Question

Problem: An article in Communications of the ACM (Vol. 30, No. 5, 1987) studied different algorithms for estimating software development costs. Six algorithms were applied to several different software development projects and the percent error in estimating the development cost was observed. Some of the data from this experiment is shown in the table below. We are interested to find if different algorithms are different in their mean cost estimation accuracy or not?

Project
Algorithm	1	2	3	4	5	6
1	1244	21	82	2221	905	839
2	281	129	396	1306	336	910
3	220	84	458	543	300	794
4	225	83	425	552	291	826
5	19	11	-34	121	15	103
6	-20	35	-53	170	104	199

1. Define the hypothesis.
2. Define the treatment, level, block and response variable.
3. What kind of test is appropriate for this design do deal with nuisance factor? Why?
4. What are the sources of variability in observed responses?
5. Do the algorithms differ in their mean cost estimation accuracy?
6. Check the assumption.
7. check the additivity assumption (use interaction plots).
8. plot the residuals versus treatment and block and explain them.
9. Which algorithm would you recommend for use in practice (use factorial plots)?

Answer 1

a) H0 : mean1 = mean2= mean3 =mean4.... = mean6 (all algorithms have same mean cost estimation accuracy)

Halternate : all algorithms dont have same mean cost estimation accuracy

b) Treatment - Algorithm 1 ,2 ,3 ,4 ,5 ,6

level - possible values of the algorithms

block - Project 1 ,2,3,4,5,6

response - values entered

c)For randomized block designs, there is one factor or variable that is of primary interest. However, there are also several other nuisance factors.

Nuisance factors are those that may affect the measured result, but are not of primary interest. For example, in applying a treatment, nuisance factors might be the specific operator who prepared the treatment, the time of day the experiment was run, and the room temperature. All experiments have nuisance factors. The experimenter will typically need to spend some time deciding which nuisance factors are important enough to keep track of or control, if possible, during the experiment.

Randomized block design test

d) sources of variablity sampling response, measurement error, random error, technical variation etc

e)The Model F-value of 2.602 implies the model is significant. There is only a 0.17% chance that a "Model F-Value" this large could occur due to noise

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
1	6	5312	885.3333	661519.5
2	6	3358	559.6667	203937.9
3	6	2399	399.8333	64260.97
4	6	2402	400.3333	69639.87
5	6	235	39.16667	3581.767
6	6	435	72.5	10442.7
1	6	1969	328.1667	216024.6
2	6	363	60.5	2082.3
3	6	1274	212.3333	57476.27
4	6	4913	818.8333	651728.6
5	6	1951	325.1667	96648.57
6	6	3671	611.8333	129780.6
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Rows	2989130	5	597826.1	5.376958	0.00172	2.602987
Columns	2287339	5	457467.9	4.114551	0.007295	2.602987
Error	2779574	25	111182.9
Total	8056044	35

f)

h)

i) The FUNCTIONAL POINTS algorithm has the losest cost estimation error.