Understanding ANOVA: Analysis of Variance in Experimental Design and Outlier Detection
This chapter discusses the principles of Analysis of Variance (ANOVA) in single-factor experiments, focusing on factors, levels, degrees of freedom, and the significance of balanced designs. It explores techniques for identifying outliers, appropriate handling of residuals, and the importance of model adequacy checks. It emphasizes the need for careful experimental design to ensure the independence of residuals and provides methods for constructing normal probability plots to assess the normality of data. Overall, it serves as a comprehensive guide for applying ANOVA effectively in research.
Understanding ANOVA: Analysis of Variance in Experimental Design and Outlier Detection
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Presentation Transcript
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
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.
