# Chapter 3 - PowerPoint PPT Presentation

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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

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?

### 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

• 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.