The data below was collected from a two-factor ANOVA experiment, factor A has 4 levels andfactor B has 3 levels:Factor B121604850Factor A25350484644494514352 From the given data,i)The estimate of the overall population mean, A =ii)The estimate of the first effect for factor A, âz=iii)The estimate of the first effect for factor B, B=

Answered: factor B has 3 levels: Factor B 1 2 60…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The data below was collected from a two-factor ANOVA experiment, factor A has 4 levels and
factor B has 3 levels:
Factor B
1
2
1
60
48
50
Factor A
2
53
50
48
46
44
49
4
51
43
52

From the given data,
i)
The estimate of the overall population mean, A =
ii)
The estimate of the first effect for factor A, âz=
iii)
The estimate of the first effect for factor B, B=

Expert Solution

Step 1

Analysis of two-way classified data with one observation per cell for fixed effect model is used to test the equality of factors means. Consider two sources of variation, A and B. A being at p levels and B being at q levels. There is one observation for each combination of A and B classification, which has been selected at random from a large population of levels A and B. Then, the model will be:

$x_{i j} = μ + α_{i} + β_{j} + ε_{i j}$

Here

$μ$ is the general mean.
$α_{i}$ is the effect of $A_{i}; (i = 1, 2, . . ., p)$ level.
$β_{j}$ is the effect of $B_{j}; (j = 1, 2, . . ., q)$ level.
$x_{i j}$ is the interaction effect of A_i and B_jlevels.
$ε_{i j}$ is the error due to chance and $ε_{i j} ~ N (0, {σ_{e}}^{2})$

The estimate of $μ$ , $α_{i}$ and $β_{j}$ are calculated as follows:

$\hat{μ} = \frac{\sum_{i} \sum_{j} x_{i j}}{p q}$ , $\hat{α_{i}} = \frac{\sum_{j} x_{i j}}{q} - \hat{μ}$ and $\hat{β_{j}} = \frac{\sum_{i} x_{i j}}{p} - \hat{μ}$ , respectively.