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Unformatted text preview: Lecture 8: Probability Lecture 8: Outline 1. Review: Normal (BellShaped) Distribution – Shape, Mean and Standard Deviation, What is ‘normal enough’, Outliers, Normal Probability Plot 1. NEW MATERIAL: Basic Probability Concepts •. Basic Terms – Probabilities for Simple event : P(A) – Probability for Joint event (and): P (A and B) (Both events must happen together) – Probability for Union event (or): P (A or B) (One or the other or both happen) – Independent events •. Presenting Data in Contingency Tables – Filling in the table (Use information given to fill in a table of probabilities) – Finding Probabilities (Try to use common sense from knowing definitions) Chapter4 Review – We talked about measures of central tendency, variability, and shape for samples of data. – Mean and Standard Deviation define what a normal curve looks like – Empirical Rule: • 68% of data that have a normal shape fall within 1 SD of the mean; • 95% of data that have a normal shape fall within 2 SD of the mean; • almost 100% of data that have a normal shape fall within 3 SD of the mean – Outliers – High side (data points bigger than Mean + 3*S), Low side (data points smaller than Mean – 3*S) – Almost Normal: 1 < Skewness, Kurtosis < 1 • If not, use Median and IQR to describe dataset – Normal Probability Plot confirms normal shape of the distribution, if it is a straight line Why is the Normal Distribution Important? So far, we have only described the characteristics of samples (‘Descriptive Statistics’). If we only care about describing a specific sample, it does not matter if the distribution is normal or not. Many times, researchers want to do more than simply describing a sample: They want to know what the exact probability is of something occurring in their sample just due to chance If the average student in my sample consumes 2,000 calories per day, what are the chances (or probability) of having a student in the sample who consumes 1,000 calories per day? We rely on the characteristics of the Normal Distribution to calculate these probabilities They want to be able to make inferences about the population based on the data collected from the sample (Does the phenomenon observed in the sample represent an actual phenomenon in the population?) Hypothesize that in the population of men and women, there is no difference in the average number of calories consumed per day. Select a sample men and a sample of women, compare the average daily calorie consumption, find that men eat 200 calories more on average. Given the ‘Null Hypothesis’, what is the probability of finding a difference this large just by chance? What is Probability?...
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 Spring '08
 Reardon,J
 Conditional Probability, Probability, Probability theory

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