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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

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?


Factor?

Level?






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



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


  • 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 or data coding or copying error.

  • 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 y or data coding or copying error.i 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 or data coding or copying error.

  • 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 or data coding or copying error.

  • How to construct the straight line?

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


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