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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?

slide3

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

slide27

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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