STA 200 Spring 2011

Objective  We want to be able to extrapolate results from a sample to the population at large.  In order to do this (and reach meaningful conclusions), the sample should be representative of the population.

Bad Sampling  Convenience Sampling  Select the individuals who are the easiest to reach  Voluntary Response Sampling  The sample selects itself via response to a general appeal (call-in polls, write-in polls)

Example (Convenience)  Suppose you want to find out if UK faculty members think there should be more math and statistics as part of the USP requirements.  To obtain the sample, suppose you visit faculty members on the 7th, 8th, and 9th floors of the Patterson Office Tower (where the math and statistics departments are located).  What’s wrong with this?

Example (Voluntary Response)  Consider a write-in poll concerning a maximum salary for athletes/actors.  Some people are going to be more motivated than others to participate in the poll. What kind of opinion might they have?

Bias  When using a bad sampling method, you get biased results. (With regard to percentages, this means you’ll get a percentage either higher or lower than you should.)  Bias occurs when certain outcomes are statistically favored because the population is incorrectly represented by the sample.

Good Sampling  Simple Random Sample  Consists of n individuals chosen in such a way that every set of n individuals has the same chance of being selected  Choosing a sample randomly significantly reduces bias. In other words, the sample will reflect the population much better.

Choosing an SRS  Nowadays, an SRS is usually chosen using a computer. However, we can also use a table of random digits (like the one in the back of the textbook).  The process:  Assign a numerical label to each individual in the population. Make sure all of the labels are the same length.  Use software or a table of random digits to select labels.

Example (Using a Table of Random Digits)  A food distributor wants to know if the boxes of cereal in a particular shipment contain the correct amount of cereal. The distributor intends to randomly select five boxes out of a shipment of 500 and weigh them.  What labels should we use?

Example (cont.)  Use the following line from the table to pick the SRS:  …  Now, use another line to pick the SRS:  …

Trusting a Sample  If an SRS (or more complicated good sampling method) is used, the sample should be quite representative of the population.  If a poor sampling method is used, this will not be the case.  Thus, if we try to extrapolate results from a poorly obtained sample to the entire population, the conclusions we reach will be rubbish.