Statistical computation using ANOVA

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Manual Computation

A research study compared the ounces of coffee consumed daily between three groups. Group1 was Italians, Group 2 French, and Group 3 American. Determine if there is a significant difference among the groups using a 5% level

(alpha is .05).

Group1: Italian

Group 2: French

Group 3: American

The Results of this study are in the following table:

The Results of this study are in the following table: n (sample size) 70 sample size 1 70 sample size 2 70 sample size 3 4.0 sample mean 1 3.7 sample mean 2 3.4 sample mean 3 4.4 variance for 5.2 variance 6.1 variance F Distribution critical values for P=0.05 Denominator (the within df - also called the error) Numerator DF (the between df) 1 2 3 5 7 10 15 20 30 60 120 500 1000 1 161.45 199.50 215.71 224.58 230.16 236.77 241.88 245.95 248.01 250.10 252.20 253.25 254.06 254.19 2 18.513 19.000 19.164 19.247 19.296 19.353 19.396 19.429 19.446 19.462 19.479 19.487 19.494 19.495 3 10.128 9.5522 9.2766 9.1172 9.0135 8.8867 8.7855 8.7028 8.6602 8.6165 8.5720 8.5493 8.5320 8.5292 4 7.7086 6.9443 6.5915 6.3882 6.2560 6.0942 5.9644 5.8579 5.8026 5.7458 5.6877 5.6580 5.6352 5.6317 5 6.6078 5.7862 5.4095 5.1922 5.0504 4.8759 4.7351 4.6187 4.5582 4.4958 4.4314 4.3985 4.3731 4.3691 7 5.5914 4.7375 4.3469 4.1202 3.9715 3.7871 3.6366 3.5108 3.4445 3.3758 3.3043 3.2675 3.2388 3.2344 10 4.9645 4.1028 3.7082 3.4780 3.3259 3.1354 2.9782 2.8450 2.7741 2.6996 2.6210 2.5801 2.5482 2.5430 15 4.5431 3.6823 3.2874 3.0556 2.9013 2.7066 2.5437 2.4035 2.3275 2.2467 2.1601 2.1141 2.0776 2.0718 20 4.3512 3.4928 3.0983 2.8660 2.7109 2.5140 2.3479 2.2032 2.1241 2.0391 1.9463 1.8962 1.8563 1.8498 30 4.1709 3.3159 2.9223 2.6896 2.5336 2.3343 2.1646 2.0149 1.9317 1.8408 1.7396 1.6835 1.6376 1.6300 60 4.0012 3.1505 2.7581 2.5252 2.3683 2.1666 1.9927 1.8365 1.7480 1.6492 1.5343 1.4672 1.4093 1.3994 120 3.9201 3.0718 2.6802 2.4473 2.2898 2.0868 1.9104 1.7505 1.6587 1.5544 1.4289 1.3519 1.2804 1.2674 500 3.8601 3.0137 2.6227 2.3898 2.2320 2.0278 1.8496 1.6864 1.5917 1.4820 1.3455 1.2552 1.1586 1.1378 1000 3.8508 3.0047 2.6137 2.3808 2.2230 2.0187 1.8402 1.6765 1.5811 1.4705 1.3318 1.2385 1.1342 1.1096 Example: , F for df = 2,207 is 3.0718 The critical value for an F test : 3.3259 "2" is the column or numerator ( between) "I used 120 as the closet value to 207" as the row or denominator (error within)