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Non-parametric Measures of Association

Non-parametric Measures of Association. Chi-Square Review. Did the | organization| split | Type of leadership for organization this year? | Factional Weak or Divided Strong Unitary| Total ------------+--------------------------------------------+----------

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Non-parametric Measures of Association

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  1. Non-parametric Measures of Association

  2. Chi-Square Review Did the | organization| split | Type of leadership for organization this year? | Factional Weak or Divided Strong Unitary| Total ------------+--------------------------------------------+---------- No split | 33 195 835 478 | 1,541 Split | 27 0 16 5 | 48 ------------+--------------------------------------------+---------- Total | 60 195 851 483 | 1,589 Pearson chi2(3) = 377.2845 Pr = 0.000

  3. Non-Parametric Statistics • Most are based on the chi-square statistic and are used to look at the relationship between two ordinal or nominal variables, allowing us to control for: • # of categories • Sample size • The statistic you want depends upon whether you have nominal or ordinal variables and how many categories the variables have.

  4. Measures of Association: Non-parametric Tests for Nominal

  5. Measures of Association: Non-parametric Tests for Ordinal

  6. Practice Problem Did the | organization| split | Type of leadership for organization this year? | Factional Weak or Divided Strong Unitary| Total ------------+--------------------------------------------+---------- No split | 33 195 835 478 | 1,541 Split | 27 0 16 5 | 48 ------------+--------------------------------------------+---------- Total | 60 195 851 483 | 1,589 Pearson chi2(3) = 377.2845 Pr = 0.000 likelihood-ratio chi2(3) = . Cramér's V = 0.4873 gamma = -0.6873 ASE = 0.084 Kendall's tau-b = -0.1659 ASE = 0.027

  7. Lambda () • Can be used to look at the relationship between two nominal variables. • Based on a logic of making a proportional reduction of error • Asymmetric measure

  8. Calculating Lambda ()- 1

  9. Calculating Lambda ()- 2

  10. Calculating Lambda ()- 3

  11. Calculating Lambda ()- 4 • We went from 40 errors to 30 errors between tables 2 and 3 by knowing the person’s religion. • To calculate lambda,  = E₁ - E₂/ E₁, where • E₁ = the smallest expected value of errors when we don’t know the categories of the independent variable (i.e., the smallest frequency of the dependent variable) • E₂ = the smallest expected number of errors when we know the categories of the independent variable (i.e., the smallest frequency of the independent variable) •  = 40-30/40 =10/40 =0.25

  12. Interpreting Lambda () • If E₁ = E₂ (=0) then knowledge of the independent variable does not help at all in error reduction—the two variables are independent. • If E₂ = 0 (=1) then knowledge of the independent variable reduces error to zero, i.e., the two variables are “perfectly dependent.”

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