Chi-square test. Wenli Lu Dept. Health statistics School of public health Tianjin medical university. Chi-square

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1 Chi-square test Wenli Lu Dept. Health statistics School of public health Tianjin medical university Chi-square =0 O E ( O E) ( O E) 2 1

2 Example Is there difference of gender distribution between treatment and control group? Characteristic of data-two two variable Group categorical variable Group 1 Treatment Group 2 Control Gender - categorical variable Male Female Trial Data Descriptive group * gender Crosstabulation group Total treatment control gender male female Total % 41.4% 100.0% % 39.3% 100.0% % 40.3% 100.0% Table 1 Characteristics of subjects in treatment and control group (N/%) Group N Male Female Treatment (58.6) 24(41.4) Control 61 37(60.7) 24(39.3) 2

3 Results All expected number are greater than 5 and n is greater than 40. Pearson Chi-Square Continuity Correction a Asymp. Sig. Value df (2-sided).051 b b. (2-sided) (1-sided) cells (.0%) have expected count less than 5. The minimum expected count is If If there is is one expected number less than 5 and greater than 1 one and expected N is greater number than less 40. than 1 Or N is less than 40. Results Table 1 Characteristics of subjects in treatment and control group (N/%) Group N Male Female Treatment (58.6) 24(41.4) Control 61 37(60.7) 24(39.3) 2 * P=0.821 Chi-square with SPSS-Compare two proportions Analyze Descriptive Crosstab 3

4 Pearson Chi-Square Continuity Correction a Asymp. Sig. Value df (2-sided).051 b b. (2-sided) (1-sided) cells (.0%) have expected count less than 5. The minimum expected count is Exercise 1 Is the difference of proportion of co-morbidity (disease history) statistically significant? 4

5 group * CHD Crosstabulation CHD group treatment no yes Total % 22.4% 100.0% control % 18.0% 100.0% Total % 20.2% 100.0% Pearson Chi-Square Continuity Correction a Asymp. Sig. Value df (2-sided).354 b b. (2-sided) (1-sided) cells (.0%) have expected count less than 5. The minimum expected count is Exercise 2 A clinical trial for a new medication for peptic ulcer Is the drug A is more effective than the drug B? Group Cure No cure Total Drug A Drug B Total Asymp. Sig. Value df (2-sided) (2-sided) (1-sided) Pearson Chi-Square b Continuity Correction a b. 1 cells (25.0%) have expected count less than 5. The minimum expected count is There is one expected number less than 5 and greater than 1 and n is greater than 40. Decision: reject the null hypothesis Conclusion: Drug A is probably more effective than Drug B. 5

6 Example 2 A polysomnographic (PSG), placebo-controlled controlled evaluation of the efficacy and safety of eszopiclone (ES) relative to placebo and zolpidem (ZO) in the treatment of primary insomnia. This multicenter, randomized, crossover study enrolled patients aged years meeting the DSM-IV criteria for primary insomnia (n = 122). Patients received 2 nights treatment each with placebo, eszopiclone and zolpidem after randomization to one of 6 treatment sequences. Visits were separated by a day washout. Objective efficacy was assessed by PSG. group * outcome Crosstabulation group Total placebo zolpidem eszopiclone outcome effective ineffective Total % 87.5% 100.0% % 70.3% 100.0% % 21.6% 100.0% % 62.3% 100.0% Assumptions / Limitations Data is from a random sample. A sufficiently large sample size is required (at least 40) Actual count data (not percentages) Adequate cell sizes should be present. >5 in all cells- if less number (<5) present apply Yates correction-2 2 rates comparison; If less number (<1) apply fisher exact tests-2 2 rates comparison Regarding to more than 2 rates comparision,, no Yates correction, no fisher exact tests; Enlarge sample size! Or Give up!) Observations must be independent. 6