PSY302, Week 4 Notes
PSY302, Week 4 Notes PSY302
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This 1 page Class Notes was uploaded by Emma Cochrane on Sunday April 24, 2016. The Class Notes belongs to PSY302 at University of Oregon taught by Jordan Pennefather in Winter 2016. Since its upload, it has received 14 views. For similar materials see Statistical Meth Psych in Psychlogy at University of Oregon.
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Date Created: 04/24/16
Distributions of Statistics we can calculate a z-score and ﬁnd the probability for a sample mean Distributions of X vs. M Distributions of X: easy and intuitive, callus of variable x in an easily imagined population Distributions of M: harder to grasp, distributions of M for all possible samples of size n from the population mean height for all possible samples of 10 men Sampling Distribution choose a sample size (e.g., n=5) take all possible samples of 5 individuals from the population calculate the means of each sample construct frequency distribution from the samples Central Limit Theorem for any population with a mean m and a standard deviation of ơ, the sampling distribution of the mean for a sample size n will: have a mean of m increasingly approach a normal distribution as n increases have a standard deviation of ơ/√n Shape of Sampling Distribution normal “parent” populations automatically have normal sampling distributions when n is larger, mean is normally distributed Variability of Sampling Distribution standard error: the standard deviation of the sampling distribution of the mean measures typical deviation of a sample mean from the true population mean quantiﬁes sampling error Sampling Error inherent in researching using statistics to estimate population parameters we have a sample error every time we use a statistic to estimate a parameter sample mean - population mean = amount of sampling error Hypothesis Testing with Z Hypothesis testing is used in statistics to make educated guesses about a population The Logic: using a sample to infer the truth about the population helps us decide whether means are diﬀerent enough to conclude signiﬁcance of the results Hypothesis testing helps us decide between two options: the diﬀerent between the sample and the population can be explained by a sampling error the diﬀerent between the sample and the population is too large to be explained by sampling error Hypotheses are always about population parameters Logic of Hypothesis Testing What you are doing: using a sample to infer the parameters of an unknown population Steps: ask the research question state hypothesis (null and alternative) about inferred population we test upside down (we try to prove ourselves wrong) use hypothesis to set decision rule collect data – ideally a random sample from a population analyze data to test hypothesis see if sample data is consistent with your hypothesis make a decision Two Choices Reject do this when statistic falls in the extreme tails of the null distribution of sample means Fail to reject do this when statistic falls in the middle of the distribution Not Always Right Type 1 Errors are “false positives” alpha Type 2 Errors are “false negatives" beta Assumptions of Z-Test random sampling was used sampling distribution is normal m and s are known and the value of s is unchanged by treatment Controlling Error Type 1 choice of alpha Type 2 power: probability that the test will correctly reject a false null hypothesis (ability of a test to detect treatment eﬀect) determined by: size of eﬀect sample size alpha level
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