***************************************************************************** * CHAPTER 15 - STATISTICS FOR BUSINESS & ECONOMICS, 4th Ed., by Paul Newbold* ***************************************************************************** * * Sample Mean for A-cars, B-cars, and C-cars on Page 596. * * The sample range for ACARS and BCARS is 1 to 7. The last observation for * CCARS is missing so the sample range for this variable is 1 to 6. The * default missing observation value of -99999 has been included in Table 15.1 * so all three variables can be read in with 7 data points. * SAMPLE 1 7 READ ACARS BCARS CCARS / LIST 22.2 24.6 22.7 19.9 23.1 21.9 20.3 22.0 23.3 21.4 23.5 24.1 21.2 23.6 22.1 21.0 22.1 23.4 20.3 23.5 -99999 * * The SUM= option on the STAT command saves the sum of A-cars in the constant * SUMA. The MEAN= option saves the mean of A-cars in the constant MEANA. * STAT ACARS / SUM=SUMA MEAN=MEANA STAT BCARS / SUM=SUMB MEAN=MEANB * * The SET SKIPMISS command is used before the sum of CCARS is calculated. If * the missing observation was included in the calculation the sum for CCARS * would be incorrect. * SET SKIPMISS STAT CCARS / SUM=SUMC MEAN=MEANC PRINT MEANA SUMA MEANB SUMB PRINT MEANC SUMC * * The overall mean of A-cars, B-cars, and C-cars on page 599. First the GEN1 * command is used to generate the constant for the number of A-cars, B-cars, * and C-cars. * GEN1 NA=7 GEN1 NB=7 GEN1 NC=6 GEN1 XBAR=(NA*MEANA+NB*MEANB+NC*MEANC)/(NA+NB+NC) PRINT XBAR * * The variability of the first group, A-cars is defined as SS1. * GENR SSA=(ACARS-MEANA)**2 STAT SSA / SUM=SS1 PRINT SS1 * * The variability of the second group, B-cars is defined as SS2. * GENR SSB=(BCARS-MEANB)**2 STAT SSB / SUM=SS2 PRINT SS2 * * The variability of the third group, C-cars is defined as SS3. * GENR SSC=(CCARS-MEANC)**2 STAT SSC / SUM=SS3 PRINT SS3 * * The Total Within-Groups variability is defined as SSW with the GEN1 command. * GEN1 SSW=SS1+SS2+SS3 PRINT SSW * * The Total Between-Groups Sum of Squares is defined as SSG with the GEN1 * command. * GEN1 SSG=NA*((MEANA-XBAR)**2)+NB*((MEANB-XBAR)**2)+NC*((MEANC-XBAR)**2) PRINT SSG * * The Total Sum of Squares is defined as SST with the GEN1 command. * GEN1 SST=SSW+SSG PRINT SST * * The Within-Groups Mean Square is defined as MSW with the GEN1 command. * GEN1 N=NA+NB+NC GEN1 K=3 GEN1 MSW=SSW/(N-K) PRINT MSW * * The Between-Groups Mean Square is defined as MSG with the GEN1 command. * GEN1 MSG=SSG/(K-1) PRINT MSG * * The F-value is: * GEN1 F=MSG/MSW PRINT F * * The above method to calculate the One-Way Analysis of Variance is the long * way. In SHAZAM, the One-Way Analysis of Variance can be easily calculated * with the ANOVA option on the STAT command. * STAT ACARS BCARS CCARS / ANOVA * *---------------------------------------------------------------------------- * Example 15.1, page 603 * SAMPLE 1 6 READ SCIAMER FORTUNE NEWYORK / LIST 15.75 12.63 9.27 11.55 11.46 8.28 11.16 10.77 8.15 9.92 9.93 6.37 9.23 9.87 6.37 8.20 9.42 5.66 * STAT SCIAMER FORTUNE NEWYORK / ANOVA *----------------------------------------------------------------------------- * Two-Way Analysis of Variance, page 624 * SAMPLE 1 15 READ X1 / BYVAR LIST 25.0 25.4 25.2 24.8 24.8 24.5 26.1 26.3 26.2 24.1 24.4 24.4 24.0 23.6 24.1 READ X2 / BYVAR LIST 24.0 24.4 23.9 23.5 23.8 23.8 24.6 24.9 24.9 23.9 24.0 23.8 24.4 24.4 24.1 READ X3 / BYVAR LIST 25.9 25.8 25.4 25.2 25.0 25.4 25.7 25.9 25.5 24.0 23.6 23.5 25.1 25.2 25.3 * * The Group Mean is calculated using the STAT command. The STAT command * automatically calculates the mean of the variable specified. The MEAN= * option stores the mean in a specified constant. * STAT X1 / MEAN=MEANX1 STAT X2 / MEAN=MEANX2 STAT X3 / MEAN=MEANX3 PRINT MEANX1 MEANX2 MEANX3 * * The Block Mean is calculated using the GENR command with the SUM(x,n) * function. The GENR statement first sums the first 3 observations of * X1 and then the next three etc until all 15 observations are done. The * values for X2 and X3 are repeated with a similiar GENR command. The * DO-loop is then used next to complete the Block Means calculation. * SAMPLE 1 5 GENR XBAR1=SUM(X1,3) GENR XBAR2=SUM(X2,3) GENR XBAR3=SUM(X3,3) PRINT XBAR1 XBAR2 XBAR3 DO #=1,5 GEN1 NXBAR#=(XBAR1:#+XBAR2:#+XBAR3:#)/9 PRINT NXBAR# ENDO * * The Cell Mean is calculated in a similar fashion as the Block Mean. The * GENR command is used. Recall in the previous example of the Block Means * the sums were calculated and stored in the vectors XBAR1, XBAR2, and XBAR3. * The Cell Means for X11, X12, X13, X14, and X15 are stored in the vector * X11. The Cell Means for X21, X22, X23, X24, and X25 are stored in the * vector X22 and X31, X32, X33, X34, and X35 are stored in the vector X33. * All that needs to be done is to determine the average for each of the * sums. * SAMPLE 1 5 GENR X11=XBAR1/3 GENR X22=XBAR2/3 GENR X33=XBAR3/3 PRINT X11 X22 X33 * * The Overall Mean is calculated with the GEN1 command. Recall that the * mean of all sample observations was calculated in the Group Means example * above. * GEN1 OVERALL=(MEANX1+MEANX2+MEANX3)/3 PRINT OVERALL * * The Two-Way Analysis of Variance Table for Fuel Consumption data of * Table 15.10, page 628. * * The following information is supplied on page 628 and 630 of the textbook. * The GEN1 command is used to generate the respective constants. * GEN1 K=3 GEN1 H=5 GEN1 L=3 GEN1 SSG=7.1565 GEN1 SSB=13.1517 GEN1 SSI=6.6045 GEN1 SSE=1.1600 GEN1 SST=28.0727 * * The Mean Squares in Column 4 of Table 15.13 on page 630 are calculated * using the formulas in Table 15.12 on page 629 and the GEN1 command. * GEN1 MSG=SSG/(K-1) GEN1 MSB=SSB/(H-1) GEN1 MSI=SSI/((K-1)*(H-1)) GEN1 MSE=SSE/(K*H*(L-1)) PRINT MSG MSB MSI MSE * * The F-ratios in Column 5 of Table 15.13 on page 630 are calculated using * the formulas in Table 15.12 on page 629 and the GEN1 command. * GEN1 FSSG=MSG/MSE GEN1 FSSB=MSB/MSE GEN1 FSSI=MSI/MSE PRINT FSSG FSSB FSSI * DELETE / ALL * *----------------------------------------------------------------------------- * Example 15.3, page 631 * * The GEN1 command is used to generate the constants required to compute the * Mean Square found in the second table on page 632. * GEN1 SSG=62.04 GEN1 SSB=0.06 GEN1 SSI=1.85 GEN1 SSE=23.31 GEN1 SST=82.26 * * The Degrees of Freedom for Tasks is equal to 1. We know that the Degrees * of Freedom Between Groups is defined as K-1. In this case K-1=1, therefore, * K=2. In the case of Worker Type, the Degrees of Freedom=1. The Degrees * of Freedom is defined as H-1 so H=2. The Degrees of Freedom for Error * is equal to 63 and the Degrees of Freedom is defined as KH(L-1)=63. * GEN1 K=2 GEN1 H=2 GEN1 L=(63+(K*H))/(K*H) PRINT L * * The GEN1 command is used to calculate the Mean Squares. * GEN1 MSG=SSG/(K-1) GEN1 MSB=SSB/(H-1) GEN1 MSI=SSI/((K-1)*(H-1)) GEN1 MSE=SSE/(K*H*(L-1)) PRINT MSG MSB MSI MSE * * The F-ratios are calculated using the formulas in Table 15.12 on page 629 * and the GEN1 command. * GEN1 FSSG=MSG/MSE GEN1 FSSB=MSB/MSE GEN1 FSSI=MSI/MSE PRINT FSSG FSSB FSSI * DELETE / ALL * *----------------------------------------------------------------------------- * STOP