Question

An experiment was planned to study the effect of Sulphate, Potash and Super Phosphate on the yield of potatoes. All the combinations of 2 levels of Super Phosphate [0 cen \left ( P0 \right ) and 5 cent \left ( P1 \right ) \left ( P1 \right )/ acre] and two levels of Sulphate and Potash [0 cen \left ( K0 \right ) and 5 cent \left ( K0 \right )/ acre]  were studied in a randomised block design with 4 replications each. The (1/70) yields [lb per plot = (1/70) acre] obtained are given in table below: 

Blocks Yields
       
                    I

(1)

23

k

25

p

22

kp

38

                   II

p

40

(1)

26

k

36

kp

38

                   III

(1)

29

k

20`

pk

30

p

20

                    IV

kp

34

k

31

p

24

(1)

28

Analyse the data and give your conclusions.

22 Apr 2024
Answer :
Word Count : 963
To analyze the given data, let's break the process into a few steps for clarity: ### 1. Understanding the Data Setup - Factors: - Super Phosphate (P) has two levels: \( P_0 \) and \( P_1 \) (0 and 5 cent/acre). - Sulphate (K) also has two levels: \( K_0 \) and \( K_1 \) (0 and 5 cent/acre). - Potash (P) has two levels: \( P_0 \) and \( P_1 \) (0 and 5 cent/acre). - Design: - The experiment is conducted using a Randomized Block Design (RBD) with 4 replications. - The yields of potatoes are measured in pounds per plot, given for each combination of factors. ### 2. Data Table | Block | \( P_0 K_0 \) | \( P_0 K_1 \) | \( P_1 K_0 \) | \( P_1 K_1 \) | |-------|----------------|----------------|----------------|----------------| | I | 23 | 25 | 22 | 38 | | II| 40 | 26 | 36 | 38 | | III| 29 | 20 | 30 | 20 | | IV| 34 | 31 | 24 | 28 | ### 3. Model Setup and Hypothesis The general linear model for a Randomized Block Design (RBD) can be written as: \[ Y_{ijk} = \mu + B_i + P_j + K_k + (P \times K)_{jk} + \epsilon_{ijk} \] Where: - \( Y_{ijk} \) = Yield for block \( i \), and factor levels \( j \) and \( k \), - \( \mu _______ _____ ______ ____ _______ _____ _____.
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