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ComparingSystems

# ComparingSystems - CPE 619 Comparing Systems Using Sample...

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CPE 619 Comparing Systems Using Sample Data Aleksandar Milenković The LaCASA Laboratory Electrical and Computer Engineering Department The University of Alabama in Huntsville http://www.ece.uah.edu/~milenka http://www.ece.uah.edu/~lacasa

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2 Part III: Probability Theory and Statistics How to report the performance as a single number? Is specifying the mean the correct way? How to report the variability of measured quantities? What are the alternatives to variance and when are they appropriate? How to interpret the variability? How much confidence can you put on data with a large variability? How many measurements are required to get a desired level of statistical confidence? How to summarize the results of several different workloads on a single computer system? How to compare two or more computer systems using several different workloads? Is comparing the mean sufficient? What model best describes the relationship between two variables? Also, how good is the model?
3 Overview Sample Versus Population Confidence Interval for The Mean Approximate Visual Test One Sided Confidence Intervals Confidence Intervals for Proportions Sample Size for Determining Mean and proportions

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4 Sample Old French word `essample' `sample' and `example' One example theory One sample Definite statement
5 Sample Versus Population Generate several million random numbers with mean μ and standard deviation σ Draw a sample of n observations: {x 1 , x 2 , …, x n } Sample mean (x) population mean ( μ ) Parameters : population characteristics Unknown, Use Greek letters ( μ, σ29 Statistics : Sample estimates Random, Use English letters (x, s) μ x

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6 μ c 1 c 2 Confidence Interval for The Mean k samples k Sample means Can't get a single estimate of μ Use bounds c 1 and c 2 : Probability{c 1 μ c 2 } = 1- α ( α is very small) Confidence interval : [(c 1 , c 2 )] Significance level : α Confidence level : 100(1- α ) Confidence coefficient : 1- α
7 Determining Confidence Interval Use 5-percentile and 95-percentile of the sample means to get 90% Confidence interval Need many samples (n > 30) Central limit theorem: Sample mean of independent and identically distributed observations: Where μ = population mean, σ = population standard deviation Standard Error: Standard deviation of the sample mean 100(1- α )% confidence interval for μ : z 1- α /2 = (1- α /2)-quantile of N(0,1) 0 -z 1- α /2 z 1- α /2

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8 Example 13.1 x = 3.90, s = 0.95 and n = 32 A 90% confidence interval for the mean = We can state with 90% confidence that the population mean is between 3.62 and 4.17.
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