Question 1) An article in Communications of the ACM [(1987, Vol. 30(5), pp. 53–7

Question 1) An article in Communications of the ACM [(1987, Vol. 30(5), pp. 53–76] reported on a study of different algorithms

for estimating software development costs. Six algorithms were applied to eight software development projects and the percent

error in estimating the development cost was observed. The data are in Table. Also, a csv file is posted for you to use to analyse

these results.

(a) It is assumed that there might be nuisance effects due to differences in projects. Based on this, what kind of experiment

design is this? Which factor is the main factor of interest? How are “projects” considered in this example, as replications or

something else?

(b) Use Minitab to create boxplots of responses for algorithms. Minitab Graph->boxplot->simple boxplot (select algorithm as

the categorical variable) . What do you observe based on boxplot?

c) Do the algorithms differ in mean cost estimation accuracy? Use α = 0.05. (Minitab->Stat->ANOVA->General Linear Model)

(d) After running part b, you can use stat->Anova->General Linear Model->comparisons to create multiple comparisons using

Fisher method. You can create groups means, groups that are significantly different or not different, and confidence plots of

difference of means. Which algorithm would you recommend for use in practice based on lower mean error, and low variability.

Question 2) An article in IEEE Transactions on Semiconductor Manufacturing (1992, Vol. 5, pp. 214–222) described an

experiment to investigate the surface charge on a silicon wafer. The factors thought to influence induced surface charge are cleaning

method (spin rinse dry or SRD and spin dry or SD) and the position on the wafer where the charge was measured. The surface

charge (×1011 q / cm3) response data follow:

a) How many replications does this experiment have for each treatment?

b) State the null and alternative hypotheses that we need to test in this problem (main effects and interaction)

c) Write down the matrix that will show the contrast signs for each effect and interaction effect (Assume

Cleaning method is factor A, and test position is factor B)

d) Estimate the factor effects and interaction effect using contrasts. Which effects are big compared to others?

e) Estimate Sum of squares using contrasts and set up the missing parts in the ANOVA table manually

Analysis of Variance for charge

Source DF Seq SS Adj MS F P

A ___ ____ ____ ___ >0.05 or <0.05
B ___ ____ ____ ___ >0.05 or <0.05
AB ___ ____ ____ ___ >0.05 or <0.05
Residual Error ___ ____ ____
Total ___ 122.347
f) Using alpha=0.05 determine which factors and interaction is significant. (perform critical value approach)
g) Draw main effect plot of A (cleaning method) -manually. X axis will show low and high levels of A, and y-
axis will show average response at low and high levels of A.