In an old experiment to understand the effect of fertilizer quantity and geograp

ID: 3060807 • Letter: I

Question

In an old experiment to understand the effect of fertilizer quantity and geographical region on the quantity of sap production in maple trees in Vermont, a two-factor analysis was performed and the following two-way ANOVA table was constructed. Data was recorded and analyzed for 45 trees grown using three different levels of fertilizer (High, Medium and Low) and three different geographical regions (Northern, Central and Southern). Each combination of fertilizer and region had 9 trees. With passage of time and the usual wear-and-tear of the paper on which the study was written, some values in the table got smudged and hence are now difficult to read. The table below shows those values as lowercase letters (a) through (). Please use the values that are still there in the table to construct the rest of the table. Answer each question below about the missing values in the boxes indicated by the corresponding letters (a) through (q). Please put a box around your final answers. Whenever exact p-values cannot be obtained, provide ranges MS : FERT (a) REGIONb) Interaction( Error Total( (0 51.0 20.6 1201.2) 624.5

Explanation / Answer

Solution:

Here, we have to complete two way ANOVA table:

We are given

Total number of observations = N = 45

Total number of fertilizers = a = 3

Total number of region = b = 3

DF for fertilizer = a – 1 = 3 – 1 = 2

DF for region = b – 1 = 3 – 1 = 2

DF for interaction = a*b = 2*2 = 4

DF error = N – ab = 45 – 3*3 = 45 – 9 = 36

DF total = 2+2+4+36 = 44

SS fertilizer = SS total – (SS region + SS interaction + SS error)

MS = SS / DF

MS fertilizer = 351.7/2 = 175.85

MS region = 51/2 = 25.5

F = MS/MS error

F fertilizer = 175.85/33.36666667 = 5.270229244

(Other calculations are done in table)

P-values are calculated by using F-table or excel by using respective degrees of freedom.

Completed ANOVA table is given as below:

S.V.

FERT

351.7

175.85

5.270229244

0.009828634

REGION

25.5

0.764235688

0.473095988

Interaction

20.6

5.15

0.154345639

0.959798889

Error

1201.2

33.36666667

Total

1624.5