Chapter 3 Monday, May 17th
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1 Chapter 3 Monday, May 17 th
2 Surveys The reason we are doing surveys is because we are curious of what other people believe, or what customs other people p have etc But when we collect the data what are we supposed to do with them?
3 Statistical ti ti techniques There are two statistical techniques that we use in order to derive results from the data: Descriptive statistics which are numerical and graphical summaries of a dataset t Inferential statistics where we use the collected data to make inference about a broader range of individuals than just those who are observed.
4 Definitions iti Population is the larger group of units about which inferences are to be made Sample is the subset of the population that we measure in order to make inference about the whole population When we are able to measure the whole population then we have a census and not a sample
5 Sample vs Census We usually prefer Sample over Census for the following reasons: Speed Money A census is not possible
6 Sampling When we do sampling we want the data to be as representative of the population as possible. There are many ways to achieve this depending on the formation of the data. Those are: Simple Random Sample Stratified Random Sampling Cluster Sampling Systematic Sampling Random Digit Sampling Multistage Samplin
7 Simple Random Sampling In a simple random sample every unit in the population p has the same probability of being chosen as a sampling unit. To achieve a simple random sampling you need First: to enumerate all the units in the population Second: a source of random numbers (Random tables or Calculator)
8 Random number tables
9 Problems with Simple Random Sample What happens if I have to do a survey and my ypopulation p is the population p of USA? First: It is hard to enumerate all the members of the population. Second: Each subgroup of the population may have different opinions that I want to be able to distinguish.
10 Stratified tifi Random Sampling In order to get a stratified random sample we: Divide the population into smaller subgroups that are called strata (singular: stratum) Example in the population of U.S.A. I might have the following strata: Caucasian, Asian, Afro- Americana, Latinos and others Then we make a random sample in each stratum to get the samples.
11 Cluster sampling In order to get a cluster sample we: Divide the population into subgroups that are called clusters. Then we select a random sample of clusters and we put into the sample everyone that belongs to that cluster Example: I want to see the difference in behavior between the people living in Chicago and Philadelphia. So I divide each city into clusters (let s say street blocks) and I make a sample of those clusters. If a cluster is selected everyone living in that block will be included in my sample
12 Differences of stratified sampling with cluster sampling Stratified sampling: Few large strata Simple random sample in each strata Cluster sampling A large number of small clusters Simple random sample of clusters Every person in the clusters selected is interviewed.
13 Systematic ti Sampling To choose a systematic sample you have To enumerate all the units in your population Then you have to divide the population units into segments. In the first segment you randomly choose a starting point For all the segments you choose the same observation as the one in the first segment
14 Systematic ti Sampling Example: A hospital has 500 patients and they want to see how happy the patients are with the facilities. They decided to take a sample of 20. So they make a list of all 500 people They divide the list into 20 segments of 25 people They randomly choose one number between 1 and 25. (Let s say they choose number 6) Then they will choose from every segment the 6 th person
15 Random digit it dialing This is a new method developed. Instead of making a list polling organizations they randomly choose land line numbers This is very closed to a simple random sample with the exception that you only reach people that have land-line telephone numbers
16 Multistage t sampling plan Multistage sampling is performed when we have any combination of the previous methods discussed
17 Problems with sampling When we are sampling from large populations p the following problems can occur: Using the wrong sampling frame Not reaching the individual selected Non-response or nonparticipation Self-selected sample Convenience or haphazard sample
18 Resulting biases The previous problems with surveys lead to a number of biases: Selection bias is when the method for selecting participants produces a sample that is not representative Non-response bias occurs when we have a representative samples but some individuals chosen do not respond or cannot be reached Response bias occurs when participants provide incorrect information
19 How accurate a sample can be? Let s say we sample individuals. Then the margin of error (or else, how accurate the sample can be) for a sample proportion is calculated by: 1 n n
20 95% Confidence Interval for Population Proportion For about 95% of properly conducted surveys the interval: sample proportion 1 1, sample proportion n n will contain the actual population proportion.
21 Example: Let s say I ask 1000 American adults to tell me how important they consider religion and I get the following answers: Very important 65% Fairly important 23% Not very important 12% No opinion 0% Find the margin of error and the 95% confidence interval for each of the 4 percentages above.
22 Choosing sample size Since the formula for the margin of error involves the sample size, that means that if we want we can calculate a desired margin of error by choosing the appropriate sample size: Example: If I want my margin of error to be 0.1 then the sample size should be.? If I want my margin of error to be then the sample size should be?
23 Just to be careful In Chapter 10 we will learn that this way of finding confidence interval is very conservative. There is a more accurate way, but this is for later
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