Homework_Ch13_Template

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Pueblo Community College *

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MISC

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Statistics

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Feb 20, 2024

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xlsx

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49

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Colo Insert your data Calculate/Identify The Answ Data Analysis Auto Calculated Auto Calculated Decision Source of Variation Sum of Squares Treatments Error Total Treatment1 Treatment2 8 8 #ofTreatments (K) 3 24 Source of Variation Sum of Squares Treatments 87.12 Error 125.37 Total 212.49 Fisher's Least Significant Diff 6 62 Hypothesized Confidence Coefficient (Coe) 0.95 SSTR =∑n*(xbar r - Dxbar)^2 SSE =∑(n j - 1)s 2 i SST =SSTR+SSE n T Sample Size ( n1 or n2 ) =count(range) Sample Mean ( Mean1 or Mean 2) =average(range) Ho: m1 = m2 H a : m1 ≠ m2
0.05 21 2.08 2.93 4 Reject Sample Results 1 5 62.0 Alpha 0.05 n (total) 15 k 3 12 2.179 MSE 5.97 xi 1 vs. 2 62.0000 1 vs. 3 62.0000 2 vs. 3 66.0000 Level of Significance ( alpha ) =1-Coe Degrees of Freedom (df) =n T - K t a /2 -value =T.INV.2T(alpha,df) LSD Value =t a /2 *SQRT(MSE*(1/n1+1/n2)) Test Statistic =ABS(mean1-mean2) Accept or Reject Reject Ho if ABS(mean1-mean2)≥LDS Sample Size =COUNT(range) Sample Mean =AVERAGE(range) Degrees of Freedom (df) =n T - K t a /2 -value =T.INV.2T(alpha,df) Pairwise Comparison
Sample Results 1 5 62.0 Alpha 0.05 n (total) 20 k 4 16 2.120 MSE 5.97 xi 1 vs. 2 62.0 1 vs. 3 62.0 1 vs. 4 62.0 2 vs. 3 66.0 2 vs. 4 66.0 3 vs. 4 52.0 Sample Size =COUNT(range) Sample Mean =AVERAGE(range) Degrees of Freedom (df) =n T - K t a /2 -value =T.INV.2T(alpha,df) Pairwise Comparison
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or Key wer ANOVA Degrees of Freedom Mean Square F MSTR/MSE Treatment3 Treatment4 Treatment5 8 Degrees of Freedom Mean Square F 2 43.56 7.30 21 5.97 23 ference (LSD) 6 66 K - 1 =(#ofTreatment - 1) MSTR =SSTR/(K - 1) n T - K =n T - #ofTreatment MSE =SSE/(n T - K) n -1 =n T - 1
Fisher's 3 Sample LSD 2 3 5 5 66.0 52.0 Change as needed xj ni 66.0000 4.0000 5 52.0000 10.0000 5 52.0000 14.0000 5 Difference Absolute Value
Fisher's 4 Sample LSD 2 3 4 5 5 5 66.0 52.0 50.0 Change as needed xj ni 62.0 0.0 5 52.0 10.0 5 50.0 12.0 5 52.0 14.0 5 50.0 16.0 5 50.0 2.0 5 Difference Absolute Value
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Fcrit F.DIST.RT(F,K-1,nT-K) Fcrit 0.004 3.47 p -Value F.INV.RT(alpha,K-1,n T -1) p -Value
nj 5 3.37 Significant 5 3.37 Significant 5 3.37 Significant Fisher's LSD Critical Value Significant Diff > CV
nj 5 3.28 Not Significant 5 3.28 Significant 5 3.28 Significant 5 3.28 Significant 5 3.28 Significant 5 3.28 Not Significant Fisher's LSD Critical Value Significant Diff > CV
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Source of Variation Sum of Squares Treatments Blocks Error Total Treatment1 Treatment2 #ofBlocks (b) #ofTreatments (K) 0 0 Source of Variation Sum of Squares Treatments 21 Blocks 30 Error 19 Total 49 SSTR =∑(xbar j - Dxbar)^2 SSBL =∑(xbar i - Dxbar)^2 SSE =SST-SSTR-SSBL SST = ∑ ∑(xbar ij - Dxbar)^2 n T
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Source of Variation Sum of Squares Factor A SSA Factor B SSB Interaction SSAB Error Total SST a 4 b 2.2 r 2 Source of Variation Sum of Squares Factor A 1.03 Factor B 15.42 Interaction 0.55 Error 76.33 SSE =SST-SSA-SSB-SSAB
Total 93.33
ANOVA: Randomized Block Design Degrees of Freedom Mean Square F MSTR/MSE MSBL/MSE (K-1)(b-1) Treatment3 Treatment4 Treatment5 Degrees of Freedom Mean Square F 2 10.5 5.53 5 6 3.16 10 1.9 15 K-1 =#ofTreatment-1 MSTR =SSTR/(K-1) b - 1 =#blocks-1 MSBL =SSBL/b-1 MSE =SSE/(K-1)(b-1) n -1 =n T - 1
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ANOVA: Two Factor with replication tool Degrees of Freedom Mean Square F a - 1 MSA/MSE b - 1 MSB/MSE (a – 1)(b – 1) MSAB/MSE (ab)(r – 1) nT - 1 Degrees of Freedom Mean Square F 3 0.34 0.04 1.2 12.85 1.48 3.6 0.15 0.02 8.8 8.67 MSA =SSA/(a-1) MSB =SSB/(b-1) MSAB =SSAB/(a-1)(b-1) MSE =SSE/(ab)(r-1)
16.6
Fcrit Fcrit 0.0000 0.0001 p -Value F.DIST.RT(Ftreat,K- 1,nT-K) p -Value
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0.5596 0.0000 Err:502 p -Value p -Value F.DIST.RT(Fa,a- 1,dferror) F.DIST.RT(Fb,b- 1,dferror) F.DIST.RT(Fi,(a-1)(b- 1),dferror) p -Value p -Value
Treatment A B C 162 142 126 142 156 122 165 124 138 145 142 140 148 136 150 174 152 128 Sample Mean 156 142 134 Sample Variance 164.4 131.2 110.4 a. Sum of Squares between treatments 1488 b. Mean Square between treatments 744 c. Sum of Squares due to error 2030 within d. Mean Square due to error 135.3333 within e. Fill out ANOVA ss df MS F p-value Treatment 1488 2 744 5.497537 0.016181 Error 2030 15 135.3333 0 0 Total 3518 17 0 0 0 5.50 p-value 0.016181 Conclusion not all are equal f. Test Stat ( F )
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Do a Single Factor Anova Test --> Anova: Single Factor Place Output at H1 SUMMARY Groups Count Sum Average Variance A 6 936 156 164.4 B 6 852 142 131.2 C 6 804 134 110.4 ANOVA test-stat Source of Variation SS df MS F Between Groups 1488 2 744 5.497537 Within Groups 2030 15 135.3333 Total 3518 17
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P-value F crit 0.016181 3.68232
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ANOV Source of Variation Sum of Squares Degrees of Freedom Treatments Error Total Treatment1 Treatment2 Treatment3 12 15 20 #ofTreatments (K) 3 47 Source of Variation Sum of Squares Degrees of Freedom Treatments 1200 2 Error 600 44 Total 1800 46 cannot conclude SSTR =∑n*(xbar r - Dxbar)^2 K - 1 =(#ofTreatment - 1) SSE (=SST-SSTR) =∑(n j - 1)s 2 i n T - K =n T - #ofTreatment SST =SSTR+SSE n -1 =n T - 1 n T
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VA Mean Square F MSTR/MSE F.DIST.RT(F,K-1,nT-K) Treatment4 Treatment5 Mean Square F 600 44.00 0.000 13.64 p -Value MSTR =SSTR/(K - 1) MSE =SSE/(n T - K) p -Value
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Fcrit Fcrit 3.21 F.INV.RT(alpha,K-1,n T -1)
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a. MSE/MSTR b. MSE/MST c. MST/MSE d. MSTR/MSE The F ratio in a completely randomized ANOVA is the ratio of _____.
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Temperature 50°C 60°C 70°C 34 33 23 24 34 28 36 37 28 39 26 30 32 30 31 A. Construct ANOVA ss df MS F p-value Treatment 70 2 35 1.78 0.2104 Error 236 12 19.67 Total 306 14 1.78 p-value 0.210447 greater than .1 Conclusion do not rejject B. Test Stat ( F )
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Do a Single Factor Anova Test --> Anova: Single Factor Place Output at H1 SUMMARY Groups Count Sum Average Variance 50°C 5 165 33 32 60°C 5 160 32 17.5 70°C 5 140 28 9.5 ANOVA Source of Variation SS df MS F Between Groups 70 2 35 1.779661 Within Groups 236 12 19.66667 Total 306 14
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P-value F crit 0.210447 3.885294
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Restaurant Survey Italian Seafood Steakhouse 13 15 24 11 18 17 14 15 25 15 27 26 19 22 22 20 16 20 17 20 27 24 16 29 Construct ANOVA ss df MS F p-value Treatment 216.0833333 2 108.0416667 6.35 0.0070 Error 357.25 21 17.01 Total 573.3333333 23 p-value 0.00696519 Conclusion conclude not all equal
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Do a Single Factor Anova Test --> Anova: Single Factor Place Output at H1 SUMMARY Groups Count Sum Average Variance Italian 8 133 16.625 17.98214 Seafood 8 149 18.625 17.69643 Steakhouse 8 190 23.75 15.35714 ANOVA Source of Variation SS df MS F Between Groups 216.0833 2 108.0417 6.350945 Within Groups 357.25 21 17.0119 Total 573.3333 23
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P-value F crit 0.006965 3.4668
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1 2 3 17 28 22 23 26 21 21 31 25 19 27 24 a. Compute SS Treatment 130.666666666667 SS Error 44 MS Treatment 65.3333333333333 MS Error 4.88888888888889 13.3636363636364 p-value 0.002021119066184 Conclusion b. LSD Fisher's 3 Sample LS Sample Results 1 2 4 4 20.0 28.0 Alpha 0.05 n (total) 12 k 3 9 2.262 MSE 4.88888888888889 Change as needed xi xj 1 vs. 2 20.0000 28.0000 1 vs. 3 20.0000 23.0000 2 vs. 3 28.0000 23.0000 Test Stat ( F ) Sample Size =COUNT(range) Sample Mean =AVERAGE(range) Degrees of Freedom (df) =n T - K t a /2 -value =T.INV.2T(alpha,df) Pairwise Comparison
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Do a Single Factor Anova Test --> SD 3 4 change 23.0 ni 8.0000 4 3.0000 4 5.0000 4 Difference Absolute Value
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Anova: Single Factor SUMMARY Groups Count Sum Average 1 4 80 20 2 4 112 28 3 4 92 23 ANOVA Source of Variation SS df MS Between Groups 130.666666666667 2 65.33333 Within Groups 44 9 4.888889 Total 174.666666666667 11 nj 4 3.54 Significant 4 3.54 Not Significant 4 3.54 Significant Fisher's LSD Critical Value Significant Diff > CV
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Variance 6.666667 4.666667 3.333333 F P-value F crit 13.36364 0.002021 4.256495
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Marketing Managers Marketing Research Advertising 9 5 7 8 5 8 7 4 7 8 4 6 9 5 7 7 4 7 A. Compute SS Treatment 39 SS Error 7.5 MS Treatment 19.5 MS Error 0.5 B. Test Stat 39 p-value 1.14041344485362E-06 Conclusion C. LSD Fisher's 3 Sample LS Sample Results 1 2 6 6 8.0 4.5 Alpha 0.05 n (total) 18 k 3 15 2.131 MSE 0.5 Change as needed xi xj 1 vs. 2 8.0000 4.5000 1 vs. 3 8.0000 7.0000 2 vs. 3 4.5000 7.0000 Sample Size =COUNT(range) Sample Mean =AVERAGE(range) Degrees of Freedom (df) =n T - K t a /2 -value =T.INV.2T(alpha,df) Pairwise Comparison
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Do a Single Factor Anova Test --> Place Output at F1 SD 3 6 7.0 ni 3.5000 6 1.0000 6 2.5000 6 Difference Absolute Value
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Anova: Single Factor SUMMARY Groups Count Sum Average Marketing Managers 6 48 8 Marketing Research 6 27 4.5 Advertising 6 42 7 ANOVA Source of Variation SS df MS Between Groups 39 2 19.5 Within Groups 7.5 15 0.5 Total 46.5 17 nj 6 0.87 Significant 6 0.87 Significant 6 0.87 Significant Fisher's LSD Critical Value Significant Diff > CV
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Variance 0.8 0.3 0.4 F P-value F crit 39 1.14041E-06 3.68232
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ANOVA: Randomized Source of Variation Sum of Squares Degrees of Freedom Treatments Blocks Error (K-1)(b-1) Total Source of Variation Sum of Squares Degrees of Freedom Treatments 700 3 Blocks 600 7 Error 400 21 Total 1700 31 p-value 0.00 Conclusion conclude not all are equal SSTR =∑(xbar j - Dxbar)^2 K-1 =#columns-1 SSBL =∑(xbar i - Dxbar)^2 b - 1 =#blocks-1 SSE =SST-SSTR-SSBL SST = ∑ ∑(xbar ij - Dxbar)^2 n -1 =n T - 1
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d Block Design Mean Square F MSTR/MSE F.DIST.RT(Ftrea,K-1,nT-K) MSBL/MSE F.DIST.RT(Fbloc,K-1,nT-K) Mean Square F 233.333333333333 12.25 0.00 85.7142857142857 4.5 0.00 19.047619047619 p -Value MSTR =SSTR/(K-1) MSBL =SSBL/b-1 MSE =SSE/(K-1)(b-1) p -Value
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Factor B Level 1 Level 2 Level 3 Level 1 145 110 95 Factor A 175 46 73 Level 2 145 147 100 105 85 116 Construct ANOVA Source of Variation ss df MS F p-value Factor A 243 1 243 0.26 0.6278 Factor B 5644.666667 2 2822.333333 3.03 0.1232 Interaction 3002 2 1501 1.61 0.2754 Error 5590 6 931.67 Total 14479.66667 11
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Do a Single Factor Anova Test --> Anova: Two-Factor With Replication Place Output at H1 SUMMARY Level 1 Level 2 Level 3 Total Level 1 Count 2 2 2 6 Sum 320 156 168 644 Average 160 78 84 107.3333 Variance 450 2048 242 2219.467 Conclusion (if p-value < alpha, reject) not sig Level 2 not sig Count 2 2 2 6 not sig Sum 250 232 216 698 Average 125 116 108 116.3333 Variance 800 1922 128 627.8667 Total Count 4 4 4 Sum 570 388 384 Average 142.5 97 96 Variance 825 1804.667 315.3333 ANOVA Source of Variation SS df MS F Sample 243 1 243 0.260823 Columns 5644.667 2 2822.333 3.029338 Interaction 3002 2 1501 1.611091 Within 5590 6 931.6667 Total 14479.67 11
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P-value F crit 0.627796 5.987378 0.123184 5.143253 0.275393 5.143253
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Nurse Tax Auditor Fast-Food Worker 3 5 4 4 6 6 5 6 6 5 4 6 3 7 8 5 5 4 6 5 5 3 4 5 A. Compute 2.53 p-value 0.1032767874 Conclusion cannot reject Alpha 0.05 2.080 D. LSD Fisher's 3 Sample LSD Sample Results 1 2 3 8 8 8 4.3 5.3 5.5 Alpha 0.05 n (total) 24 k 3 21 2.080 MSE 1.38 Change as needed xi xj 1 vs. 2 4.2500 5.2500 1.0000 1 vs. 3 4.2500 5.5000 1.2500 2 vs. 3 5.2500 5.5000 0.2500 Test Stat ( F ) t (alpha/2) =T.INV.2T(alpha,dfW) Sample Size =COUNT(range) Sample Mean =AVERAGE(range) Degrees of Freedom (df) =n T - K t a /2 -value =T.INV.2T(alpha,df) Pairwise Comparison Difference Absolute Value
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Do a Single Factor Anova Test --> Anova: Single Factor Place Output at F1 SUMMARY Groups Count Nurse 8 Tax Auditor 8 Fast-Food Worker 8 ANOVA Source of Variation SS Between Groups 7 Within Groups 29 Total 36 ni nj 8 8 1.22 8 8 1.22 8 8 1.22 Fisher's LSD Critical Value
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Sum Average Variance 34 4.25 1.357143 42 5.25 1.071429 44 5.5 1.714286 df MS F P-value F crit 2 3.5 2.534483 0.103277 3.4668 21 1.380952 23 Not Significant Significant Not Significant Significant Diff > CV
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