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Lecture 17

Statistics

DATA 8

Spring 2017

Slides created by John DeNero (denero@berkeley.edu) and Ani Adhikari (adhikari@berkeley.edu)

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Announcements

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Probability & Simulation (Review)

(Demo)

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Statistics

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Why sample?

Probability

Statistics

Sampling

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Estimation

Statistical Inference:

Making conclusions based on data in random samples

Example:

Use the data to guess the value of an unknown number

Create an estimate of the unknown quantity

fixed

depends on the random sample

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Terminology

Parameter

A number associated with the population

Statistic

A number calculated from the sample

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A statistic can be used as an estimate of a parameter

(Demo)

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Attendance

bit.ly/data8here

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Estimation

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How many enemy planes?

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Assumptions

  • Planes have serial numbers 1, 2, 3, …, N.
  • We don’t know N.
  • We would like to estimate N based on the serial numbers of the planes that we see.

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The main assumption

  • The serial numbers of the planes that we see are a uniform random sample drawn with replacement from 1, 2, 3, …, N.

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Discussion question

If you saw these serial numbers, what would be your estimate of N?

170 271 285 290 48

235 24 90 291 19

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One idea: 291. Just go with the largest one.

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The largest number observed

  • Is it likely to be close to N?
    • How likely?
    • How close?

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Option 1. We could try to calculate the probabilities and draw a probability histogram.

Option 2. We could simulate and draw an empirical histogram.

(Demo)

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Verdict on the estimate

  • The largest serial number observed is likely to be close to N.
  • But it is also likely to underestimate N.

Another idea for an estimate:

Average of the serial numbers observed ~ N/2

New estimate: 2 times the average

(Demo)