual frequency while T means theoretical frequency

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14 Basic idea of 2 test Given a set of observed frequency distribution A 1, A 2, A 3 to test whether the data follow certain theory. If the theory is true, then we will have a set of theoretical frequency distribution: T 1, T 2, T 3 Comparing A 1, A 2, A 3 and T 1, T 2, T 3 If they are quite different, then the theory might not be true; Otherwise, the theory is acceptable.

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15 the respected frequency is set by the hypothesis and by the ratio after merging

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16 the test statistic :the value of reflects the fitness of actual frequency and expected frequency

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17 from formula 8-2,we can see that the value of also depends on the size of (exactly the size of ). is decided by the number of the grids, but not the sample size.

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18 1 establish hypothesis, and set the criteria of the test H 0 : 1 = 2 H 1 : 1 2 =0.05 3. The process of hypothesis test

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19 2 to calculate the test statistic

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21 4.The specific formula fourfold table data

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22 distribution is a continuous one, while the fourfold table data is dispersible, the value of calculated by the latter is also dispersible, in order to improve the continuousness of the statistic distribution,the continuousness correcting is needed.

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24 5.The corrected formula

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25 the conditions in choosing test formula for the fourfold table data special formula corrected formula Fishier exact probabilities method

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26 eg 8-2 one doctor want to compare the effect of treatment A (simple chemotherapy) and treatment B (complex chemotherapy) in curing Lymphoid tumor he divided 40 patients with such illness into two groups at random,the results are in table 8-3, whether the remission rate of the two treatments are the same ?

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27 in this case, n=40, 1

40 Caution: (1) Either 2 2 table or R C table are all called contingency table. 2 2 table is a special case of R C table (2) When R>2, H 0 is rejectedonly means there is difference among some groups. Does not necessary mean that all the groups are different. (3) The 2 test requires large sample, By experience, The theoretical frequencies should be greater than 5 in more than 4/5 cells; The theoretical frequency in any cell should be greater than 1. Otherwise, we can not use chi-square test directly.

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41 If the above requirements are violated, what should we do? (1) Increase the sample size. (2) Re-organize the categories, Pool some categories, or Cancel some categories

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42 Multiple comparison between multiple rates

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43 Bonferroni method

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