In: Statistics and Probability
Students in a business statistics course performed a single factor analysis to test the strength of three brands of trash bags. One-pound weights were placed into a bag one at a time until the bag broke. A total of 30 bags, 10 for each brand, were used. An Analysis of Variance was performed on the data to determine if the average breaking strengths were the same for the three brands. The value of MSW in the resulting ANOVA table was 12.11. Brand Sample Size Average GLAD 10 36.30 HEFTY 10 34.90 TUFFSTUFF 10 19.30 Given that the null hypothesis of equal breaking strengths was rejected, determine where the differences are.
We will Tukey test to determine the differences.
Tukey critical value is calculated using the below formula
is a critical value of the studentized range for α, the number of treatments or samples r, and the within-groups degrees of freedom . We get this value from studentized range table.
is the within groups mean square from the ANOVA table and n is the sample size for each treatment.
From Anova table,
= 12.11 , = Number of observations - Number of groups = 3 * 10 - 3 = 27
n = 10, r = 3
From studentized range table, = 3.506
So,
If the differences are greater than the critical value of 3.8582, the differences are significant.
GLAD - HEFTY = 36.30 - 34.90 = 1.4
GLAD - TUFF = 36.30 - 19.30 = 17
HEFTY - TUFF = 34.90 - 19.30 = 15.6
Thus, the differences between (GLAD ,TUFF) and (HEFTY ,TUFF) are significant.