[The following information applies to the questions displayed below.] Three samp
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Question
[The following information applies to the questions displayed below.]
Three samples of each of three types of PVC pipe of equal wall thickness are tested to failure under three temperature conditions, yielding the results shown below. Research questions: Is mean burst strength affected by temperature and/or by pipe type? Is there a “best” brand of PVC pipe?
Burst Strength of PVC Pipes (psi)
Perform Tukey multiple comparison tests. (Input the mean values within the input boxes of first row and input boxes of the first column. Round your t-values and critical values to 2 decimal places and other answers to 1 decimal place.)
Tukey simultaneous comparison t-values (d.f. = 18)
Tukey simultaneous comparison t-values (d.f. = 18)
Three samples of each of three types of PVC pipe of equal wall thickness are tested to failure under three temperature conditions, yielding the results shown below. Research questions: Is mean burst strength affected by temperature and/or by pipe type? Is there a “best” brand of PVC pipe?
Explanation / Answer
We may use two-way ANOVA
The hypothesis
Row Effect
H0: temperature means are the same
H1: temperature means differ
Column Effect
H0: pipe type means are the same
H1: pipe type means differ
Interaction effect
H0: there is no interaction effect
H1: there is interaction effect
By using R
a1 = aov(C$x ~ C$T + C$P)
> posthoc <- TukeyHSD(x=a1, 'C$T', conf.level=0.95)
> a1
Call:
aov(formula = C$x ~ C$T + C$P)
Terms:
C$T C$P Residuals
Sum of Squares 3584.296 29079.185 2811.704
Deg. of Freedom 2 8 16
Residual standard error: 13.25638
Estimated effects may be unbalanced
> posthoc
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = C$x ~ C$T + C$P)
$`C$T`
diff lwr upr p adj
B-A 14.22222 -1.902562 30.347007 0.0885703
C-A -14.00000 -30.124785 2.124785 0.0944922
C-B -28.22222 -44.347007 -12.097438 0.0009687
>
SUMMARY PVC1 PVC2 PVC3 Total Hot Count 3 3 3 9 Sum 806 854 775 2435 Average 268.6667 284.6667 258.3333 270.5556 Variance 196.3333 220.3333 577.3333 380.5278 Warm Count 3 3 3 9 Sum 945 1005 912 2862 Average 315 335 304 318 Variance 133 124 49 261.75 Cool Count 3 3 3 9 Sum 1063 1083 1001 3147 Average 354.3333 361 333.6667 349.6667 Variance 134.3333 124 32.33333 225 Total Count 9 9 9 Sum 2814 2942 2688 Average 312.6667 326.8889 298.6667 Variance 1495 1246.611 1244.75 ANOVA Source of Variation SS df MS F P-value F crit Sample 28536.96 2 14268.48 80.73114 1.03E-09 6.012905 Columns 3584.296 2 1792.148 10.13998 0.001124 6.012905 Interaction 172.5926 4 43.14815 0.244132 0.909467 4.579036 Within 3181.333 18 176.7407 Total 35475.19 26Related Questions
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