Analysis of variance (ANOVA)

1
Analysis of variance (ANOVA)

• Week 11 lecture 1

2
Recap

• When do we need to do hypothesis testing?
• Whats the logic behind hypothesis testing?
• What is tested in hypothesis testing?
• How do you report the result of hypothesis
  testing?
• What is the level of significance?
• What is the most important statistics you should
  look at when making conclusion from hypothesis
  testing?

3
Parametric and nonparametric statistics

• Parametric statistics
• Based on certain assumptions on the data
• The data are in an interval or ratio scale
• The data fall in a normal distribution
• Nonparametric statistics
• No such assumptions are made

4
One-way ANOVA

• Assesses whether the means of two or more groups
  are statistically different from each other
• Dependent variable is interval or ratio scale
• Independent variable has two or more levels
• Approximately normal distribution of the measure
  in the two groups is assumed
• F-score
• Between-sample variation/within-sample variation

5
One-way ANOVA in excel

• You want to compare the property sales prices in
  Sydney, NSW. Independent random samples of 10
  properties were selected from each of 4 different
  neighborhoods (A,B,C,D)
• Whats the null hypothesis
• Test gives two-tailed p-value

6
Two-way ANOVA

• Analyzing data from factorial design
• One interval/ratio dependent variable
• Two independent variables
• Access the main and interaction effect of
  independent variables

7
2 factor design without replication

• Example cache comparison

workload Two caches One caches No caches
ASM 54.0 55.0 106.0
TECO 60.0 60.0 123.0
SIEVE 43.0 43.0 120.0
DHRYSTONE 49.0 52.0 111.0
SORT 49.0 50.0 108.0
8
2 factor design with replication

• Example 223 factorial design
• The memory-cache experiments were repeated three
  times each. The result is shown below (from week
  9 lecture 2)

Cache size Memory size Memory size
Cache size 4M 8M
1 K 15, 18, 12 45, 48,51
2K 25, 28, 19 75,75,81