Perform an ANOVA table and Tukey Test For quality assurance

Perform an ANOVA table and Tukey Test

For quality assurance purposes, you wish to compare three brands of high-strength bolts for their shear capacity (in kN). Samples of the three brands (all of which had 19 mm diameters) were obtained and tested for shear capacity. The results for the three brands appear below. Justify which brand to use. (adapted from [Khisty et al. 2012])

Solution

Sol)

Using SPSS we can Perform Anova And Tukey Test

Null hypothesis: there is no differences between all the means of three bands

Alternative hypothesis: there is a differences between all the means of three bands

Conclusion: p=0.784 and alpha=0.05

P value> alpha hence there is significant difference between all the means.ie., all means are not equal

Now

If your ANOVA test shows that the means aren’t all equal, your next step is to determinewhich means are different, to your level of significance. You can’t just perform a series of t tests, because that would greatly increase your likelihood of a Type I error.

To overcome this problem ,John Tukey gave one answer to this question, the HSD (Honestly Significant Difference) test. You compute something analogous to a t score for each pair of means, but you don’t compare it to the Student’s t distribution.

Descriptives
Capacities
	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean	Minimum	Maximum
Lower Bound	Upper Bound
brand1	7	82.5714	5.06153	1.91308	77.8903	87.2526	75.00	90.00
barnd2	9	83.8889	5.86184	1.95395	79.3831	88.3947	76.00	92.00
brand3	11	82.3636	4.36515	1.31614	79.4311	85.2962	76.00	89.00
Total	27	82.9259	4.92971	.94872	80.9758	84.8761	75.00	92.00