IChi square test statisticH<0V Cannot be negative because all discrepancies aresquared. Will be zero only in the unusual event that eachobserved frequency exactly equals the correspondingHO:L:expected frequency.V Larger the discrepancy between the expectedfrequencies and their corresponding observedfrequencies, the larger the observed value of chi-squareB
Chi square test statistic ✓ Cannot be negative because all discrepancies are squared. ✓ Will be zero only in the unusual event that each observed frequency exactly equals the corresponding expected frequency. ✓ Larger the discrepancy between the expected frequencies and their corresponding observed frequencies, the larger the observed value of chi-square
KProbability for chi squaretest statistic can be obtainedfromthe chi-square probability distribution.Table 2.1 Partial Tableof Critical Values of Chi-SquareLevelof Significance (non-directional test)df.05.025.01.005.001df= 213.846.635.027.88df= 310.83aieor27.3810.605.9913.829.21df = 437.819.3511.3416.2712.840.0549.4913.2814.8618.4711.14511.0712.8315.0916.7520.52rejectregion1018.3120.4823.2125.1929.59601012014161126.7631.2619.6821.9224.73x2
Table 2.1 Partial Table of Critical Values of Chi-Square Probability for chi square test statistic can be obtained from the chi-square probability distribution. 0.05 reject region
KThe decision ruleH:u<0The quantity ≥(-) will e small f the observed andEexpected frequencyare closetogether and will be large ifthe differences are large.The computed value of x? is compared with the tabulatedvalue of with K-1 degrees of freedom. The decision rulethen is: reject Ho if x? is greater than or equal to thetabulated x2 for the chosen value of αE
The decision rule The quantity will be small if the observed and expected frequency are close together and will be large if the differences are large. The computed value of χ 2 is compared with the tabulated value of with K-1 degrees of freedom. The decision rule, then is: reject H0 if χ 2 is greater than or equal to the tabulated χ 2 for the chosen value of α. − E O E 2 ( )