EEM332 Lecture Slides 1

EEM332Design of Experiments

En. Mohd Nazri Mahmud

MPhil (Cambridge, UK)

BEng (Essex, UK)

nazriee@eng.usm.my

Room 2.14

Ext. 6059

EEM332 Lecture Slides 2

Agenda

1 Using P-Values in Hypothesis Testing2 Variability in the data3 Single factor experiment with more than two levels of factor4 Analysis of variance5 Demo example of ANOVA calculation using Excel6 Assignments

EEM332 Lecture Slides 3

Using P-valuesOne way to report the results of a hypothesis testing is to state that the null Hypothesis was or was not rejected at a specified alpha-value or level of Significance.

This is often inadequate because it gives the decision maker no idea aboutwhether the value of the test statistics was just barely in the rejection region or whether it was very far into the region.

To avoid this, P-value approach has been adopted widely in practice.

The P-value is the probability that the test statistics will take on a value that isat least as extreme as the observed value of the statistics when the nullhypothesis is true.

The P-value is the smallest level of significance that would lead to rejectionof the null hypothesis.

EEM332 Lecture Slides 4

Using P-values-Example Minitab output

y

The null hypothesis would be rejected at any level of significance, alpha greaterAnd equal to 0.042

EEM332 Lecture Slides 5

Comparison of the variability in the dataIn many experiments, we are interested in possible variability in the databecause there are cases in which the variability needs to be small.

Therefore, we need to examine tests of hypothesis and confidence interval for the variances using chi-square distribution and the F-distribution

To test whether or not the variance is equal to a constant we use Table 2-7p53.With corresponding hypothesis, test statistics and criteria for rejection. The appropriate reference distribution is the chi-square distribution (Appendix III,p.607)With n-1 degrees of freedom

To test the equality of variances, we use Table 2-7p53 with corresponding hypothesis, test statistics and criteria for rejection. The appropriate reference distribution is the F-distribution (Appendix IV,p.608-612)With n1 -1 numerator degrees of freedom and n2-1 denominator degrees of freedom.

EEM332 Lecture Slides 6

Comparison of the variability in the dataExample 2.2

EEM332 Lecture Slides 7

Comparison of the variability in the dataExercise

EEM332 Lecture Slides 8

Single factor experiment with more than two levels of factor

Single factor with 2 levels – Example 2-1p24

Single factor with > two levels – Example 3-1p.61– If we wish to test whether the 4 means are

different or not, we do not use t-Test because it is tedious to do 6 pairs of comparison

– An appropriate procedure is the Analysis of Variance (ANOVA)

EEM332 Lecture Slides 9

Analysis of varianceAnalysis of variance (ANOVA) is based on the idea of partitioning of thetotal variability into its component parts. It is used for testing the equality or inequality of treatment means.

The total variability in the data as measured by the Total Corrected Sum of Squares can be partitioned into a sum of squares of the differences betweenthe treatment averages and the grand average, plus a sum of squares of thedifference of observations within treatments from the treatment average

If the between-treatment error is much larger than the within-treatment error, It is likely that the treatments means are different.

SST = SSTreatments + SSE

EEM332 Lecture Slides 10

Analysis of variance

Computing the values using Microsoft ExcelExample 3-1p. 70

EEM332 Lecture Slides 11

Analysis of variance – Individual Assignments using excel

Question 1

The tensile strength of portland cement is being studied.Four different mixing techniques can be used economically.A completely randomised experiment was conducted and the following data collected.

Mixing Technique

Tensile Strength

1 3129 3000 2865 2890

2 3200 3300 2975 3150

3 2800 2900 2985 3050

4 2600 2700 2600 2765

Perform ANOVA using Excel to test the hypotheses that mixing techniques affectthe tensile strength

EEM332 Lecture Slides 12

Analysis of variance - AssignmentsQ 2

A manufacturer of television sets is interested in the effect of tube conductivityof four different types of coating for color picture tubes. The following conductivity dataare obtained.

Coating Type

Conductivity

1 143 141 150 146

2 152 149 137 143

3 134 136 132 127

4 129 127 132 129

Perform ANOVA using Excel to test the hypotheses that coating types affectthe conductivity.

EEM332 Lecture Slides 13

Analysis of variance - AssignmentsQ 3

Four different designs for a digital circuits are being studied in order to comparethe amount of noise present. The following data have been obtained.

Circuit designs

Noise observed

1 19 20 19 30 8

2 80 61 73 56 80

3 47 26 25 35 50

4 95 46 83 78 97

Perform ANOVA using Excel to test the hypotheses whether the noise are the samefor all the four designs or not.

EEM332 Lecture Slides 14

Analysis of variance - Assignments

Deadline : Friday 13th February 12:00pmSubmit hardcopies and softcopies (Excel files)

Tomorrow’s class (Friday 6th February will be in Mechatronic Lab Level 2)We will do the assignments using Excel and Minitab )