MATH117_Lecture_Lock3-3 - Section 3.3 Constructing Bootstrap Confidence Intervals Statistics Unlocking the Power of Data Lock5 Outline Bootstrap samples

# MATH117_Lecture_Lock3-3 - Section 3.3 Constructing...

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Statistics: Unlocking the Power of Data Lock 5 Section 3.3 Constructing Bootstrap Confidence Intervals
Statistics: Unlocking the Power of Data Lock 5 Outline Bootstrap samples Bootstrap distribution Standard error from bootstrap distribution 95% confidence interval using SE from bootstrap distribution
Statistics: Unlocking the Power of Data Lock 5 Confidence Intervals Population Sample Sample Sample Sample Sample Sample . . . Calculate statistic for each sample Sampling Distribution Standard Error (SE): standard deviation of sampling distribution Margin of Error (ME) (95% CI: ME = 2×SE) Confidence Interval statistic ± ME
Statistics: Unlocking the Power of Data Lock 5 Summary To create a plausible range of values for a parameter: o Take many random samples from the population, and compute the sample statistic for each sample o Compute the standard error as the standard deviation of all these statistics o Use statistic 2 SE One small problem…
Statistics: Unlocking the Power of Data Lock 5 Reality … WE ONLY HAVE ONE SAMPLE!!!! How do we know how much sample statistics vary, if we only have one sample?!? BOOTSTRAP!
Statistics: Unlocking the Power of Data Lock 5 Sample: 52/100 orange Where might the “true” p be? ONE Reese’s Pieces Sample ˆ 0.52 p
Statistics: Unlocking the Power of Data Lock 5 Imagine the “population” is many, many copies of the original sample (What do you have to assume?) “Population”
Statistics: Unlocking the Power of Data Lock 5 Reese’s Pieces “Population” Sample repeatedly from this “population”
Statistics: Unlocking the Power of Data Lock 5 To simulate a sampling distribution, we can just take repeated random samples from this “population” made up of many copies of the sample In practice, we can’t actually make infinite copies of the sample… … but we can do this by sampling with replacement from the sample we have (each unit can be selected more than once) Sampling with Replacement
Statistics: Unlocking the Power of Data Lock 5 Suppose we have a random sample of 6 people:
Statistics: Unlocking the Power of Data Lock 5 Original Sample A simulated “population” to sample from
Statistics: Unlocking the Power of Data Lock 5 Bootstrap Sample : Sample with replacement from the original sample, using the same sample size.