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# Psychology 302: Week 3 lecture notes PSY 302

UO

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This 3 page Class Notes was uploaded by Shannon Hardman on Tuesday October 20, 2015. The Class Notes belongs to PSY 302 at University of Oregon taught by Laurent S in Fall 2015. Since its upload, it has received 11 views. For similar materials see Statistical Meth Psych in Psychlogy at University of Oregon.

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Date Created: 10/20/15

WEEK 3 NOTES PROBABILITY Probability number of select outcomestotal number of possible outcomes 0 A ratio of a given outcome to all possible outcomes 0 Ranges from 0 to 1 no chance to 100 chance 0 Probability is the same as proportion Odds Relative Probability 0 Odds probability of outcome occurringprobability of outcome NOT occuring Given as desired outcomes nondesired outcomes 0 Probability and Random Sampling 0 For certain properties of probabilities to hold true some things are required 0 Each individual in the population must have an equal chance of being selected 0 Sampling with replacement the probability of being selected must stay constant from one selection to the next 0 Larger samples are better approximations of the population 0 Probability as quotArea Under the Curvequot 0 If every possible score from a population is under a curve such as the normal distribution that is 100 of scores are under the curve we can nd out exactly where any given score is in the distribution 0 We can also tell exactly what proportion of scores are higher or lower than this score or the area under the curve between any two scores 0 We can also get the probability that any randomly selected score from the population would be higher or lower than a particular score EX If 5 of scores are above a particular score and 95 below a randomly selected score from the distribution will have a 5 chance of being higher and a 95 chance of being lower 0 How do we do this 0 We use zscores Zscores denote precisely where under the curve any score resides in a normal distribution 0 Area under the curve 0 Zscore tables often divide the distribution into the tail small portion and the body big portion This can be thought of as quotarea lef quot and quotArea rightquot of any score 0 Because the distribution is symmetrical the proportion and probability of scores greater than 2 and less than 2 are identical 0 Ex Proportion in taigtz 15 15 proportion in tail ltz15 Zscores above the mean are positive and zscores below the mean are negative but proportions and probabilities are always positive SAMPLING DISTRIBUTIONS OF MEANS o Distributions of Statistics 0 We have calculated zscores which tell us how probable a score is e is a score common or unique 0 We can also assess the probability of drawing any particular sample mean o Is some sample quotextremequot or quotregularquot 0 Samples are different from individual scores because when they39re randomly selected they39re less likely to be extreme Larger samples are more likely to select scores from throughout the distribution and to thus approximate the population mean Distributions of Scores and Sample Means 0 Distribution of X5 0 Lower case sigma subscript x average distance of xs from mu typical variability of xs 0 ln Distributions of means the mean of that distribution is the mean of all the means 0 Lowercase sigma subscript M the average distance of means from mu typical variability of means 0 The mean from all sample means is expected to be equal to the population mean Sampling Error 0 Sampling Error Inherent in research using samples to estimate population parameters 0 Different samples drawn from the same population will have different properties 0 Samples are only subset of the population only part of what you39re trying to understand 0 This is problematic We need to quantify the amount of error that we are likely to nd in any given sample 0 Standard error of the mean the standard deviation of the sampling distribution of means Lowercase sigma m lowercase sigmasqrtN Measures the average deviation of a sample mean M from the population mean mu Quanti es the sampling error Larger Ns sample sizes have smaller standard errors because they more accurately estimate the population mean Central Limit Theorem 0 For any population with a mean of mu and a standard deviation of sigma the sampling distribution of the mean for a sample size of n will 0 Have a mean of mu Increasingly approach a normal distribution as n increases Shape of the Sampling Distribution 0 Normally distributed populations automatically have normal sampling distributions 0 For nonnormal distributions With very small ns 23 sampling distributions of Ms will be similar to the distribution of xs raw scores When ns are large the sampling distribution of Ms will be normal

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