The Language of Sampling Lecture 6 Sections 2.1 – 2.4 Fri, Aug 31, 2007

Why Sample? Studying a sample gives us only partial information about a population. So why not study (observe) the entire population? Samples are random, so how can we expect a sample to be representative of the population?

Why Sample? We can prove mathematically that the larger a sample is, the more likely it is to be representative of the population. More specifically, the “margin of error” for large samples is very small.

The Language of Sampling Unit or subject. Variable. Population size N. Sample size n. Parameter. Statistic.

Case Study 4 Alcohol-related traffic deaths up in Virginia. Alcohol-related traffic deaths up in Virginia  Are the data from a population or a sample?  What are the variables?  What are the parameters or statistics?

Parameters and Statistics For numerical data, we usually use the average of the values in the sample. For non-numerical data, we usually use the proportion of observations in a specific category.

Case Study 1 Study: Men Enjoy Watching Bad Guys Suffer Study: Men Enjoy Watching Bad Guys Suffer  What statistics were used?  What were the parameters?

Random vs. Representative Random sample. Representative sample.

Bias A sampling method is biased if it systematically produces a sample whose characteristics differ from those of the population, i.e., unrepresentative. Note that we are describing the method as biased.

Random vs. Bias The purpose of randomness is to prevent bias.

Biased Sampling Two characteristics that biased sampling methods often exhibit.  Convenience sample.  Volunteer sample.

Four Types of Bias Selection bias. Nonresponse bias. Response bias. Experimenter bias (Sec. 3.5, p. 176).

Whose Fault is it? Selection bias originates with the sampling procedure (therefore, the researchers). Nonresponse bias originates with the subjects who were selected for the sample, but chose not to participate. Response bias originates with the subjects who are in the sample.

Whose Fault is it? Experimenter bias originates with the researcher.

Examples Phone surveys. Use random-digit dialing.  Convenience sample?  Volunteering sample?  Selection bias?  Non-response bias?  Response bias?  Experimenter bias?

Examples Mailed surveys, including . Mail individuals a survey and ask them to respond.  Convenience sample?  Volunteering sample?  Selection bias?  Non-response bias?  Response bias?  Experimenter bias?

Examples Internet survey. Post the survey questions on the internet and let visitors respond at will.  Convenience sample?  Volunteering sample?  Selection bias?  Non-response bias?  Response bias?  Experimenter bias?

Examples Estimating average family size. Randomly select individuals and ask them how many siblings they have.  Selection bias?

Examples To estimate average family size, we should take a random sample of families, not individuals.