Statistics 100 Lecture Set 2

Lecture Set 2 Chapter 2 … please read Will be doing chapter 3 in the next lecture set Some suggested problems: –Chapter 2: 2.3, 2.5, 2.7, 2.19

Sampling? Why do we take samples? Why not just measure whole population?

Sampling badly Consider the following web-poll: What do you think about the quality of the data collected?

Sampling badly This survey reports a summary of the sampled responses –Reported numbers are facts –No question about their truth …and one may wish to interpret them in terms of the population –Statements relating the numbers to the population are inferences. –May be right or wrong

Sampling badly Book (page 25) gives example of poll where readers of an advice column are asked “If you had to do it all over again, would you have children” –70% of respondents said NO!!!!! –What do you think of this?

Sampling badly This is a voluntary response sample –Offer questions, ask openly for responses –No control over who responds –Who responds?

Sampling badly The 1948 presidential election campaign was a hard fought race between Harry Truman and Thomas Dewey What happened?

Sampling badly The 1948 presidential election campaign was a hard fought race between Harry Truman and Thomas Dewey What happened? Was an example of a convenience sample (selection of individuals who are easiest to reach)

Bias Voluntary response and convenience samples are generally biased! Biased sample means not representing the intended population so that certain outcomes are systematically favoured BAD!

What do you think? Write-in opinion polls? Customer comment cards? Sampling students passing through the academic quadrangle? Student interviews? Radio call-in surveys?

What do you think? If you want to test for bird flu, how do you sample chickens in a farm? –Take the nearest birds to the entry? –Walk through the pen and pick up the closest birds to you as you go?

Simple random samples A simple random sample (SRS) of size n chosen in such a way that every sample of size n individuals from the population has the same chance of being selected The idea is that the sample is chosen randomly, free of personal or systematic bias Have more confidence in a SRS because it aims to avoid bias

Simple random samples To do a SRS, typically each individual is assigned a label and a computer program is used to select a sample from the population How to conduct a SRS (example) 1.Call the population size N 2.Call the sample size n 3.Label each member of the population 1, 2, 3, … N 4.Select a number between 1 and N at random 5.Repeat step 4 until n unique numbers are selected 6.Those n individuals are the sample You can’t do randomization in your head!

EXAMPLE Let us visit –Need to number the population 1, 2, 3, …, 300 Does it matter what order I number them in? –Just for fun, draw a sample of 10 people. –Would every sample give you the same answer? –Do it again and see ….

EXAMPLE A university has 30,000 undergrads and 10,000 grad students A survey of the University’s students’ opinions is conducted by selecting 300 of the 30,000 undergrads and 100 of the 10,000 grads Does each person have an equal chance of being chosen? Is this a SRS?

EXAMPLE Denver police want to know the opinions of the Hispanic population with respect to racial profiling The Police Department chooses a SRS of 200 mailing addresses in Hispanic neighborhoods Population? Sample? Are the results likely biased?

EXAMPLE A national survey of TV network news viewers found that 48% of respondents said they would believe a phone-in poll of 300,000 people instead of a random sample of of 1,000 people What do you believe? Why?