Nonparametric Tests: Chi Square   Lesson 16

Parametric vs. Nonparametric Tests n Parametric hypothesis test about population parameter (  or  2 ) l z, t, F tests l interval/ratio data n Nonparametric tests l do not test a specific parameter l nominal & ordinal data l frequency data ~

Chi-square (  2 ) n Nonparametric tests l same 4 steps as parametric tests n Chi-square test for goodness of fit l single variable n Chi-square test for independence l two variables n Same formula for both l degrees of freedom different l f e calculated differently ~

Sample Data:  2 n Frequency Expected frequency ( f e ) f e = pn Observed frequency ( f o )  f o = n n Degrees of freedom:Goodness of fit l C-1 l C = number of cells (categories)  2 cv from table B.5, page 364 ~

Chi-square (  2 )

Assumptions & Restrictions n Independence of observations l any score may be counted in only 1 category n Size of expected frequencies If f e < 5 for any cell cannot use  2 l More likely to make Type I error l Solution: use larger sample ~

 2 Test for Goodness of Fit n Test about proportions (p) in distribution n 2 different forms of H 0 l No preference category proportions are equal l No difference from comparison population e.g., student population 55% female and 45% male? n H 1 : the proportions are different ~

No preference: H 0 CokePepsi ½½ Null Hypotheses:  2 No difference: H 0 FemaleMale 55%45%

SPSS: No Preference n Data in 1 column n Analyze Nonparametric Legacy Dialogs Chi square n Dialogue box l Test Variable List l Expected Values  All categories Equal l Options  Descriptives (frequencies) ~

SPSS: No Difference n Same menus as No Preference l But must specify proportions or frequencies n Dialogue box l Expected Values  Values l Specify & Add vales one at time l In same order as defined values for variable in variable view ~

*Effect Size: 1 Variable n N = total sample size across all categories n df = #categories – 1 n zero = no difference n 1 = large difference ~

 2 Test for Independence n 2 variables are they related or independent nH0:nH0: l distribution of 1 variable is the same for the categories of other l no difference n Same formula as Goodness of Fit different df ~

 2 Test for Independence n Differences from Goodness of Fit n df = (R-1)(C-1) l R = rows l C = columns n Expected frequency for each cell

Example n Does watching violent TV programs cause children to be more aggressive on the playground? n Data: frequency data l Violent program: yes or no l Aggressive: yes or no ~

 2 Test for Independence Yes No Violent TV YesNo Aggressive

SPSS: Test for Independence n Two variables n Two-Way Contingency Table Analysis n Data: 1 column for each variable n Analyze Descriptives Crosstabs n Dialogue Box l Variables  Rows or Columns l Statistics  Chi Square, *Phi ~

Effect Size (  ): 2 Variables n N = total sample size across all categories n Phi values: 0-1 n Interpret similar to Pearson’s r n Small =.1; medium =.3, large =.5 ~