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PSYC 3301

Learn about populations and samples in statistics, understand the difference between parameters and statistics, and explore how to make inferences about populations using inferential statistics.

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PSYC 3301

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  1. PSYC 3301 Review of Statistics

  2. Populations and Samples Imagine 4 years from now Bush and Gore are again running against each other. Someone asks you who is going to win the election. What is the best way to find out who will win the election? Hold an election What is the next best way to predict the outcome of the election? Take a poll What is a poll?

  3. Populations • A population is the group of interest as defined by the investigator. If you are trying to predict the outcome of a presidential election, what population are you interested in? The group of people who will vote on election day What is the best way to find out about a population? Test, measure, or otherwise examine EVERYBODY in the population What is the next best way? Take a sample

  4. Samples A sample is a subset of the population Researchers are almost always interested in populations, but as a practical matter you can only study samples. One of the most important functions of statistics is to provide a set of tools that allow researchers to make inferences about populations when all they have is information about a sample.

  5. Parameters and Statistics A pollster determines that 51% of a sample of 1,500 potential voters will vote for Gore. Is this an example of a parameter or a statistic? statistic A parameter is: a characteristic of a population A statistic is: a characteristic of a sample a Parameter is to a Population as a Statistic is to a Sample

  6. A quick note on sampling methods Simple random sample: Obtain a comprehensive list of all the individuals in a population and randomly select a subset from that list This ensures that your sample is: 1 – unbiased: each individual in the population has an equal chance of being chosen for the sample 2 – independent: selection of one individual does not influence the selection of another How does the typical political poll violate the assumptions if random sampling?

  7. Descriptive and Inferential Statistics What are descriptive statistics? Descriptive statistics produce numbers that summarize or describes a sample What are inferential statistics? Inferential statistics allow you to use measurements from a sample to estimate a population parameter.

  8. Estimating From a Sample Imagine you have been contracted by Boeing to design the seats for the new Boeing 797. How could you determine how wide the seats should be? Let’s estimate REWs from the population of potential airline passengers…. Randomly select samples of 5 from the data on the next slide

  9. Boeing Example The mean of the population of numbers in the grid is 17.040 What is the mean of your sample? Is this a statistic or a parameter? statistic Is the mean of your sample exactly 17.040? Is the mean of your sample exactly the same as the mean of other samples in the class?

  10. Relation between samples and populations Because sample statistics are almost always different from each other, and rarely equal to population parameters, we use inferential statistics to: Estimate population parameters from sample statistics

  11. Variables: Quantitative and Qualitative A variable is measure that can change or vary What are some examples of variables? A quantitative variable tells you something about the amount or degree of the variable What are some examples of quantitative variables? A qualitative categorizes items/individuals, but does not provide information about magnitude. What are some examples of qualitative variables?

  12. S. S. Steven’s Scales of Measurement What is a nominal scale? A scale that categorizes items What is a ordinal scale? A scale that categorizes and rank orders items What is a interval scale? A scale that categorizes and rank orders items, and has equal intervals What is a ratio scale? A scale that categorizes and rank orders items, has equal intervals, and a zero that means the absence or none of the thing being measured

  13. Scales of measurement: examples Give some examples of nominal scales? Give some examples of ordinal scales? Give some examples of interval scales? Give some examples of ratio scales? The classification of scales is important for choosing the kind of statistic you will use.

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