Question

Consider a study involving turbulent water jets. Shape factor was determined for five different nozzle designs at six levels of jet efflux velocity. Researchers were particularly interested in potential differences in shape factor between nozzle designs, with jet efflux velocity considered a nuisance factor. The data for this experiment are provided below. The first column provides the nozzle design number, the second column provides the jet efflux velocity (in m/s), and the third column provides the shape factor measurement. Note that the run order is not provided.

3. Use SAS and determine which pairs of nozzle designs have significantly different treatment means using both the LSD and Tukey methods. NOTE: You may use the lsmeans or means statement in PROC GLM to make this determination. You do not need to perform calculations by hand.

4. Which method (LSD or Tukey’s) would you recommend using to determine significant differences among pairs of treatment means for this experiment? Clearly explain your choice.

5. Determine if the model assumptions are reasonably met. Be sure to state the assumptions of the test and identify which plot/test can be used to evaluate each assumption.

Design	JEV	SF
1	11.73	0.78
2	11.73	0.85
3	11.73	0.93
4	11.73	1.14
5	11.73	0.97
1	14.37	0.8
2	14.37	0.85
3	14.37	0.92
4	14.37	0.97
5	14.37	0.86
1	16.59	0.81
2	16.59	0.92
3	16.59	0.95
4	16.59	0.98
5	16.59	0.78
1	20.43	0.75
2	20.43	0.86
3	20.43	0.89
4	20.43	0.88
5	20.43	0.76
1	23.46	0.77
2	23.46	0.81
3	23.46	0.89
4	23.46	0.86
5	23.46	0.76
1	28.74	0.78
2	28.74	0.83
3	28.74	0.83
4	28.74	0.83
5	28.74	0.75

Answer 1

We ran the data set on the program and obtained the following for the LSD test

The p value <0.05 .hence the test results are significant.

Also to find the pair of nozzles, we find hte idfference in each of the three parameters and check for points having difference of means greater than the LSD.

Design		JEV		SF
Design	Diff	JEV	Diff	SF	Diff
1	1	11.73	0	0.78	0.07
2	1	11.73	0	0.85	0.08
3	1	11.73	0	0.93	0.21
4	1	11.73	0	1.14	-0.17
5	-4	11.73	2.64	0.97	-0.17
1	1	14.37	0	0.8	0.05
2	1	14.37	0	0.85	0.07
3	1	14.37	0	0.92	0.05
4	1	14.37	0	0.97	-0.11
5	-4	14.37	2.22	0.86	-0.05
1	1	16.59	0	0.81	0.11
2	1	16.59	0	0.92	0.03
3	1	16.59	0	0.95	0.03
4	1	16.59	0	0.98	-0.2
5	-4	16.59	3.84	0.78	-0.03
1	1	20.43	0	0.75	0.11
2	1	20.43	0	0.86	0.03
3	1	20.43	0	0.89	-0.01
4	1	20.43	0	0.88	-0.12
5	-4	20.43	3.03	0.76	0.01
1	1	23.46	0	0.77	0.04
2	1	23.46	0	0.81	0.08
3	1	23.46	0	0.89	-0.03
4	1	23.46	0	0.86	-0.1
5	-4	23.46	5.28	0.76	0.02
1	1	28.74	0	0.78	0.05
2	1	28.74	0	0.83	0
3	1	28.74	0	0.83	0
4	1	28.74	0	0.83	-0.08
5		28.74		0.75

Clearly Nozzle 1 and 5 are the pair of nozzles having significantly different treatment means as per LSD.

The simulation program gives the followin results for the tukey test

Clealry Samples A Vs C and AVs D and D Vs E are pairs of nozzles having significant difference.

Tukey test is more reliable .