1 / 30

Chi-Square

Chi-Square. Test of significance for proportions FETP India. Competency to be gained from this lecture. Test the statistical significance of proportions using the relevant Chi-square test. Key elements. Principles of the Chi-square Comparison of a proportion with an hypothesized value

odetta
Télécharger la présentation

Chi-Square

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Chi-Square Test of significance for proportions FETP India

  2. Competency to be gained from this lecture Test the statistical significance of proportions using the relevant Chi-square test

  3. Key elements • Principles of the Chi-square • Comparison of a proportion with an hypothesized value • Chi-square for 2x2 tables • Chi-square for m x n tables • Testing dose-response with Chi-square

  4. Analyzing quantitative and qualitative data

  5. Chi-square: Principle • The Chi–square test examines whether a series of observed (O) numbers in various categories are consistent with the numbers expected (E) in those categories on some specific hypothesis (Null hypothesis) • O= Observed value • E= Expected value Principle

  6. How the Chi-square works in practice • X2 = 0 when every observed value is equal to the expected value • As soon as an observed value differs from the expected value, the X2 exceeds zero • The value of the X2 is compared with a tabulated value • If the calculated value of X2 exceeds the tabulated value under the column p = 0.05, the null hypothesis is rejected Principle

  7. Chi-square table:Percentage points of X2 distribution Principle

  8. Use of Chi-square to compare a proportion with a hypothesized value • The reported coverage for measles in a sub-center is 80% • The chief medical officer of the district suspects that this coverage could be overestimated • Validation survey with 80 children selected using simple random sampling • 56/80 (70%) vaccinated Hypothesized value

  9. Chi-square calculations

  10. Interpretation of the Chi-square • The calculated value of X2 (i.e., 5) with 1 degree of freedom exceeds the table value (3.84) at 5% level • Hence, the medical officer rejects the null hypothesis that the coverage is 80% Hypothesized value

  11. Use of Chi-square to compare proportions between two samples • Cholera outbreak affecting a village • Cases clustered around a pond • Hypothesis generating interviews suggest that many case-patients washed their utensils in the pond • The investigator compares those who washed their utensils with the others in terms of cholera incidence 2x2 tables

  12. Incidence of diarrhea (cholera) among persons who washed utensils in a pond and others, South 24 Parganas, West Bengal, India, 2006 2x2 tables

  13. Chi-square to test the difference in the two proportions • The proportion of persons affected by cholera in the exposed and unexposed groups differ • Three steps to test whether this difference is significant: • Calculate expected values • Compare observed and expected to calculate the Chi-square • Compare the Chi-square with tabulated value 2x2 tables

  14. Step 1: Calculate the expected values (1/2) • 51% of the population became sick • If the cholera occurred at random, these proportions apply to the two groups, exposed and unexposed 2x2 tables

  15. Step 1: Calculate the expected values (2/2) • 51% of the 56 who washed utensils (=28) should have been sick • All other numbers can de deducted by subtraction (one degree of freedom) 2x2 tables

  16. Step 2: Compare observed and expected values 2x2 tables

  17. Step 3: Interpretation of the Chi-square • The calculated value of X2 (i.e., 68.6) with 1 degree of freedom exceeds the table value (3.84) at 5% level • Hence, we reject the Null hypothesis that the attack rate of cholera is equal in the exposed and unexposed group • This may suggest washing utensils in the pond is a source of infection if other elements of the investigation also support the hypothesis 2x2 tables

  18. Simpler Chi-square formula 2x2 tables

  19. Application of simpler Chi-square formula to the cholera example 2x2 tables

  20. Corrected Chi-square formula Note that the corrected value will always be smaller than the uncorrected which tends to exaggerate the significance of a difference 2x2 tables

  21. Example of a 4x2 table Degrees of freedom = (Nbr of rows-1) x (Nbr of columns-1)=(4-1)x(2-1)= 3x1=3 N x N tables

  22. Calculation of the Chi-square for a 4x2 table • Overall prevalence of cataract = 9.6% • Apply 9.6% proportion to all groups to calculate expected values • Use generic formula N x N tables

  23. Interpretation of a Chi-square for a m x n table • The Chi-square tests the overall Null hypothesis that all frequencies are distributed at random • If the Null hypothesis is rejected, it means the distribution is heterogeneous • It is not possible to: • “Attribute” the difference to a particular group • Regroup categories according to differences observed and test with a 2x2 table (i.e., post-hoc analysis) • Test with multiple 2x2 tables (i.e., multiple comparisons) N x N tables

  24. Key rule about Chi-square • Chi- square test should be applied on qualitative data set out in the form of frequencies • Chi– square test should not be done on: • Percentages • Rates • Ratios • Mean values N x N tables

  25. Limitations to the use of Chi-square • When sample size is small, other exact tests (e.g., Fisher exact test) are preferred and calculated with computer • N < 30 • Expected value < 5 • When several expected cell frequencies are less than one, it is better to amalgamate rows / columns N x N tables

  26. Testing a dose-response relationship with a Chi-square • Overall m x n Chi-square • Tests the null hypothesis that the odds ratios do not differ • No particular conditions needed • Overall test, easy to compute • Rough conclusions • Chi-square for trend Dose-reponse

  27. Exposure to injections with reusable needles and acute hepatitis B, Thiruvananthapuram, Kerala, India, 1992 Heterogeneous exposures categories Overall 3x2 Chi-square : 42, 2 degrees of freedom, p<0.00001 Dose-reponse

  28. Testing a dose-response relationship with a Chi-square • Overall m x n Chi-square • Chi-square for trend • Tests for a linear trend for the increase of the odds ratios with increased levels of exposure • Requires equal interval in the exposure categories • Can be calculated on a computer • Refined conclusions Dose-reponse

  29. Odds of typhoid according to raw onion consumption, Darjeeling, West Bengal, India, 2005-2006 Homogeneousexposures categories Chi-square for trend: 16.8; P-value: 0.0004 Dose-reponse

  30. Take home messages • The Chi-square compares expected and observed counts • The Chi-square can compare an actual proportion with a theoretical one • The Chi-square is the basic test to compare proportions in epidemiological 2x2 tables • The Chi-square can be used also as a global test for m x n tables • Specific Chi-squares can be used to test for dose-response effect

More Related