SOC101Y University of Toronto 2014-15 Robert Brym Online Mini-Lecture #8 Sampling

A researcher wants to study all 50 of these people but time and financial constraints necessitate her studying only 7 of them. All 50 form the population; the 7 selected for analysis form the sample.

Non-representative Sample POPULATION SAMPLE = 3 (75%) = 1 (25%) = 12 (60%) = 8 (40%)

Representative Sample POPULATION SAMPLE = 6 (60%) = 4 (40%) = 12 (60%) = 8 (40%)

Examples of Non-representative Samples VOLUNTARY RESPONSE SAMPLE CONVENIENCE SAMPLE It’s convenient to go to a mall and ask passers-by to fill in a questionnaire, but people who frequent most malls are disproportionately urban, middle-class, teenagers, and elderly people. Convenience samples are usually biased (unrepresentative) in one way or another. Ann Landers’ daily advice column appeared in about 1,200 North American newspapers from 1943 to 2002. In 1975, she asked readers, “If you could live your life over again, would you have children?” About 10,000 respondents mailed in their answers. Around 70 percent said “no.” A survey based on a representative sample conducted just afterwards found that about 10 percent of respondents answered “no” to the same question.

Probability Sampling A probability sample is more or less representative of the population of interest because units (e.g., people) are chosen randomly. “More or less” because the larger the sample, the less likely the sample will be unrepresentative. Nineteen out of every twenty random samples of 1,500 will have a maximum margin of error  2.5%. A sampling frame is a list of all the units in the population of interest. A randomizing method is a way of ensuring that every unit in the sampling frame has a known and equal chance of being selected. For example, you can sample every 10th or 100th person in the sampling frame or give everyone in the frame a discrete, sequential number and then use a computer’s random number generator to select n people.

Sampling Error I In a survey of 1,500 Canadians, a sociologist finds that support for party A is 48% while support for party B is 50%. In 19 of 20 random samples of 1,500, these measures are accurate  2.5%. The sampling error is indicated in braces below. Because the measures fall within overlapping margins of error (indicated by the pink area), we must conclude that the measured difference in the popularity of the two parties is not statistically significant. Party A ---------{-------48%-------}------------------- Party B ---------------{-------50%-------}------------- 2.5% sampling error 2.5% sampling error

Sampling Error II Here, the measures fall outside the margins of error; the margins of error do not overlap, as indicated by the pink area. We conclude that the measured difference in the popularity of the two parties is statistically significant. 2.5% sampling error Party A -----{------48%------}----------------------- Party B ----------------------------{-------55%------}

Q. What is the difference between a representative sample and a non-representative sample? A. In a representative sample, sample characteristics closely match population characteristics. In a non-representative sample, sample characteristics less closely match population characteristics.

Q. A sociologist draws a random sample of size n from a population Q. A sociologist draws a random sample of size n from a population. At the same time, another sociologist draws a random sample of n+250 from the same population. Which sample has the smaller sampling error? A. The larger random sample (n+250) has a smaller sampling error.

Q. In sampling, what is a randomizing method? Give an example. A. In sampling, a randomizing method is a way of ensuring that every unit in the sampling frame has a known and equal chance of being selected. For example, you can sample every 10th or 100th person in the sampling frame or give everyone in the frame a discrete, sequential number and then use a computer’s random number generator to select n people.

Q. In 2014, a sociologist draws a random sample of 1,500 Canadians and finds that 54% of respondents prefer cherry Jello over grape Jello. In 2015, the sociologist draws another random sample of 1,500 Canadians and finds that 51% of respondents prefer cherry Jello. Has the percentage of Canadians who prefer cherry Jello declined? Why or why not? A. We can’t say for sure whether the percentage has declined. Sampling error is about 2.5% in both surveys given the size of the samples. In the 2014 survey, the 54% means that in 19 of 20 similar samples, between 51.5% and 56.5% of Canadians preferred cherry Jello. In the 2015 survey, the 51% means that in 19 of 20 similar samples, between 48.5% and 53.5% of Canadians preferred cherry Jello. Because the margins of error overlap (the 51.5% - 53.5% range is found in both margins of error), we don’t know if preference for cherry Jello has actually declined in the Canadian population.

SOC101Y University of Toronto 2014-15 Robert Brym END Online Mini-Lecture #8 Sampling