Chapter 3
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Chapter 3. Analysis of Variance (ANOVA). Lets recap…. In the previous class…. Another way to describe this experiment is as single factor experiment, with 2 level. Factor: mortar formulation Level: modified and unmodified What if more than 2 level involved?. Factor? Level?.

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Chapter 3

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Chapter 3

Chapter 3

Analysis of Variance (ANOVA)


Lets recap

Lets recap…

  • In the previous class…

Another way to describe this experiment is as single factor experiment, with 2 level.

Factor: mortar formulation

Level: modified and unmodified

What if more than 2 level involved?


Chapter 3

Factor?

Level?


Analysis of variance

Analysis of variance


Degree of freedom

Degree of freedom


Ss for equal sample size

SS for equal sample size


Ss for unequal sample size

SS for unequal sample size


Importance of balance design equal sample size

Importance of balance design (equal sample size)

  • The test procedure is relatively insensitive to small departures from the assumption of equality of variances.

  • The power of the test is maximized


Confidence interval

Confidence interval


Model adequacy checking

Model adequacy checking

  • Is done by examination of residuals

Outlier- the residual that is very much larger than the other

If the underlying error distribution is normal, this plot will resemble a straight line


Chapter 3

  • Frequently the cause of outlier is a mistake in calculations or data coding or copying error.

  • If this is not the cause, the experimental circumstances surrounding this run must be carefully studied.

  • If the outlying response is particularly desirable value (low cost, high strength), the outliers may be more informative than the rest of data.

  • We should careful not to reject an observation outlier without reasonable ground.

  • A rough check for outliers can be done by examining the standardized residuals.

  • A residual bigger than 3 or 4 standard deviations from zero is potential outlier.


Residual vs time plot

Residual vs time plot

  • If the model is adequate, the residuals should be structureless.

  • This plot helps in detecting correlation between residuals.

  • Imply the independence assumption-should do proper randomization of experiment

  • A change in error over time- indicate the skill of experimenter


Residual vs average y i plot

Residual vs average yi plot

  • If the model is adequate, the residuals should be structureless.

  • A defect that occasionally shows up on this plot is nonconstant variance.

  • The variance of the observations increase as magnitude of the observation increase. (normally cause by measuring instruments)

  • For equal sample, F test only slightly affected.


Normal probability plot

Normal probability plot

  • How to construct?

  • Arrange the value for x-axis in order (lowest to highest). This new order is j

  • For normal % probability values (y-axis), use the formula of (j-0.5)/N.

  • Example: normal probability vs residual plot

    original data after sorting

    Lets do it together!


Normal probability plot1

Normal probability plot

  • How to construct the straight line?

    draw the line approximately between 25th and 75th percentile point.


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