Suppose that this experiment had been conducted in 5.35. three blocks, with each

Question

Suppose that this experiment had been conducted in 5.35. three blocks, with each replicate a block Assume that the observations in the data table are given in order, that is, the first observation in each cell comes from the first replicate, and so on. Reanalyze the data as a factorial experiment in blocks and estimate the variance component for blocks. Does it appear that blocking was useful in this experiment? Glass Block Phosphor Type 1 280 2 290 3 285 1 230 300 310 295 290 285 290 260 240 235 220 225 230 2 235 3240

Explanation / Answer

Result:

To test the block effect, calculated F=0.07, P=0.937 which is > 0.05 level.

Block effect is not significant.

Data:

Glass

Block

phosphor

data

1

1

1

280

1

1

2

300

1

1

3

290

1

2

1

290

1

2

2

310

1

2

3

285

1

3

1

285

1

3

2

295

1

3

3

290

2

1

1

230

2

1

2

260

2

1

3

220

2

2

1

235

2

2

2

240

2

2

3

225

2

3

1

240

2

3

2

235

2

3

3

230

MINITAB output

General Linear Model: data versus Glass, Block, phosphor

Method

Factor coding

(-1, 0, +1)

Factor Information

Factor

Type

Levels

Values

Glass

Fixed

2

1, 2

Block

Fixed

3

1, 2, 3

phosphor

Fixed

3

1, 2, 3

Analysis of Variance

Source

DF

Adj SS

Adj MS

F-Value

P-Value

Glass

1

14450.0

14450.0

228.66

0.000

Block

2

8.3

4.2

0.07

0.937

phosphor

2

933.3

466.7

7.38

0.008

Error

12

758.3

63.2

Total

17

16150.0

Model Summary

S

R-sq

R-sq(adj)

R-sq(pred)

7.94949

95.30%

93.35%

89.43%

Coefficients

Term

Coef

SE Coef

T-Value

P-Value

VIF

Constant

263.33

1.87

140.54

0.000

Glass

1

28.33

1.87

15.12

0.000

1.00

Block

1

0.00

2.65

0.00

1.000

1.33

2

0.83

2.65

0.31

0.759

1.33

phosphor

1

-3.33

2.65

-1.26

0.232

1.33

2

10.00

2.65

3.77

0.003

1.33

Regression Equation

data

=

263.33 + 28.33 Glass_1 - 28.33 Glass_2 + 0.00 Block_1 + 0.83 Block_2 - 0.83 Block_3
- 3.33 phosphor_1 + 10.00 phosphor_2 - 6.67 phosphor_3

Fits and Diagnostics for Unusual Observations

Obs

data

Fit

Resid

Std
Resid

11

260.00

245.00

15.00

2.31

R

R Large residual

Glass

Block

phosphor

data

1

1

1

280

1

1

2

300

1

1

3

290

1

2

1

290

1

2

2

310

1

2

3

285

1

3

1

285

1

3

2

295

1

3

3

290

2

1

1

230

2

1

2

260

2

1

3

220

2

2

1

235

2

2

2

240

2

2

3

225

2

3

1

240

2

3

2

235

2

3

3

230

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