Statistics2x2'x2'yates 'x'2
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This document summarizes Yates's correction for continuity, a statistical method used when testing for independence in contingency tables with small sample sizes. It describes how Yates's correction works by subtracting 0.5 from the difference between observed and expected frequencies to prevent overestimation of statistical significance. While useful for small data, Yates's correction may overcorrect results, so its use is now limited. The document also provides an example of applying Yates's correction to a 2x2 contingency table and defines key terms like chi-square tests, expected and observed frequencies, and contingency tables.
Statistics2x2'x2'yates 'x'2
- 2. Presentation topic 2x2’x2’ yates ‘x’2 ( with illustration) Presented by: Mangal Kardile
- 3. Yates's correction for continuity • Theory by Frank Yates (1902-1994) was one of the pioneers of 20th century Statistics • In Statistics Yates's correction for continuity (or Yates's chi-square test) is used in certain situations when testing for independence in a contingency table. • In some cases, Yates's correction may adjust too far, and so its current use is limited.
- 4. Yates's correction for continuity Yates's chi-square test - used in certain situations when testing for independence in a contingency table Right-handed Left-handed Totals Males Females 43 9 44 4 52 48 Total 87 13 100
- 5. Chi square – a Goodness of Fit • Karl Pearson- used x2 distribution for devising a test • To determine how well experimentally obtained results fit in the results expected theoretically on some hypothesis.
- 6. Hypothesis of Normal distribution • Expected results or frequencies are determined on the basis of the Normal distribution curve • E.g. Classification of group of 200 individuals as very good, good, average, poor, very poor • The observed frequencies are – Very good 55 Good 45 Average 35 Poor 35 Very poor 30
- 7. Normal distribution curve • Normal distribution of adjustment scores into five categories
- 8. Chi square testing fo- observed frequency Computation of x2 Contingency table fe- expected frequency • fo fe fo – fe ( fo - fe )2 ( fo – fe )2 / fe 14 19.4 -5.4 29.16 1.50 66 62.5 3.5 12.25 0.19 10 8 2.0 4.00 0.50 27 21.6 5.4 29.16 1.35 66 69.5 -3.5 12.25 0.18 7 9 -2.0 4.00 0.44 Total 190 190 x2 = 4.16
- 9. Using Yates's correction • When problem arising particularly in a 2x2 table with 1 degree of freedom • The procedure is to subtract 0.5 from the absolute value of the difference between observed and expected frequency • So each (fo) which is larger than it’s (fe) is decreased by 0.5 and each (fo) which is smaller than it’s (fe) is increased by 0.5
- 10. Yates's correction for small data • The effect of Yates's correction is to prevent overestimation of statistical significance for small data. • This formula is chiefly used when at least one cell of the table has an expected count smaller than 5. • Unfortunately, Yates's correction may tend to overcorrect. This can result in an overly conservative result that fails to reject the null hypothesis when it should. • So it is suggested that Yates's correction is unnecessary even with quite low sample sizes,such as
- 11. Pearson’s chi squared statistics • The following is Yates's corrected version of Pearson’s chi-sqared statistics • where: • Oi = an observed frequency • Ei = an expected (theoretical) frequency, asserted by the null hypothesis • N = number of distinct events ORA a b NA B c d NB NS NF N S F
- 12. Summary • The chi square test is used as a test of significance, when we have data that are given or can be expressed in frequencies / categories. • It does not require the assumption of a normal distribution like z and t or other parametric tests. • Sum of the expected frequencies must always be equal to the sum of the observed frequencies in a x2 test. • It is a completely distribution free and non-parametric test.
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