Ap Stats

Sample Types:

  • Simple Random Sample (SRS) - Choosing individuals from the population in such a way that every individual and group of individuals has an equal chance of being selected.

  • Systematic Random Sample - Choosing individuals from a population by selecting a random starting point and selecting sample members using a fixed 'sampling interval.'

  • Cluster Sampling - Spitting the population into heterogeneous clusters to make sampling more practical. Then, select one or a few clusters at random and perform a census within each of them. If each cluster represents the full population fairly, then cluster sampling will be unbiased.
    In this method, we survey all people from some clusters.
    For instance, if we want to find the average word length of a fiction book, one thing that we could do is choose several pages (as long as the words on the page are representative of the words in the rest of the book). Each page would be a 'cluster'.

  • Stratified Random Sample - A sampling method that first divides the population into groups of similar individuals called strata. Then, a separate SRS in each stratum is done and the SRS's are combined to form the full sample.

  • For this method, we sample some people from all strata.

  • For instance, if we wanted to choose a random sample of students from MHHS, we may choose to do it using the stratified random sample approach. First divide the school population into strata, which could be the student's grade. Choose a SRS from each grade and combine each SRS to form the full sample.

  • Multi-stage Sample Design - A sampling strategy may include multiple stages that combine the above sampling methods.
    Example: When surveying students at a high school, strata may be chosen to be all 9th graders, all 10"h graders, all 11'h graders, and all 12'h graders. Then we can define clusters within each stratum:

  • All 12'h grade classes are clusters within the 12'h grade stratum.

  • All 11" grade classes are clusters within the 11"h grade stratum.

  • All 10"h grade classes are clusters within the 10"h grade stratum.

  • All 9" grade classes are clusters within the 9th grade stratum.

Finally, several randomly selected clusters within each stratum can be chosen and censused.

Overarching Ideas:

Population

• Population - The entire group of individuals we want information about. A population can be huge, like "all the women." It can be small like "all statistics students at Mount Hebron HS."

Sample

  • Census - When data is collected about an entire population, making it so that everybody is "sampled." This is costly and takes a long time, usually.

  • Sampling Frame - A list of individuals from which a sample is chosen. This should be the entire population but in practice this is difficult.

  • Sample - A part of the population that we actually examine in order to gain information.

  • Pilot - A trial run of a survey you eventually plan to give to a larger group, using a draft of your survey questions administered to a small sample drawn from the same sampling frame you intend to use. By analyzing the results of this smaller survey, you can often discover ways to improve the survey before conducting a larger sampling process.

  • Parameter - A value that tells you something about the population. For example...

  • " represents a population mean

  • o represents a population standard deviation p represents a population proportion

  • Statistic - A value that tells you something about a sample. For example...

  • * represents a sample mean

  • s represents a sample standard deviation

  • P represents a sample proportion

  • Statistical Inference - Concluding about the population based on the sample.

Bias:

  • Bias - The design of a study is biased if it systematically favors certain outcomes. Bias does not have to be intentional. But, it must be avoided.

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    Convenience Sample- Data is collected from a conveniently available pool of respondents.
    Voluntary Response Bias - Bias created by a sample being composed of people that volunteer to participate. This can lead to overrepresentation of people with strong opinions.

  • Undercoverage - When some groups are left out of the process of choosing the sample. This may be intentional or unintentional. For instance, if I were to do some type of survey via email, there would be undercoverage because I would not be including people without computers.

  • Nonresponse - When the individuals chosen for the sample cannot be contacted or refuse to cooperate.
    Think of how many surveys you have decided not to fill out and you can see why nonresponse is a problem.

  • Response Bias - When the accuracy of responses are affected due to a variety of factors including the wording, interviewer, and/or lying.

  • Wording of Questions- Confusing or leading questions can introduce bias.