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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?

Level?

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

- 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

- 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 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

- 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 plot

- How to construct the straight line?

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

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