10/12/2004 9:20 amGeog 237a1 Sampling Sampling (Babbie, Chapter 7) Why sample Probability and Non-Probability Sampling Probability Theory Geography 237 Geography 237 Geographic Research: Methods and Issues

10/12/2004 9:20 amGeog 237a2 Why Sample? What is a sample? Why do we sample in social research?

10/12/2004 9:20 amGeog 237a3 Two Classes of Sampling Non-Probability Sampling not based on probability theory representativeness not as important rapport; difficult populations qualitative research e.g., snowball sampling Probability Sampling based on probability theory representativeness imperative e.g., simple random sample

10/12/2004 9:20 amGeog 237a4 Non-Probability Sampling Convenience Sample whomever is available pre-test a questionnaire e.g., students in geog237, attendees at the Canadian Association of Geographers annual meeting

10/12/2004 9:20 amGeog 237a5 Non-Probability Sampling Purposive Sample units selected based on researcher judgment wide variety vs representative qualitative research e.g., most vocal people at a public meeting

10/12/2004 9:20 amGeog 237a6 Non-Probability Sampling Snowball Sample new respondents selected based on recommendation of existing respondents difficult populations rapport important e.g., homeless, members of activist group

10/12/2004 9:20 amGeog 237a7 Non-Probability Sampling Quota Sample representativeness important matrix theoretically important population components cells = weightings same as sample e.g., see below; sample of 1000, how many women in Windsor? CityMenWomen$0-50K$50K + London45%55%60%40% Windsor49%51%57%53%

10/12/2004 9:20 amGeog 237a8 Non-Probability Sampling Key “Informants” insiders who know much about phenomenon of interest knowledgeable and articulate “reconnaissance” prior to contact with others help decide probability sampling scheme e.g., mayor and councilors to speak about residents small town

10/12/2004 9:20 amGeog 237a9 Probability Sampling Principles/Terminology Representativeness sample microcosm of population same variation (e.g., gender, age, ethnicity) Avoid “Bias” selection bias – those in sample not representative of those in population Equal Probability of Selection all members in population i.e., random selection

10/12/2004 9:20 amGeog 237a10 Probability Sampling Problems with These? Source:

10/12/2004 9:20 amGeog 237a11 Probability Sampling Principles/Terminology Population group about whom you want to draw inferences more theoretical than quantifiable e.g., Ontarians, smokers

10/12/2004 9:20 amGeog 237a12 Probability Sampling Principles/Terminology Study Population group from which sample is actually drawn subset of population e.g., voters registered for 2003 provincial election, people who buy cigarettes at stores in London

10/12/2004 9:20 amGeog 237a13 Probability Sampling Principles/Terminology Sampling Frame the actual list from which elements are drawn e.g., voter registry list; people observed buying cigarettes Sample subset of study population used for making statistical inferences e.g., 400 voters…

10/12/2004 9:20 amGeog 237a14 sample sample frame study population population Probability Sampling Relationship Between Terms

10/12/2004 9:20 amGeog 237a15 Probability Sampling Principles/Terminology Element the unit that comprises the population, sample population and the sample typically the same as unit of analysis e.g., individuals, households

10/12/2004 9:20 amGeog 237a16 Probability Sampling Sampling Distribution Parameter a number computed from a population a summary description of some aspect of a population no random variation – “true” value often unknown (hence, the need to sample) e.g., median income of Canadians

10/12/2004 9:20 amGeog 237a17 Probability Sampling Sampling Distribution Statistic a number computed from a sample meant to represent the corresponding population parameter random variation (sampling error) e.g., median income of 20% sample of Canadian Census

10/12/2004 9:20 amGeog 237a18 Probability Sampling Sampling Distribution Sampling Error How good are the results based on sample “n”? function of: parameter, sample size, and standard error Standard Error average difference between a statistic and a parameter function of: parameter and sample size

10/12/2004 9:20 amGeog 237a19 Probability Sampling Sampling Distribution

10/12/2004 9:20 amGeog 237a20 Probability Sampling Sampling Distribution Properties of Sampling Error as sample size increases standard error decreases ˆ sampling error decreases the greater the split in the parameter the greater the standard error ˆ greater the sampling error –i.e. more homogeneous populations have lower sampling error

10/12/2004 9:20 amGeog 237a21 Probability Sampling Types Simple Random Sample all elements in sample frame assigned numbers random numbers for sample chosen and applied to list e.g., random number tables, see next.

10/12/2004 9:20 amGeog 237a22 Probability Sampling Simple Random Sample

10/12/2004 9:20 amGeog 237a23 Probability Sampling Simple Random Sample

10/12/2004 9:20 amGeog 237a24 Probability Sampling Types Systematic Sample practical alternative to simple random sampling every kth (sampling interval) element in a list typically total sample frame divided by sample size to determine sampling interval threat: periodicity; whereby k = periodicity e.g., every other household (typically odd and even numbers on same side of street!)

10/12/2004 9:20 amGeog 237a25 Probability Sampling Systematic Sample

10/12/2004 9:20 amGeog 237a26 Probability Sampling Types Stratified (Random) Sample sample frame split into mutually exclusive homogenous sub- groups random or systematic sampling within these groups homogeneity of sub-groups reduces sampling error e.g., gender; age categories; census tracts in London

10/12/2004 9:20 amGeog 237a27 Probability Sampling Types (Multistage) Cluster Sample impractical to compile and count elements in a single list (e.g., all Canadian university students) obtain lists for subgroups (i.e., all universities) randomly select some of the subgroups (e.g., 10 universities) randomly select within those lists (i.e., simple or systematic of 200 students) total sample N = 2000

10/12/2004 9:20 amGeog 237a28 Probability Sampling Probability Sampling (Multistage) Cluster Sample