# ANOVA

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True or False: When the sum of squares within or sum of squares error (SSE) is added to the sum of squares among (SSA), the result is the total sum of squares (SST).

The technique of analysis of variance was originated in England by ___________ while conducting agricultural experiments.

a. Student

b. Gauss

c. Pascal

d. Fisher

Johnson's Service Center has devised three potential options available to preferred customers who redeem coupons and buy at least 10 gallons of fuel when they stop in. Option A is a flat 3 cents off each gallon. Option B is a combination of 2 cents off plus another $1 discount on the regular price of a $5 deluxe car wash. Option C is a $2 discount on the same $5 deluxe car wash but no reduction in the fuel purchase. The owner, Harold Johnson, ran each option on three different two-week trial periods and tracked daily sales receipts from those customers who redeemed their coupons. Results are shown in the table below:

Option A

$453

507

513

521

511

615

601

552

551

505

515

512

476

427

Option B:

$492

514

536

511

528

678

611

653

596

516

534

543

498

437

Option C:

$467

525

516

500

435

462

411

674

512

559

624

711

512

416

Harold elected to conduct a one-way ANOVA for his single-factor experiment.

Multiple choice using the information above:

What is the total sum of squares (SST)?

a. 211,049.6

b. 204,880.6

c. 198,711.6

d. 173,512.1

and again using the info above:

What are the values of the F statistic and the critical value at the 0.05 level of significance?

a. 5.325, 19.55

b. 1.653, 5,18

c. 0.937, 3.24

d. 0.605, 3.24

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Answer d: Fisher

Let mean of A: <y1>, mean of B = <y2> and of C = <y3>

sum(yi1) = 7259

=> <y1> = 7259/14 = 518.50

sum(yi2) = 7647

=> <y2> = 7647/14 = 546.21

sum(yi3) = 7324

=> <y3> = 7324/14 = 523.14

Grand mean:

<y> = sum(k =1,3) [nk * <yk> ]/sum(k=1,3)[nk]

where, ...

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- BEng, Allahabad University, India
- MSc , Pune University, India
- PhD (IP), Pune University, India

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