Stat 100 Mar. 27

Work to Do Read Ch. 3 and Ch. 4

The Basic Problem Using a sample to estimate something about a population Example – do a survey to estimate percent of Americans opposed to the death penalty

Possible Sources of Error in a Sample Value Margin of error = Random sampling effect; “luck of the draw” Bias in way of getting the sample or asking questions Reliability of measurement process Validity of variable measured

Margin of Error A sample result probably won’t equal true population value Margin of error = Possible amount of error due to the act of taking a sample Sample size is main determinant of margin of error. The larger the sample size, the smaller the margin of error.

Calculating Margin of Error for a Percent Approximate calculation = More exact is

Important point Margin of error only measures likely error due to act of random sampling It DOES NOT measure effects of bad questions, bad sampling method, and so on.

Bias Systematic factors that force a sample result to be pushed in a particular direction from the true population value. This has nothing to do with sample size! It has to do with how you get the data or how things are measured.

Examples of Bias Use of a volunteer sample – especially for controversial questions False information or nonresponse for sensitive questions A bad measuring scale – like a scale that always gives a weight that’s too high Wording of a question that biases result toward a certain answer.

Example Pepsi examines three bottling methods. Bottle supposed to contain 1000 ml (a liter) For each method, actual contents of 4 bottles are –Method 1: 998, 1002, 1000, 1000 –Method 2: 995, 996, 995, 996 –Method 3: 999, 1001, 999, 1001 Which method appears to be biased?

Answer Method 2. All 4 values are below For methods 1 and 3, there’s random variation from 1000, but average is Bias = a general shift in one direction

Important point - Bias has NOTHING to do with sample size It’s not a bias to have a small sample size – Small sample just introduces a lot of random luck that might cause the answer to go one way or the other.

Reliability of a measurement A measurement is reliable if we’d get very close to the same value if the measurement were repeated. Some critics say that IQ scores lack reliability. Same person might get two quite different scores if they take the test twice Blood pressure has this problem too.

Validity of a measurement A measurement is valid if it measures what it’s supposed to A measurement is not valid if it’s not measuring what it’s supposed to. Example: Your answer to “How much did you study yesterday?” should not be used as your answer to “How much do you study per day?”

Validity Psychologists often ask questions about some characteristic like “anxiety” Often, the debate is whether the questions asked really measure “anxiety” What about the SAT? Is it a valid measure of academic performance or potential? (I don’t know!)