Simple Random Sample (SRS) & Voluntary Response Sample: Examples: A Voluntary Response Sample: Examples: Systematic Sample Best Used When

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1 Simple Random Sample (SRS) & Voluntary Response Sample: In statistics, a simple random sample is a group of people who have been chosen at random from the general population. A simple random sample is an unbiased way of surveying Each person is chosen at random so everybody has an equal chance to be chosen Examples: An example of a simple random sample would be a group of 25 employees chosen out of a hat from a company of 250 employees. In this case, the population is all 250 employees, and the sample is random because each employee has an equal chance of being chosen. As another example, in the lottery, when a sample of 6 numbers is randomly generated from a population of 49, each number has an equal chance of being selected and each combination of 6 numbers has the same chance of being the winning combination. A Voluntary Response Sample:. A Voluntary Response Sample: consists of people who choose themselves by responding to a general appeal Voluntary response samples: are biased because people with strong opinions, especially negative opinions, are most likely to respond. Examples: A very common example is when someone is called by a surveyor and chooses to participate. Usually when the person decides to answer the questions asked within the survey, it is because they have strong biased opinions on the topic. A news show in Kansas asks viewers to participate in an online poll about gay marriage. This would be a voluntary sample. The sample is chosen by the viewers, not by the survey administrator. and since the sample was taken in Kansas and they are pretty anti gay, the survey ended up 99% against it and 1% for it since only the people heavily on one side would bother to vote Systematic Sample Used when sampling a fixed percent of the population, a random starting point is chosen and then you select every nth individual for your study, where n is the sampling interval Sampling interval found by evaluating Population size Sample size Best Used When wanting to survey a specific percent of a population randomly in a large group. For example, if you have 20 people and only want to survey 25% of them you would survey every 4 th person. Population size = 20

2 Sample size=20/5 = 4 Example 1: You want to sample 8 houses out of 120 on a street. Population size = 120 Sample size = 120/15 = 8 Therefore, if you chose a random start point of 11 you would survey every 15 th house. (11, 26, 41, 56, 71, 86, 101 and 116) Example 2: There are 200 houses on your street, you want to survey 20% of them. What houses would you survey if the random starting point is 18? Solution: Population size = 200 Sample size = 200/20 = 10 Therefore, every 20 th house would be surveyed. 18, 38, 58, 78, 98, 118, 138, 158, 178 and 198 are the houses that would be surveyed if the random start point is 18. Stratified Sample Stratified Sampling Definition: a stratified sample is a probability sampling technique in which the researcher divides the entire population into different subgroups, or strata and then randomly selects the final subjects proportionally from the different strata/subgroups. Example 1: If you wanted to get a stratified sample of university students, you would first have to organize the population by what class they are in and then select the appropriate numbers of freshmen, sophomores, juniors and seniors. This ensures that you have a reasonable amount of subjects from each class in the final sample. Example 2: More of a real world example of using stratified sampling would be for a political survey. If the respondents needed to reflect the diversity of the population, the researcher would specifically seek to include participants of multiple minority groups, like race or religion, based on their proportionality to the total population. Example 3: Another example would be in someone was researching how many high school students play sports, on average. The researcher would take the same number of students from each grade to figure out the average. Example 4: If you want to convey a survey of how many high school students are in after school sports, you ask the same number of students from each grade (30 from grade 9, 30 from grade 10, 30 from grade 11 and 30 from grade 12) which will give you a better idea of how many students play sports on average.

3 In conclusion, using stratified sampling is a good way to get a general idea of the average number of whatever data you want to find from a large population. Cluster Sampling - Used if obtaining information is impossible or impractical due to the size of the sampling population. It takes a random group or cluster of population and studies it rather than the whole population Example - Studying the academic performance of all high school students in Canada [First thing to do is break all of this potential data into clusters (provinces, major cities, etc.)] [Then perform random sampling on all high school students from that randomly chosen cluster] Destructive Sampling - A technique where the samples are destroyed during the random sampling process. Usually the samples must be destroyed to test how well it works and its usefulness Example Fireworks is an example of this. One would need to set a random sample of fireworks off to make sure they actually explode. On an assembly line, let s say, every 50th firework would need to go through the destructive sampling process and then they would assume the rest of the fireworks after that will react the same. Multi-Stage Sampling and Convenience Sampling: Multi-Stage Sampling Sampling that is carried out in stages using smaller and smaller sample sizes at each stage. Two-stage sampling design: primary units then secondary units Example 1: Target wants to estimate that average employee satisfaction with their job (scale of 1-7) 1. They have 135 stores in Canada and a total number of employees of Sample 13 stores 3. Interview 20% of employees (approx. 520 employees) 4. Examine results Example 2: To survey how much electricity is being used in Cambridge at 6 o clock pm First survey the city Then the subdivision Then a street Then individual houses Conclude results Convenience Sampling a non-probability sampling technique where subjects are selected because of their convenient accessibility and proximity to the researcher. Example 1: You want conduct a survey of stores shopped at in a mall You go early Monday morning for four weeks After conducting the survey you found most people liked to shop at Sears, The Bay, Alia and Tanjay, and Target Conclude results Example 2: You want to see people s opinions on pets Stand on a high traffic side walk Ask the first 100 people their opinions on pets Take notes and conclude data

4 Longitudinal Study This type of study is an observational method which involves observing the same subjects over a long period of time. This study method can take place for years, decades and even generation of certain families (animals or humans). One cannot interfere in any way, shape or form with the subject during the study period. Often a smaller sample group as it is very costly to observe participants over this long of a time period. Usually used in Psychology to determine development of trends along someone's lifespan. Examples include climate change, psychology, animal mutation, etc. The British Office of Population Censuses and Surveys, in 1971, followed 1% of the British population. This study resulted in the correlation of factors such as mortality and incidence of cancer, alongside variables like housing and status of employment. Cross-Sectional Study Collects data from multiple sources varying in a specific factor at the same time This type of research is often used in developmental psychology but the principles and process of this study can also be used in other fields such as social science and education. Similar to longitudinal study, there is no manipulation of data or variables. It is known because it allows researchers to analyze and study many things at the same time. Often used to examine the relativity of something in a given area. Basically you grab many variables from the test group and inspect for cause and effect relationships, such as the prevalence of an illness and its possible causes. Used in population studies and crop health in different areas. Example: A study was performed in Rural Children to observe the loneliness of left behind children. This study resulted in the data that many children let are left behind at birth are at risk of loneliness in later life. (Very flat conclusion, not complex like the longitudinal study conclusion because this takes a place at only ONE point in time unlike the other one which is over a long study period)

5 Survey questions are used to quickly and accurately retrieve data from a set group of individuals to be reviewed later. The several types of questions are as follows: Information Question: Unlike the other three types, this form of question is used to gather data on the person(s) responding to the questions; the who, what, when, and where. This can later be used for investigating possible trends or correlations between the answers and a certain group of people. I.e. Gender: M F Or Age: < > Check-list Question: This differs from the other types due to the applicability of all the given answers. The respondent may choose one, none, or as many as apply to them directly. i.e. Choose all applicable: Basketball Baseball Cricket Lacrosse Hockey Soccer Ranking Question: These give multiple answers in which all may be relevant, and asks the person to rank them in any number of ways. It could be used to see a person s preference towards something, or show where their values lie. I.e. Rank in order of importance (1, most important to 5, least important): Graduating high school Finding friends Getting a summer job Learning to drive Choosing a Career Rating Question: Rating questions are probably the most common type. These give a set of answers, where the respondent chooses only the best response. I.e. How satisfied are you with X? Very satisfied Satisfied Very Dissatisfied Dissatisfied Questionnaire Question Types Information Questions A question looking for information and not an opinion. Three or more multiple choice questions that are mutually exclusive, meaning that if one answer is true, the other 2 or more answers are false.

6 Example: Which form of media do you consume most? a) Television b) Internet c) Radio d) Newspaper e) Other, please specify: Check-list Questions Questions that have multiple answers that are not necessarily exclusive, so the person answering has to check every option that applies to the question. Example: What type of television shows do you watch? (check all that apply) Mystery Drama Comedy Romance Horror Science Fiction Ranking Questions A question that gives the answerer several choices that they have to rank from most to least correct or applicable. Example: favourite. Rate the following flavours of ice cream from your most favourite to least Vanilla Chocolate Strawberry Cookies and Cream Mint Chocolate Chip Rating Questions Usually used to obtain customer feedback on the service a business provided. Example: How satisfied were you with your overall dining experience (please pick one)? Very Satisfied Satisfied Dissatisfied Very Dissatisfied

8 To be meaningful, the margin of error should be qualified by a probability statement (often expressed in the form of a confidence level) Occurs whenever a population is incompletely sampled Confidence Level refers to the percentage of all possible samples that can be expected to include the true population parameter Absolute Quantity is equal to a confidence interval radius for the statistic Relative Quantity is the absolute margin of error expressed as a percent of the true value Only accounts for random sampling error Does not take into account systematic errors (non-response, interactions between the survey and subjects' memory, motivation, communication and knowledge) Examples 1. If 49 percent of American voters prefer McCain to Obama, with a margin of error of 3 percent is that 49 percent of those questioned prefer McCain to Obama. The 3 percent margin of error means we can be 95 percent confident that the true value of support is somewhere between 46 (49 minus 3) to 52 (49 plus 3). The true value is how the whole population would vote. With a poll showing 49 percent support for McCain, and a margin of error of three points, we cannot conclude with confidence that Obama is ahead. 2. A poll that claims 29 percent of children at Carson Elementary School prefer hamburgers to chicken nuggets. The elementary school consists of 500 students, 445 who were polled, and 95 percent of the time the answers were evenly split. In this example the population size is 500 and the sample size is 445, with a standard deviation is 95 percent. Therefore, the margin of error is 3.95.

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