***************************************************************************** * CHAPTER 10 - STATISTICS FOR BUSINESS & ECONOMICS, 4th Ed., by Paul Newbold* ***************************************************************************** * * Example 10.1, page 388 * * A random sample of children is N, the number of these children that * preferred peanut butter ripple ice cream is PB, the number of these * children that preferred bubblegum surprise is BS, and the number of these * children that expressed no preference is NP. * GEN1 N=100 GEN1 PB=56 GEN1 BS=40 GEN1 NP=4 * * The Null Hypothesis is that there is no overall preference in this * population for one flavor over the other. Before the analysis can be * performed, the sample of children that expressed no preference must be * subtracted from the original sample size to yield the group of children * that gave a response for either ice cream flavours. * GEN1 N=N-NP * * The sample proportion preferring peanut butter ripple is defined as PXHAT. * GEN1 PXHAT=PB/N PRINT PXHAT * * The test statistic is then calculated using the GEN1 command. * GEN1 STAT=(PXHAT-0.5)/(SQRT((0.5)**2/N)) PRINT STAT * DELETE / ALL * *---------------------------------------------------------------------------- * Example 10.2, page 393 * * A sample of thirty-one matched pairs of firms is N. The smaller of the * rank sums, 189, was for those pairs where the ratio was higher for the * firm without sophisticated postaudit procedures is T. * GEN1 N=31 GEN1 T=189 * * The Wilcoxon statistic under the Null Hypothesis that the distribution of * differences in ratios is centered on 0 against the Alternative Hypothesis * that the ratio of market valuation to replacement cost of assets tends to * be lower for firms without sophisticated postaudit procedures. * * First the Mean of T is calculated. Then the Variance of T and the Standard * Deviation of T. * GEN1 MEANT=(N*(N+1))/4 GEN1 SIGMA2T=(N*(N+1)*(2*N+1))/24 GEN1 SIGMAT=SQRT(SIGMA2T) * * The Wilcoxon Statistic is calculated using the previously determined Mean * and Standard Deviaton of T. * GEN1 WILCOXON=(T-MEANT)/SIGMAT PRINT MEANT SIGMA2T SIGMAT WILCOXON * DELETE / ALL * *---------------------------------------------------------------------------- * Example 10.3, page 398 * * A random sample of the performance of firms that does not give management * forecasts of earnings is defined as N1 and a random sample of the * performance of firms that give management forecasts of earnings is defined * as N2. The sum of the ranks for firms not disclosing management earnings * forecasts is defined as R1. * GEN1 N1=80 GEN1 N2=80 GEN1 R1=7287 * * The Null Hypothesis is that the central locations of the population * distributions of earnings variabilities are the same for the two types of * firms. * * The Mann-Whitney statistic is calculated with the GEN1 command. * GEN1 U=(N1*N2)+((N1*(N1+1))/2)-R1 PRINT U * * The Mean, Variance and Standard Deviation of the Mann-Whitney statistic is: * GEN1 MEANU=(N1*N2)/2 GEN1 SIGMA2U=(N1*N2*(N1+N2+1))/12 GEN1 SIGMAU=SQRT(SIGMA2U) PRINT MEANU SIGMA2U SIGMAU * * The Decision Rule is: * GEN1 DR=(U-MEANU)/SIGMAU PRINT DR * DELETE / ALL * *----------------------------------------------------------------------------- * STOP