CS457 - System Performance Evaluation - Winter 2008

Questions and Comments

  1. A2.
  2. Statistics 206

Lecture 14

Analysing Data

You have some data. What next?

  1. Can you see any patterns? Exploratory data analysis.
  2. Are the patterns real?
  3. How big are the patterns?
  4. Does it matter? Should you do anything about it?

Reprise the patterns we saw in the application of Little's Law.


Zero-factor Designs

Reminder from STAT206

  1. Measure a response variable r times. This is the sample of measurements.
  2. Calculate the average.
  3. Can you conclude that the average is greater than zero?

The standard technique

  1. Assume that the variation is additive and normally distributed
  2. Calculate the average
  3. Calculate the standard deviation of the sample.
  4. Calculate the T-statistic.
  5. Look up in a table and find the number you calculated.

A different technique

  1. Assume that each data point has the form yi = \mu + ei, and that ei is a sample from a normal distribution
  2. Calculate the average, which is your estimate for \mu
  3. Calculate the variance of {yi}, SST, which has a chi-square distribution
  4. Calculate the variance of {ei = yi - \mu}, SSE, which has a chi-square distribution
  5. Calculate the difference, SS0, which has a chi-square distribution
  6. Calculate the ratio SS0/SSE, which has an F distribution
  7. Look up in a table to find the number you calculated

This technique is called analysis of variance

Technical point. Degrees of freedom.

One-factor Designs

  1. Factor has a levels.
  2. Model is yij = \mu + \alpha_j + eij
  3. Estimate \mu by \mu = (1/ar) \sum_ij yij
  4. Variance is SST = \sum_ij (yij - \mu)^2 =? \sum_ij (yij)^2 - ar(\mu)^2
  5. Estimate \alpha_j by by \alpha_j = (1/r) \sum_i (yij - \mu)