广东农垦经济和社会发展“十二五”规.pptVIP

Comparison Methodology Meaning of a sample Confidence intervals Making decisions and comparing alternatives Special considerations in confidence intervals Sample sizes EstimatingConfidence Intervals Two formulas for confidence intervals Over 30 samples from any distribution: z-distribution Small sample from normally distributed population: t-distribution Common error: using t-distribution for non-normal population Central Limit Theorem often saves us The z Distribution Interval on either side of mean: Significance level ? is small for large confidence levels Tables of z are tricky: be careful! The t Distribution Formula is almost the same: Usable only for normally distributed populations! But works with small samples Making Decisions Why do we use confidence intervals? Summarizes error in sample mean Gives way to decide if measurement is meaningful Allows comparisons in face of error But remember: at 90% confidence, 10% of sample means do not include population mean Testing for Zero Mean Is population mean significantly nonzero? If confidence interval includes 0, answer is no Can test for any value (mean of sums is sum of means) Example: our height samples are consistent with average height of 170 cm Also consistent with 160 and 180! Comparing Alternatives Often need to find better system Choose fastest computer to buy Prove our algorithm runs faster Different methods for paired/unpaired observations Paired if ith test on each system was same Unpaired otherwise Comparing Paired Observations Treat problem as 1 sample of n pairs For each test calculate performance difference Calculate confidence interval for differences If interval includes zero, systems aren’t different If not, sign indicates which is better Example: Comparing Paired Observations Example: Comparing Paired Observations H-V 2 -2 -7 5 6 -1 -7 6 7 3 2 1 -1 6 Mean 1.4, 90% interval (-0.75, 3.6) Can’t reject the hypothesis that difference is 0. 70% interval is (0.10, 2.76) Comparing Unpaired Obse