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# Psych 2220 Chapter 6 Notes PSYCH 2220 - 0020

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This 2 page Class Notes was uploaded by Carolyn Kwon on Sunday February 28, 2016. The Class Notes belongs to PSYCH 2220 - 0020 at Ohio State University taught by Joseph Roberts in Spring 2016. Since its upload, it has received 19 views. For similar materials see Data Analysis in Psychology in Psychlogy at Ohio State University.

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Date Created: 02/28/16

Psych 2220 Data Analysis Chapter 6 Notes - Calculating a z score from a raw score: ???? = (????− ????) where ???? is the raw score; ???? is the popl mean; ???? is the popl standard deviation ???? - The z distribution always has a mean of 0 and a standard deviation of 1. - Calculating a raw score from a z score: ???? = ???? ???? + ???? where ???? is the ???? score; ???? is the popl standard deviation; ???? is the popl mean - Transforming z scores into percentiles: (mean = 0 ; standard deviation = 1) ~2% ~14% ~34% ~34% ~14% ~2% - Distribution of Means: o The distribution wold be narrower (if we created a distribution of means of 10 scores rather than 3 scores) because there would be more scores tobalance the occasional extreme score. o The larger the sample size, the smaller the spread of the distribution of means. o A distribution of means has the same mean as a distribution of scores that is from the same population, but will have a smaller standard deviation. - The mean of a distribution of means: ????????(“mu sub m”) where ???? = the mean of a population & ???? signifies this population is composed of a sample means - The standard deviation of the distribution of means: ????????(“sigma sub m”) where ???? = the SD of the population & ???? signifies this population is composed of a sample means - Remember: the larger the sample size, the narrower the distribution of means and the smaller the standard deviation of the distribution of means (also known as Standard Error) - Formula for Standard Error: ???? ????????= where ???? = SD of the population divided by the square root of ???? = sample size √???? - The Central Limit Theorem o A distribution of means faithfully obeys the central limit theorem (even when a population of individual scores that are not normally distributed, the distribution of means approximates a normal curve as the sample gets larger) - Three important characteristics of a distribution of means: 1) As sample size increases, the mean of a distribution of means remains the same. 2) The standard deviation of a distribution of means (aka the standard error) is smaller than the SD of a distribution of scores. As sample size increases, the SE becomes even smaller. 3) The shape of a distribution of means approximates the normal curve if the distribution of population of individual scores has a normal shape or if the size of each sample that makes up the distribution is at least 30 (this is the Central Limit Theorem). - Using the CLT to make comparison with z scores: o We can also find the z score when we use a distribution of mean instead of a distribution of scores (aka z statistic): (????− ???? ???? ???? = ???? where ???? = mean of sample; ???? ???? mean of a dist. of means; ????????= standard error ???? o The z statistic tells us how many standard error a sample mean is from the population mean. o From the z statistic we can determine how extreme the mean number is in terms of a percentage Example: A z statistic that is above 1.96 indicates most extreme 5%. o Note: 0.05 or 5% cut off is a reasonable standard that gives us a reasonable chance of detecting a real finding while minimizing the likelihood to commit a Type I error. Review: Type I Error is rejecting the null hypothesis when the null is actually true. Type II Error is accepting (or failing to reject) the null hypothesis when the null is false.

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