Inferential statistics-part 2Chi-Square Test
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Inferential Statistics Part - 2 deals with Nonparametric test. Only Chi-square is discussed here.
Inferential statistics-part 2Chi-Square Test
- 1. Inferential Statistics Part 2 By; Mrs. Babitha K Devu Assistant Professor SMVDCoN
- 2. Concepts & Definition • A non-parametric statistical test is a test whose model does NOT specify conditions about the parameters of the population from which the sample was drawn. • It does not require measurement so strong as that required for the parametric tests. • Most non-parametric tests apply to data in an ordinal scale, and some apply to data in nominal • They do not make numerous or stringent assumptions about parameters.
- 4. Types of Non-Parametric Tests
- 5. Chi-square Test • This is non parametric test to find out the association between two events in binomial (only two outcome) or multinomial (multiple outcome) samples. • It is represented by Χ2 . It is used to find out association between two discrete attributes. • Eg. Association between smoking in pregnancy and low birth weight babies, blood pressure and renal diseases, obesity and coronary diseases. • It is used to find the significant difference in two or more than two proportions.
- 6. Chi-square Test Prerequisites of Chi-square test. • 1. Preferably random sample but not necessarily. • 2. Qualitative data measured on nominal or ordinal scale. (frequency data not the means.) • 3. Sample size should be more than 30. • 4. Lowest expected frequency not less than 5.
- 7. Chi-square Test Steps of Chi-square test. • Make contingency table • Note the frequencies observed in each class of one event row wise and numbers in each group of other event column wise. • Determine the expected number (E) in each cell of table on assumption of null hypothesis. • E = column or vertical total x row or horizontal total / sample total. • Find the difference between the observed and the expected frequencies in each cell (O - E)
- 8. Chi-square Test Steps of Chi-square test. • Calculate X2 (Chi-square) value for each cell by the formula X2 = (O – E)2 / E • Sum up the Chi-square values of all cells to get the chi-square value. • X2 df = Σ (O – E)2 / E • Calculate df from the number of categories in each event. df = (c-1)(r-1) where c is the total number of columns and r is the total number of rows. • Refer the X2 table. If the calculated value is greater than the tabulated value then reject the null hypothesis.
- 9. Chi-square Example • Below given contingency table shows the effect smoking on low birth weight of the babies. Find the significance of association between smoking and low birth weight of the babies. • H0 = There is no significant association between smoking and low birth weight of babies among mothers. Low birth weight No low birth weight Smoker 211 73 Non smoker 111 286
- 10. Chi-square Example • Determine the expected number (E) in each cell of table by using following formula. E = column or vertical total x row or horizontal total / sample total. Low birth weight No low birth weight Total Smoker 211 73 284 Non smoker 111 286 397 Total 322 359 681
- 11. Chi-square Example • E1 = 322x284/681 = 134.28 • E2 = 322x397/681 = 187.71 • E3 = 359x284/681 = 149.71 • E4 = 359x397/681 = 209.28 • Calculate the Chi-square value for each cell • X 2 1 = (211 – 134.28)2 / 134.28 = 43.83 • X 2 2 = (111 – 187.71)2 / 187.71 = 31.34 • X 2 3 = (73 – 149.71)2 / 149.71 = 39.3 • X 2 4 = (286 – 209.28)2 / 209.28 = 28.12 • Σ X2 = 142.59
- 12. Chi-square Example • Calculate df, (c-1)(r-1) = (2-1)(2-1) = 1 • Table value for df 1 under probability of 0.01 is 6.635. • If the calculated value is greater than the tabulated value then reject the null hypothesis. • 142.59 > 6.635, hence the null hypothesis is rejected at the significance of 0.01.