1 / 10

Chi Square

Chi Square. Chi Square. z, t and F tests are parametric (assume a normal distribution) Chi square is non-parametric (distribution free) A test of significance when data are expressed in frequencies or are expressed in percentages or proportions that can be reduced to frequencies. Three uses:

astra-nolan
Download Presentation

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

  2. Chi Square • z, t and F tests are parametric (assume a normal distribution) • Chi square is non-parametric (distribution free) • A test of significance when data are expressed in frequencies or are expressed in percentages or proportions that can be reduced to frequencies. • Three uses: • To determine if a certain distribution differs from some predetermined theoretical distribution. • Testing hypotheses concerning the significance of the difference of the responses of two or more groups to stimuli. • Testing goodness of fit.

  3. ( O - E ) 2 Chi Square x2 =  O 100 Flips of a coin Contingency table ( 40 - 50 ) 2 ( 60 - 50 ) 2 + = O E 50 50 40 50 Heads ( 10 ) 2 ( 10 ) 2 = + 60 50 Tails 50 50 100 100 100 100 = + 50 50 df = 1 = 2 + 2 = 4.00

  4. Example 91 patients w/MI Treatment: Propranolol vs. Placebo Outcome: Survival > 28 days vs. Death < 28 days H0: treatment w/propranolol does not significantly influence the proportion of MI patients who survive at least 28 days. Ha: treatment w/propranolol does significantly influence the proportion of MI patients who survive at least 28 days.

  5. ( O - E ) 2 x2 =  E Box 11–2 2 X 2 Contingency TableO = observed counts E = expected counts Outcome Survived > 28 days Death Propranolol (O) 38 33.13 7 11.87 45 45 Propranolol (E) Treatment 29 33.87 17 12.13 Placebo (O) 46 46 Placebo (E) 67 91 24 Row total E 1,1 = X Column total Study total

  6. ( O - E ) 2 x2 =  E ( 7 – 11.87 ) 2 ( 29 – 33.87 ) 2 ( 17– 12.13 ) 2 ( 38 – 33.13 ) 2 = + + + 11.87 33.87 12.13 33.13 (4.87 ) 2 (4.87 ) 2 (4.87 ) 2 ( 4.87 ) 2 = + + + 11.87 33.87 12.13 33.13 23.72 23.72 23.72 23.72 = + + + 11.87 33.87 12.13 33.13 + + + = 0.72 2.00 0.70 1.96 = 5.38 df = (R – 1)(C – 1) = (2 –1)(2 – 1) = 1

  7. [( O - E )-0.5] 2 x2 =  O Small numbers method (Yates correction for continuity) Box 11–2 2 X 2 Contingency TableO = observed counts E = expected counts Outcome Survived > 28 days Death Propranolol (O) 38 33.13 7 11.87 45 45 Propranolol (E) Treatment 29 33.87 17 12.13 Placebo (O) 46 46 Placebo (E) 67 91 24 Row total E 1,1 = X Column total Study total

  8. [(O - E)-0.5] 2 x2 =  E [(38 – 33.13)-0.5] 2 [(7 – 11.87)-0.5] 2 [(29 – 33.87)-0.5] 2 [(17– 12.13)-0.5] 2 + = + + 12.13 11.87 33.87 33.13 [(4.87)-0.5] 2 [(4.87)-0.5] 2 [(4.87)-0.5] 2 [(4.87 )-0.5] 2 + = + + 12.13 11.87 33.87 33.13 19.09 19.09 19.09 19.09 + = + + 12.13 11.87 33.87 33.13 + + + 0.576 1.608 .563 1.573 = = 4.32 df = (R – 1)(C – 1) = (2 –1)(2 – 1) = 1

  9. Chi Square in a large table O SA A NO D SD Group 1 54 Group 2 98 Group 3 48 70 44 26 26 34 200 E 54 Group 1 98 Group 2 48 Group 3 70 44 26 26 34 200 ( 48 – 34.3 ) 2 ( 12 –8.2 ) 2 ( 12 – 18.9 ) 2 +…. + + x2 =  34.3 8.2 18.9 df = (R – 1)(C – 1)

  10. Mid-term review • Types of data • Normal distribution • Variance • Standard deviation and z scores • 2 X 2 table • Hypothesis testing H0: HA: • t-test • Pearson r/Linear regression • Chi square

More Related