Non-parametric Tests e.g., Chi-Square

When to use various statistics n Parametric n Interval or ratio data n Name parametric tests we covered Tuesday n Non-parametric n Ordinal and nominal data

To compare two groups on Mean Scores use t-test. For more than 2 groups use Analysis of Variance (ANOVA) Can’t get a mean from nominal or ordinal data. Chi Square tests the difference in Frequency Distributions of two or more groups.

Chi-Square X 2 n Chi Square tests the difference in frequency distributions of two or more groups. n Test of Significance n of two nominal variables or n of a nominal variable & an ordinal variable n Used with a cross tabulation table

Chi-Square 2 Chi-Square =

Logic of Chi-Square Analysis n If the observed values are different enough from the expected values, you reject the null hypothesis n If the observed values and the expected values are similar, you fail to reject the null hypothesis

Example: Work & Pregnancy n The impact of working on pregnancy  Ha: Working during pregnancy increases the risk of miscarriage  H 0 : Working during pregnancy has NO impact on the risk of miscarriage

Example: Work & Pregnancy n Suppose in general population 5 in 100 pregnancy results in miscarriage n Probability(p) =.05 or 5%

Example: Work & Pregnancy 1000Total 950 (95%) No 50 (5%) Yes Total (n=1000) Miscarriage

Example: Work & Pregnancy 500 No Work (n=500) (95%) 50 (5%) Total (n=1000) 500Total No Yes Work (n=500) Miscarriage  H 0 : Working during pregnancy has NO impact on the risk of miscarriage ?

Example: Work & Pregnancy (95%) 25 (5%) No Work (n=500) (95%) 50 (5%) Total (n=1000) 500Total 475 (95%)No 25 (5%)Yes Miscarriage Work (n=500) Miscarriage  If NULL hypothesis TRUE, both work & no work groups would have same probability of miscarriage. EXPECTED values:

Example: Work & Pregnancy (98%) 10 (2%) No Work (n=500) (95%) 50 (5%) Total (n=1000) 500Total 460 (92%)No 40 (8%)Yes Miscarriage Work (n=500) Miscarriage  The actual values in your data = OBSERVED VALUES

p =.001

Tourist Expenditure: Mainlander vs. Japanese Chi-Square x 2 = 7.34, df = 2, p<.001

Excel

Finished Chart

The Stats for Chart

Use SPSS Crosstabs (for nominal and ordinal data) n Click…. Analyze n Descriptive statistics n Crosstabs n Highlight variables for row n Highlight variable for column n Click statistics, click chi-square or correlation n Etc.

Both chi square (non-parametric test) and t-test (parametric test) … n Examines if observed difference between groups in your data is true difference n True difference = difference that exists in the population n H 0 says there is no difference in the population

Which values are compared? Chi-Square t-test Frequencies in each cell Mean and Standard Deviation of each group

If H 0 is true… Chi-Square t-test The values in the frequency table will look like Expected Values The distribution of both groups will look like Population Distribution

Chi- square: If H 0 is true… Males = Females (No difference) 70% 30% FemaleTotalMale 70% NO 30% YES

t-test: If H 0 is true … Total Female Male Mean # of cases Test score

t-test: If H 0 is NOT true … Total Female Male # of cases Test score Mean

t-test: If H 0 is NOT true … Total Female Male # of cases Test score Mean