CS457 - System Performance Evaluation - Winter 2010


Public Service Announcements

  1. Mid-term conflicts

Lecture 13 - Data Analysis III

Analysis of Variance (ANOVA) aka Linear Models (pdf)

Zero Factor Analysis of Variance

New Concepts

General idea

  1. To work it out from first principles
    1. Assume underlying distribution from which data is drawn has finite variance.
    2. N data points
    3. Mean is normally distributed
    4. Variance is distributed by a chi-square distribution with N degrees of freedom
    5. The treatment variance, the difference between two variances, is distributed by a chi-square distribution with N1=1 degrees of freedom.
    6. Ratio between the treatment variance and the remaining error variance is distributed by an F distribution with N-1 and N1 degrees of freedom
    7. Check the ratio (15.3 * (N-N1)/ 541.4 * N1 in the first case, 1381.3 * (N1-1) / 1068.0 * N1 in the second) against the percentage points of the F distribution
  2. Of course, for a test as simple as this there are other, and better, ways of doing the test.

One Factor Analysis of Variance

New Concepts

The Linear Model

The Calculation

Two Tables

One factor, cleaning requests, which has 3 levels.

Measure cleaning time

  1. cache
    0, 0, 0, 0
  2. penalty: white
    20, 20, 19, 18
  3. penalty: black
    401, 402, 400, 399 
Data with mean removed
cache -139.9 -139.9 -139.9 -139.9 -139.9
penalty: white -119.9 -119.9 -120.9 -121.9 -120.7
penalty: black 261.1 262.1 260.1 259.1 260.6
ANOVA Table
Sum of
squares
Degrees of
Freedom
Mean
Square
Computed
f
Treatments 408163.2 2 204081.6 236998
Error 7.7 9 0.86
Total Error 408170.9 11

Significant at the 1% level for f > 7.21

Regression

Data for Ips removed
Cleaning time 20 20 19 18
Total IPs 9128 8352 7849 7404
IPs removed 2362 1954 1600 1442

Assumption

I assume that you have seen linear regression and are able to do it for the assignment

Two Factor Analysis of Variance

New Concepts

The Linear Model

The Calculation

Two Tables

ANOVA Table without interaction
Sum of Squares Degrees of Freedom Mean Square Computed f
Treatment a
Treatment b
Error
Total

ANOVA Table with interaction
Sum of Squares Degrees of Freedom Mean Square Computed f
Treatment a
Treatment b
Treatment ab
Error
Total


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