Supplement 2--One-way ANOVA case in point (revised) Data in matrix format: alfalfa strain (j = one particular to k ) a b c i = 1 to n one particular 3. a couple of 4. a couple of 4. almost 8 2 five. 4 5. 5 5. 4 three or more 2 . 4 6. 0 4. you 4 several. 1 3. 1 five. 9 a few 3. 2 3. being unfaithful 5. 2 SUM Xj 21. 3 21. several 24. some nj meanj s 2 j

m 8. your five 9. several 5. being unfaithful 6. 5 6. 8 36. 9 5 six. 38 2 . 107 l =4

TOTAL

1 A. Does the pressure of alfalfa affect nitrogen fixation levels? B. Ho: Ој1 = Ој2 sama dengan Ој3 = Ој4 ': at least one mean is different two We'll make use of О± sama dengan. 02, two-tailed в‡’ О±/2 =. 01 (your publisher does not provide an О± sama dengan. 005 table) dfnum sama dengan k - 1 = 4 - 1 = 3 dfdenom = nT - k = twenty - 5 = of sixteen critical N. 01, 3, 16 sama dengan 5. twenty nine 3 5 SSTR Farrenheit = 5. 7536 (see work at left)

104. 300 20. 500 5. 215

Sum Xij nT total mean

your five 4. 26 3. 768 j =1 4. 5601

5 four. 34 1 . 133 j =2 several. 8281 j =2 four. 5320

five 4. 88 0. 497 j =3

SSTR

zero. 5611 twenty three. 4361 j =3 1 . 9880 m =4 eight. 4280

TOTAL 32. 3855 TOTAL 40. 0200

Decision rule: Deny Ho in the event F > 5. twenty nine

SSE

l =1 12-15. 0720

SSE

F sama dengan 5. 7536 reject Ho

ANOVA table Sum of Source of variation squares Therapies SSTR Error SSE Total SST

df k-1 N-k N-1

Indicate Square Farrenheit MSTR MSE

FTR Ho

F

critical F sama dengan 5. twenty nine

5 Decision: Reject Ho because F > a few. 29 Bottom line: At О± =. 02, we determine that the stress of alfalfa grown considerably affects the mean amount of nitrogen fixation.

Source of Amount of variance squares df Treatments thirty-two. 3855 three or more Error 31. 0200 sixteen Total sixty two. 4055 nineteen

Mean Rectangular F 10. 7952 a few. 7536 1 . 8763

Fisher's LSD pairwise t-tests

Ho: Ојi sama dengan Ој m

* * *

1В v. В 2 1В v. В 3 1В v. В 4 2В v. В 3 2В v. В 4 3В v. В 4

t вЂђ0. 0923 вЂђ0. 7157 вЂђ3. 6015 вЂђ0. 6233 вЂђ3. 5091 вЂђ2. 8858

ni 5 5 a few 5 five 5

nj-new jersey 5 5 5 five 5 5

xi

xj

4. twenty six 4. 26 4. twenty six 4. 34 4. 34 4. 88

4. thirty four 4. 88 7. 32 4. 88 7. 32 7. 38

MSE 1 . 87625

TAKE NOTE: Here, the i and j subscripts do not refer to rows (observations) and and columns (treatments), even though that is how they had been used up to this point. i refers to the 1st treatment imply of the set tested (Ојi) and j to the second (Ојj).

essential t. 01, 16 = 2 . 583 where (df = nT - k)В

* = significant in О± /2 =. 01 Type I Error Rates (p. 511) and cumulative experimentwise О±В (О±ew) 0. 88584 в†ђ probability of making simply no Type I actually errors in 6 checks = (1 - О± )6 = 0. 98 6 0. 11416 в†ђ probability of getting at least one Type I problem in 6th tests sama dengan cumulative experimentwise alpha error risk sama dengan О± ew = 1 - (1 - О± )6 = 1 -- 0. 98 6 0. 00333 в†ђ Bonferroni altered О± sama dengan О± /6

ANOVAВ inВ MINITABВ В

InputВ file: В В ALFALFANOVA. MTWВ Download this kind of file through the WebCT internet site

Procedure:

Stat ANOVA One-wayвЂ¦ Response: Nitrogen (y) Factor: Strain (x) Click ComparisonsвЂ¦ check Fisher's and set friends and family error charge to 1* OK ALRIGHT *this pieces О±/2 sama dengan. 01

One-way ANOVA: Nitrogen (y) vs . Strain (x)

Source Pressure (x) Error Total H = 1 ) 370 DF 3 of sixteen 19 DURE 32. 39 30. 02 62. forty one MS twelve. 80 1 . 88 N 5. 75 P zero. 007

R-Sq = fifty-one. 90%

R-Sq(adj) = forty two. 88%

Level a n c g

N your five 5 a few 5

Indicate 4. 260 4. 340 4. 880 7. 380

StDev 1 ) 941 1 . 064 0. 705 1 . 452

Specific 98% CIs For Suggest Based on Put StDev ---+---------+---------+---------+-----(---------*---------) (---------*---------) (--------*---------) (---------*---------) ---+---------+---------+---------+-----3. 2 some. 8 six. 4 almost 8. 0

Put StDev sama dengan 1 . 370 Fisher 98% Individual Self confidence Intervals Simultaneous confidence level = 91. 58% All Pairwise Comparisons among Levels of Strain (x)

(I'm not sure how Minitab computes this. ASW's method provides 88. 584%) Unhelpfully, Minitab conducts the Fisher's LSD test applying confidence times only. Reject Ho if 0 would not lie inside the interval. If 0 is in the interval for the difference, in that case we cannot be 98% assured that the difference is substantially different from no, i. electronic., that there is zero difference. We have marked the significant results having a * and bold printing. They're the same results we acquired above.

Tension (x) = a deducted from: Strain (x) Reduced Center Uppr --------+---------+---------+---------+b -2. 158 0. 080 2 . 318 (------*-------) c -1. 618 0. 620 installment payments on your 858 (------*-------) d* zero. 882 a few. 120 a few. 358...