Samples, Good and Bad Goal of Sampling We want to make a statement about a large group of individuals (the population), but oftentimes it is not practical or even possible to measure each individual in the population. In this case, we choose a sample of individuals that is (hopefully) representative of the population. What happens when our sample is not representative of the population? How to Sample Badly The design of a statistical study is _____________ if it systematically favors certain outcomes. A ___________________________________ chooses itself by responding to a general appeal. -individuals volunteer themselves to be in the sample -also called a ___________________________________________ Selection of whichever individuals are easiest to reach is called _________________________. -researcher chooses who to ask to participate -individuals can still choose not to participate Convenience samples and voluntary response samples are often biased. Example 1 Ann Landers once asked the readers of her nationally syndicated newspaper advice column, “If you had it to do over again, would you have children?” She received nearly 10,000 responses, almost 70% saying “no.” Is it true that 70% of parents regret having children? Example 2 A student at the university is conducting a survey to find the opinion of her fellow students on the availability of student parking on campus. She stands outside of a dorm and polls fellow students as they leave the dorm. Which bad sampling method is this?Chapter 2 Page 2 Example 3 The popular radio Ace&TJ Show recently asked fans to vote on their website to the following question A nurse at KATE MIDDLETON'S hospital who was pranked by two Australian DJs last week was found DEAD in her home on Friday. Police suspect SUICIDE. The DJs are off the air until further notice...a decision they made along with their radio station. Should the radio DJ's be fired? This is an example of which type of sampling? The most basic, good sampling method is known as the Simple Random Sample. The simple random sample is at the heart of all good sampling schemes. A simple random sample (SRS) of size n individuals from the population is chosen in such a way that: – Every set of n individuals has an equal chance to be the sample actually selected – Every individual has an equal chance of being chosen for the sample The easiest way to do this is to place names in a hat (the population) and draw out a handful (the sample). Step 1: Label. Assign a numerical label to every individual in the population. Be sure that all labels have the same number of digits if you plan to use a table of random digits. Step 2: Software or Table. Use random digits to select labels at random. Use software whenever possible – tables are old fashioned! http://bcs.whfreeman.com/scc7e/ - Choose “Statistical Applets”, then “Simple Random Sample”. There are lots of other computer generators available: www.randomizer.org, TI-83, 84, and 89 calculators, www.dougshaw.com/sampling, Statistical packages like R, SAS, Minitab, etc…. If you are using a table of random digits…. Population labels must each contain the same number of digits Spaces in the random digits table have no meaning (they are just place holders) You can start anywhere you like in the table (across rows, up a column, down a column,…) Some people start their population labels at 0 and some start them at 1 (be aware) Skip repeated codes and those outside the range of labelsChapter 2 Page 3 Example 4 Take a Simple Random Sample (SRS) of 3 people. Step 1: Label your “population” elements. Step 2: (Using random sampling generator) Obtain the sample. Step 2: (Using random digits table) Obtain the sample. Since we are using the pesky table of random digits, be sure each label (code) has the same number of digits! Use the following line from a random digits table. Note: In practice you would choose any line you want, but in class we will use the same line so we learn how to use the table. 05497 12005 13659 81273 Bautista Nemeth Bolen Podboy Clottey Ray Counts Schumacher Draper Tower Hoffman Walters Kumar Wang Li Weimer Lovesky Yu Marin ZhangChapter 2 Page 4 Example 5 Take a Simple Random Sample (SRS) You are reporting on apartments in Columbia. You decide to select 5 complexes at random for in-depth interviews with residents. 01-Abbott Arms 08-Claire Tower 15-Keswick 02-Asbury Arms 09-Colony East 16-Landmark 03-Ashland 10-Cornell Arms 17-Paces Run 04-Bent Tree 11-Fairways 18-Ravenwood 05-Briargate 12-Fox Run 19-Riverview 06-Brook Pines 13-Green Oaks 20-Stone Ridge 07-Cedarwood 14-Hunter’s Green 21-Whaley’s Mill Use the following portion of Table A at line 140 (read across the row) to sample 5 complexes. 12975 13218 13048 45144 72321 21940 00360 02428 96767 35964 23822 96012 Some final thoughts - Can you Trust a Sample? We can’t trust results from convenience and voluntary response samples, because they are chosen in ways that invite bias. We have more confidence in results from a SRS, because it avoids bias. The first question to ask of any sample is whether it was chosen at random. Clearly, the SRS is a handy tool for getting a random sample, but it is not sophisticated enough to deliver the kind of information we want in many cases. We need more sampling options…coming up
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