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EPE/EDP 557 Class #2 Notes

Review: Central Tendency Variability. The Normal Curve z-scores T-scores Probability Odds Introduction to Inferential Statistics. EPE/EDP 557 Class #2 Notes. EPE/EDP 557. The Normal Curve Key features Scores cluster around the center of distribution The normal curve is symmetrical

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EPE/EDP 557 Class #2 Notes

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  1. Review: Central Tendency Variability The Normal Curve z-scores T-scores Probability Odds Introduction to Inferential Statistics EPE/EDP 557Class #2 Notes

  2. EPE/EDP 557 • The Normal Curve • Key features • Scores cluster around the center of distribution • The normal curve is symmetrical • Mean = Median = Mode • Constant relationship with SD • 1 SD from the mean = point of inflection • The normal curve is asymptotic to abscissa (curve never touches X-axis)

  3. EPE/EDP 557 • The Normal Curve

  4. EPE/EDP 557 • z Distribution & z Scores • z Distribution: normally distributed set of scaled values with a mean of zero and a standard deviation of one. • z Score: Standard deviation score

  5. EPE/EDP 557 • z Score Transformations

  6. EPE/EDP 557 • T Scores • Converted z Score • Mean of 50 and Standard Deviation of 10 • From z to T: T = z(10) + 50 • From T to z:

  7. EPE/EDP 557 • Probability • The number of times an event (s) can occur out of the total number of events (t) • Each event must have an equally likely outcome • The p assigned to each event equal to or greater than zero or equal to or less than one • The sum of the probabilities assigned to each event must equal one.

  8. EPE/EDP 557 • Odds • Where probability is based on how often an event will occur, odds are based on how often an event will not occur • If p>50, odds are on • If p<50, odds are against

  9. EPE/EDP 557 • Inferential Statistics • Using measurements taken from samples (statistics) to predict characteristics of populations (parameters) • Measuring the few and generalizing to the many

  10. EPE/EDP 557 • Inferential Statistics • Making accurate predictions requires a Representative Sample (a sample that reflects the characteristics of the population) • Sampling Error: The difference between a sample value and the actual population value • Sampling Error is NOT a mistake • Sampling Error is an expected deviation • Sampling Error =

  11. EPE/EDP 557 • Inferential Statistics • Sampling Bias (as opposed to Sampling Error): Systematic differences between a sample and the population from which the sample was drawn; constant sampling error in one direction

  12. EPE/EDP 557 • Inferential Statistics • Sampling Distribution: Distribution composed of measures taken from successive random samples • Sampling Distribution Mean = Population Mean • The Standard Deviation of a Sampling Distribution is the Standard Error of the Mean ( ), a measure of sampling error variability

  13. EPE/EDP 557 • Inferential Statistics • Central Limit Theorem: if repeated random samples are drawn from a population that is normally distributed along some variable, the sampling distribution of all theoretically possible sample means will be a normal distribution • The mean of the sampling distribution will equal the population mean • The standard deviation of the sampling distribution is the Standard Error of the Mean

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