Focus FoxSelect the best option:Which of the following is a condition that must be met in order to carry out a chi-square goodness-of-fit test?a. The population must be normally distributed, or the

sample size must be greater than 30b. The cell counts for our sample have to be

approximately the same as the expected countsc. All observed cell counts must be greater than 5d. All expected counts must be greater than 5e. More than one of these conditions must be met

Chi-Square Test HomgeneityChi-Square Test for Homogeneity – two way tableIf Random – random samples from each population or groups in randomized experimentIf Large Sample Size – all expected counts are at least 5If Independent – individual observations & 10% conditionH0: there is no difference in the distribution of a categorical variable for several populations or treatmentsHa: there is a difference in the distribution of a categorical variable for several populations or treatmentsFind expected countsdf = (number of rows – 1)(number of columns – 1)P-value is the area to the right of χ2 under the density curve

Chi-Square Test HomgeneityH0: there is no difference in the distributions of wine purchases at this store when no music, French accordion music, or Italian string music is played.Ha: there is a difference in the distributions of wine purchases at this store when no music, French accordion, or Italian string music is played.

Previously calculated test statistic χ2 = 18.28

Wine No Music French Italian TotalsFrench 30 39 30 99

Italian 11 1 19 31

Other 43 35 35 113

Totals 84 75 84 243

Chi-Square Test Homgeneity

Previously calculated test statistic χ2 = 18.28Use Table C to find the P-value.

Now use χ2cdf command on calculator

Wine No Music French Italian TotalsFrench 30 39 30 99

Italian 11 1 19 31

Other 43 35 35 113

Totals 84 75 84 243

Chi-Square Test Homgeneity

Previously calculated test statistic χ2 = 18.28Interpret the P-value from the calculator in context.

What conclusion would you draw?

Wine No Music French Italian TotalsFrench 30 39 30 99

Italian 11 1 19 31

Other 43 35 35 113

Totals 84 75 84 243

Chi-Square Test HomgeneityUsing Technology:

Enter the observed data in Matrix ASelect χ2 test - STATS – TESTS – χ2 - Test

Observed: [A]Expected: [B]

Choose calculate then 2nd Enter and DrawSelect and enter Matrix [B]

Tables are commonly referenced by dimensions row by column – 2x3

Pg. 706

Chi-Square Test HomgeneityFollow-Up AnalysisThe chi-square test for homogeneity allows us to compare the distribution of a categorical variable for any number of populations or treatments. If we reject the null of no difference, follow-up analysis is required- Examine which cell in the two-way table show large

deviations between observed and expected counts.- Look at the which contribute the most to the chi-

square statistic

Pg. 709 – minitab output and analysis