M10801811-Homework 3.docx - EXPERIMENTAL DESIGN \u2013 HOMEWORK 03 Name Truong Xuan Dan ID M10801811 Question 1 a To test the mixing technique whether

# M10801811-Homework 3.docx - EXPERIMENTAL DESIGN –...

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EXPERIMENTAL DESIGN – HOMEWORK 03 Name: Truong Xuan Dan ID: M10801811 Question 1: a. To test the mixing technique whether impact on Tensile Strength, I proposal to test difference among means of Tensile Strength regards to each technique . 1-a. One-way ANOVA: X1, X2, X3, X4 Method Null hypothesis All means are equal Alternative hypothesis Not all means are equal Significance level α = 0.05 Equal variances were assumed for the analysis. Factor Information Facto r Level s Values Factor 4 X1, X2, X3, X4 Analysis of Variance Sourc e DF Adj SS Adj MS F- Value P- Value Factor 3 48974 0 16324 7 12.73 0.000 Error 12 15390 8 12826 Total 15 64364 8 Model Summary S R-sq R- sq(adj) R- sq(pred) 113.2 51 76.09 % 70.11% 57.49% Means Facto r N Mea n StDe v 95% CI X1 4 2971. 0 120.6 (2847.6, 3094.4) X2 4 3156. 3 136.0 (3032.9, 3279.6) X3 4 2933. 8 108.3 (2810.4, 3057.1) X4 4 2666. 3 81.0 (2542.9, 2789.6) Pooled StDev = 113.251 As can be seen from table Analysis of Variance, p-Value < 0.05 means that null hypothesis be rejected. In other words, the mean of tensile strength is significantly difference and, obviously, mixing techniques affect the strength of cement.
b. Graphical display compares the mean tensile strengths for 4 mixing techniques. c. Fisher LSD method Fisher One-way ANOVA: X1, X2, X3, X4 Method Null hypothesis All means are equal Alternative hypothesis Not all means are equal Significance level α = 0.05 Equal variances were assumed for the analysis. Factor Information Facto r Level s Values Factor 4 X1, X2, X3, X4 Analysis of Variance Sourc e DF Adj SS Adj MS F- Value P- Value Factor 3 48974 0 16324 7 12.73 0.000 Error 12 15390 8 12826 Total 15 64364 8 Model Summary S R-sq R- sq(adj) R- sq(pred) 113.2 51 76.09% 70.11% 57.49% Means
Facto r N Mea n StDe v 95% CI X1 4 2971. 0 120.6 (2847.6, 3094.4) X2 4 3156. 3 136.0 (3032.9, 3279.6) X3 4 2933. 8 108.3 (2810.4, 3057.1) X4 4 2666. 3 81.0 (2542.9, 2789.6) Pooled StDev = 113.251 Fisher Pairwise Comparisons Grouping Information Using the Fisher LSD Method and 95% Confidence Facto r N Mean Grouping X2 4 3156.3 A X1 4 2971.0 B X3 4 2933.8 B X4 4 2666.3 C Means that do not share a letter are significantly different. Fisher Individual Tests for Differences of Means Differenc e of Levels Differenc e of Means SE of Differenc e 95% CI T-Value Adjuste d P-Value X2 - X1 185.3 80.1 (10.8, 359.7) 2.31 0.039 X3 - X1 -37.3 80.1 (-211.7, 137.2) -0.47 0.650 X4 - X1 -304.8 80.1 (-479.2, -130.3) -3.81 0.003 X3 - X2 -222.5 80.1 (-397.0, -48.0) -2.78 0.017 X4 - X2 -490.0 80.1 (-664.5, -315.5) -6.12 0.000 X4 - X3 -267.5 80.1 (-442.0, -93.0) -3.34 0.006 Simultaneous confidence level = 81.57% According to Fisher LSD test for making pairwise comparison of mean tensile strength, there are 3 groups A (Tech. 2), B (Tech.3 , 1), C (Tech 4). The meaning of group information is similar to our testing in a) part – Mean of 4 tensile strength is unequal.

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