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# Aron chpt 4 sample and probability f2011

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### Aron chpt 4 sample and probability f2011

1. 1. Sample and Population <ul><li>Population </li></ul><ul><ul><li>entire set of things of interest </li></ul></ul><ul><ul><ul><li>e.g., the entire piggy bank of pennies </li></ul></ul></ul><ul><ul><ul><li>e.g., the entire population of individuals in the US </li></ul></ul></ul><ul><li>Sample </li></ul><ul><ul><li>the part of the population about which you actually have information </li></ul></ul><ul><ul><ul><li>e.g., a handful of pennies </li></ul></ul></ul><ul><ul><ul><li>e.g., 100 men and women who answered an online questionnaire about health care usage </li></ul></ul></ul>
2. 2. Why Study Samples vs. Populations <ul><li>It is usually more practical to obtain information from a sample than from the entire population. </li></ul><ul><li>The goal of research is to make generalizations or predictions about populations or events in general. </li></ul><ul><li>Much of social and behavioral research is conducted by evaluating a sample of individuals who are representative of a population of interest. </li></ul>
3. 3. What is Sampling? Population Sample Using data to say something ( make an inference ) with confidence, about a whole (population) based on the study of a only a few (sample). Sampling Frame Sampling Process What you want to talk about What you actually observe in the data Inference
4. 4. Methods of Sampling <ul><li>Random Selection </li></ul><ul><li>method of choosing a sample in which each individual in the population has an equal chance of being selected </li></ul><ul><li>A sample “n” is selection from population ‘N” </li></ul><ul><li>Selection process with no pattern; unpredictable </li></ul><ul><li>Reduces the likelihood of researcher bias </li></ul><ul><li>Researcher can calculate the probability of certain outcomes </li></ul><ul><ul><ul><li>Several different ways to conduct random sampling </li></ul></ul></ul><ul><ul><ul><li>Random numbers table, drawing out of a hat, coin flips, etc </li></ul></ul></ul><ul><li>Why Random Assignment is best? </li></ul><ul><li>Samples that are assigned in a random fashion are most likely to be truly representative of the population under consideration. </li></ul><ul><li>Haphazard Selection (Convenience Sampling) </li></ul><ul><ul><li>method of selecting a sample of individuals to study by taking whoever is available or happens to be first on a list </li></ul></ul><ul><ul><ul><li>This method of selection can result in a sample that is not representative of the population. </li></ul></ul></ul>
5. 5. Sample Size and Sampling Error <ul><li>Sample selection is usually mentioned in the methods section of a research article. </li></ul><ul><li>Appropriate sampling methods must be evaluated. </li></ul><ul><li>All other things being equal, smaller samples (e.g., those with fewer than 1,000 respondents) have greater sampling error than larger samples. </li></ul><ul><ul><li>To better understand the notion of sampling error, it is helpful to recall that data from a sample provide merely an estimate of the true proportion of the population that has a particular characteristic </li></ul></ul>
6. 6. Statistical Terminology for Sample and Populations <ul><li>Population Parameters </li></ul><ul><ul><li>mean, variance, and standard deviation of a population </li></ul></ul><ul><ul><li>are usually unknown and can be estimated from information obtained from a sample of the population </li></ul></ul><ul><li>Sample Statistics </li></ul><ul><ul><li>mean, variance, and standard deviation you figure for the sample </li></ul></ul><ul><ul><li>calculated from known information </li></ul></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved
7. 7. Probability <ul><li>Expected relative frequency of a particular outcome </li></ul><ul><ul><li>outcome </li></ul></ul><ul><ul><ul><li>term used for discussing probability for the result of an experiment </li></ul></ul></ul><ul><ul><li>expected relative frequency </li></ul></ul><ul><ul><ul><li>number of successful outcomes divided by the number of total outcomes you would expect to get if you repeated an experiment a large number of times </li></ul></ul></ul><ul><ul><ul><li>long-run relative-frequency interpretation of probability </li></ul></ul></ul><ul><ul><ul><ul><li>understanding of probability as the proportion of a particular outcome that you would get if the experiment were repeated many times </li></ul></ul></ul></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved
8. 8. Steps for Figuring Probability <ul><li>Determine the number of possible successful outcomes. </li></ul><ul><li>Determine the number of all possible outcomes. </li></ul><ul><li>Divide the number of possible successful outcomes by the number of all possible outcomes. </li></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved
9. 9. Figuring Probability <ul><li>You have a jar that contains 100 jelly beans. </li></ul><ul><li>9 of the jelly beans are green. </li></ul><ul><li>The probability of picking a green jelly bean would be </li></ul><ul><ul><li>9 (# of successful outcomes) or 9% </li></ul></ul><ul><ul><li>100 (# of possible outcomes) </li></ul></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved
10. 10. Range of Probabilities <ul><li>Probability cannot be less than 0 or greater than 1. </li></ul><ul><ul><li>Something with a probability of 0 has no chance of happening. </li></ul></ul><ul><ul><li>Something with a probability of 1 has a 100% chance of happening. </li></ul></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved
11. 11. p <ul><li>p is a symbol for probability. </li></ul><ul><ul><li>Probability is usually written as a decimal, but can also be written as a fraction or percentage. </li></ul></ul><ul><ul><li>p < .05 </li></ul></ul><ul><ul><li>Threshold for significance in research </li></ul></ul><ul><ul><ul><li>the probability is less than .05 </li></ul></ul></ul><ul><ul><ul><li>So, you are saying that there is less than a 5% chance of the differences you see in your research results being from something other than random chance variation </li></ul></ul></ul><ul><li>Probability is discussed in the context of reporting statistical significance of study results. The p-value is the probability of the findings being by something other than chance occurrence. </li></ul><ul><li>Researcher will set the threshold prior to doing the research; </li></ul><ul><li>Threshold p-value is usually p< .05 or p< .01 </li></ul>
12. 12. Probability, Z Scores, and the Normal Distribution <ul><li>The normal distribution can also be thought of as a probability distribution. </li></ul><ul><ul><li>The percentage of scores between two Z scores is the same as the probability of selecting a score between those two Z scores. </li></ul></ul>