2.  What is chi-square  CHIDIST  Non-parameteric statistics 2

3.  A main branch of statistics  Assuming data with a type of probability distribution (e.g. normal distribution)  Making inferences about the parameters of the distribution (e.g. sample size, factors in the test)  Assumption: the sample is large enough to represent the population (e.g. sample size around 30).  They are not distribution-free (they require a probability distribution) 3

4.  Nonparametric statistics (distribution-free statistics)  Do not rely on assumptions that the data are drawn from a given probability distribution (data model is not specified).  It was widely used for studying populations that take on a ranked order (e.g. movie reviews from one to four stars, opinions about hotel ranking). Fits for ordinal data.  It makes less assumption. Therefore it can be applied in situations where less is known about the application.  It might require to draw conclusion on a larger sample size with the same degree of confidence comparing with parametric statistics. 4

5.  Nonparametric statistics (distribution-free statistics)  Data with frequencies or percentage  Number of kids in difference grades  The percentage of people receiving social security 5

6.  One-sample chi-square includes only one dimension  Whether the number of respondents is equally distributed across all levels of education.  Whether the voting for the school voucher has a pattern of preference.  Two-sample chi-square includes two dimensions  Whether preference for the school voucher is independent of political party affiliation and gender 6

7. O: the observed frequency E: the expected frequency One-sample chi-square test 7

8. Preference for School Voucher formaybeagainsttotal 23175090 Question: Whether the number of respondents is equally distributed across all opinions?  One-sample chi-square 8

9.  Step1: a statement of null and research hypothesis There is no difference in the frequency or proportion in each category There is difference in the frequency or proportion in each category 9

10.  Step2: setting the level of risk (or the level of significance or Type I error) associated with the null hypothesis  0.05 10

11.  Step3: selection of proper test statistic  Frequency  nonparametric procedures  chi- square 11

12.  Step4. Computation of the test statistic value (called the obtained value) category observed frequency (O) expected frequency (E)D(difference)(O-E) 2 (O-E) 2 /E for23307491.63 maybe1730131695.63 against50302040013.33 Total90 20.60 12

13.  Step5: determination of the value needed for rejection of the null hypothesis using the appropriate table of critical values for the particular statistic  Distribution of Chi-Square  df = r-1 (r= number of categories)  If the obtained value > the critical value  reject the null hypothesis  If the obtained value < the critical value  accept the null hypothesis 13

14. 14

15.  Step6: a comparison of the obtained value and the critical value is made  20.6 and 5.991 15

16.  Step 7 and 8: decision time  What is your conclusion, why and how to interpret? 16

17.  We’ll settle the age-old debate of whether people can actually detect their favorite cola based solely on taste. For 30 coke-lovers, I blindfold them, and have them sample 3 colas…is there a true difference, or are these preference differences explainable by chance? 17

18.  Null: There are no preferences: The population is divided evenly among the brands  Alternate: There are preferences: The population is not divided evenly among the brands 18

19.  df = C -1 = 3 -1 = 2, set α =.05  For df = 2, X 2 -crit = 5.99 19

20. category observed frequency (O) expected frequency (E)D(difference)(O-E) 2 (O-E) 2 /E Coke1310390.9 Pepsi910110.1 RC Cola810240.4 Total30 1.4 20

21.   Conclude that the preferences are evenly divided among the colas when the logos are removed. 21

22.  CHIDIST (x,degrees_freedom)  CHIDIST(20.6,2)  0.000036<0.05  CHIDIST(1.40,2)  0.496585304>0.05 22