Homework 5

This homework is based on the following example:

Bearings for high-speed turbine engines can be made of many different types of compounds.  The times to fatigue failure (in units of millions of cycles) for high-speed bearings were measured for five different types of compounds.  Compounds I and II are made of an alloy containing lead.  Compounds III, IV, and V are made of an alloy containing iron.  Compounds I and III were made by US companies and compounds II, IV and V were made by foreign companies.  The data are listed below:

 Compound Failure Time Compound Failure Time Compound Failure Time Compound Failure Time Compound Failure Time I 3.03 II 3.19 III 3.46 IV 5.88 V 6.43 I 5.53 II 4.26 III 5.22 IV 6.74 V 9.97 I 5.6 II 4.47 III 5.69 IV 6.9 V 10.39 I 9.3 II 4.53 III 6.54 IV 6.98 V 13.55 I 9.92 II 4.67 III 9.16 IV 7.21 V 14.45 I 12.51 II 4.69 III 9.4 IV 8.14 V 14.72 I 12.95 II 5.78 III 10.19 IV 8.59 V 16.81 I 15.21 II 6.79 III 10.71 IV 9.8 V 18.39 I 16.04 II 9.37 III 12.58 IV 12.28 V 20.84 I 16.84 II 12.75 III 13.41 IV 25.46 V 21.51

The goal of this homework is to compare the average failure times for the bearings made from the 5 different compounds.

1.          Use PROC MEANS to calculate the average times to fatigue failure for each of the 5 compounds.  Which compound had the longest average time to fatigue failure?  The shortest time?

2.          Use PROC UNIVARIATE to construct side-by-side box plots.  Based on these plots, do you notice any obvious differences between the 5 compounds?

3.          Use PROC GLM to compute the analysis of variance for these data.  Based on the overall F-test, is there a significant difference between the treatment means for the 5 different compounds?  State the null and alternative hypotheses for the test, and report the F-statistic and p-value.

4.          Based on what you know about the compounds, come up with 2 pre-planned comparisons for the means.  Define the contrasts associated with these comparisons and use the contrast statement in PROC GLM to test your hypotheses.  Be sure to state the null and alternative hypotheses for your test, report the p-value, and state your conclusion in non-statistical terms.

5.          Now, use multiple comparison methods to compare all possible pairs of treatment means.  Using PROC GLM, do the multiple comparisons using the F-protected LSD, Tukey, and Duncan methods.  For each method, which means are declared to be the same, and which methods are declared to be significantly different.

6.          Based on your findings write a short (one paragraph) summary of your results, and make recommendations about which compound(s) you would use if your goal was to create ball-bearings with the longest time to fatigue failure.