Question

An experiment was performed in which nest of treatments and sub-treatments were

arranged to perform a nested ANOVA. In this experiment, there are three treatment groups

A,B,C and three nested subtreatment groups, L1, L2, L3, and four subsamples S1, S2, S3, S4.

a. Load the data file into MATLAB. Use the command xlsread to load the data.

A	L1	S1	50
A	L1	S2	55
A	L1	S3	60
A	L1	S4	65
B	L1	S1	70
B	L1	S2	75
B	L1	S3	85
B	L1	S4	90
A	L2	S1	100
A	L2	S2	105
A	L2	S3	110
A	L2	S4	115
B	L2	S1	115
B	L2	S2	120
B	L2	S3	130
B	L2	S4	135
C	L1	S1	42
C	L1	S2	35
C	L1	S3	28
C	L1	S4	45
C	L2	S1	136
C	L2	S2	142
C	L2	S3	155
C	L2	S4	151
A	L3	S1	11
A	L3	S2	14
A	L3	S3	18
A	L3	S4	10
B	L3	S1	19
B	L3	S2	28
B	L3	S3	35
B	L3	S4	42
C	L3	S1	5
C	L3	S2	8
C	L3	S3	7
C	L3	S4	2

b. Using the anovan command run a nested ANOVA on the data. Use the MATLAB

documentation to help you choose the correct model and the nesting relationship matrix.

Report the ANOVA table for the given data.

c. Use boxplot (with notch and whisker options) to create two graphics of the data that has

an x-axis that is treatment (A,B,C) and another that has an x-axis of subtreatment (L1, L2,

L3). For both plots the y-axis is of the data in the datafile. Interpret the results of the

experiment using the ANOVA table and the graphics by addressing the hypotheses tested by

the ANOVA.

d. Perform a random block ANOVA using this data.

1	hi	1
1	hmid	2
1	lmid	4
1	lo	4
2	hi	11
2	hmid	12
2	lmid	13
2	lo	14
3	hi	21
3	hmid	22
3	lmid	23
3	lo	24

Blocks are denoted in column 1 by 1,2,or3; treatments are given by hi,hmid,lmid,lo. Is there a block effect, is there

a treatment affect. Re-run this experiment as a one-way anova, does the F-statistic change?

Why?

Now run multicompare on the output of the block anova results to compare

treatment pairs within blocks. Interpret.

Answer 1

(b) The corrected ANOVA table is:

Between-Subjects Factors Samples 1 2 3 4 SubtreatmentGroups 1 12 12 2 12 TreatmentGroups 1 12 12 2 3 12 Tests of Between-Subjects Effects Dependent Variable: Data Type lIl Sum of Squares Mean Square df F Sig. Source Corrected Model 82862.972a 35 2367.513 Intercept 161738.028 1 161738.028 754,972 Samples 3 251.657 SubtreatmentGroups 73411.722 2 36705.861 TreatmentGroups 2515.389 2 1257.694 Samples SubtreatmentGroups 213.611 6 35.602 Samples TreatmentGroups 255.944 6 42.657 SubtreatmentGroups TreatmentGroups 5441.111 4 1360.278 Samples SubtreatmentGroups TreatmentGroups 270.222 12 22.519 Error .000 0 Total 244601.000 36 Corrected Total 82862.972 35 a. R Squared 1.000 (Adjusted R Squared ) LL

(c) The boxplot with treatment groups is:

200.00 150.00 100.00 50.00 00 1 2 3 TreatmentGroups Data H

The boxplot with sub treatment groups is:

200.00 150.00 100.00 50.00 00 1 2 3 SubtreatmentGroups Data

The ANOVA table supports the claim considering the error term is zero.

(d) The block ANOVA result is:

Between-Subjects Factors N Blocks 1 8 2 8 11 Treatments 1 2 6 3 15 4 3 Tests of Between-Subjects Effects Dependent Variable: Samples Type lll Sum of Squares Mean Square df F Sig Source 765.013a Corrected Model 69.547 11 1.461 .243 1385.939 Intercept 1 1385.939 29.118 000 Blocks 437.592 2 218.796 4.597 028 Treatments 276.877 3 92.292 1.939 167 235.080 39.180 569 Blocks Treatments 6 .823 Error 713.950 15 47,597 Total 2816.000 27 Corrected Total 1478.963 26 a. R Squared 517 (Adjusted R Squared 163)

Yes, there is a block effect.

Yes, there is a treatment effect.

The One-Way ANOVA results are:

Oneway ANOVA Samples Sum of Mean Square Squares df F Sig. Between Groups 248.179 2,420 2 124.089 110 Within Groups 24 1230.784 51.283 Total 1478.963 26

Yes, there is a change in F-statistic because blocks and treatments are separated in One_way ANOVA.

Please give me a thumbs-up if this helps you out. Thank you!