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Midterm

# Statistics Midterm 2 Review.docx

7 Pages
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School
University of Guelph
Department
Psychology
Course
PSYC 1010
Professor
Hank Davis
Semester
Summer

Description
Statistics Midterm 2 Review Stephanie Oliveira CHAPTER 6: The Normal Curve, Standardization and Z scores  Normal Curve: a specific bell-shaped curve that is unimodal, symmetric and defined mathematically. Standardization, z Scores, and the Normal Curve  Standardization: Converts individual scores from different normal distributions to a shared normal distribution with a known mean, standard deviation, and percentiles. The Need for Standardization  Z Score: the number of standard deviations a particular score is from the mean. Transforming Raw Scores into Z Scores. (X - m) z = s Transforming Z scored into Raw Scores X = z(s)+m  Z distribution: a normal distribution of standardized scores.  Standard normal distribution: a normal distribution of z scores.  The standardization distribution allows us to do the following: 1. Transform raw scores into standardized scores called z scores. 2. Transform z scored back into raw scores 3. Compare z scores to each other—even when the z scores represent raw scores on different scales. 4. Transform z scored into percentiles that are more easily understood. Transforming z Scores into Percentiles.  Z scores are useful because: 1. They give us a sense of where a score falls in relation to the mean of its population (in terms of the standard deviation of its population) 2. Z scores allow us to compare scores from different distributions 3. Z scores can be transformed into percentiles. 1 Statistics Midterm 2 Review Stephanie Oliveira The Central Limit Theorem  Central limit Theorem: refers to how a distribution of sample means is a more normal distribution than a distribution of scores, even when the population distribution is not normal.  The central limit theorem demonstrates two important principles: 1. Repeated sampling of means approximated a normal curve, even when the original population is not normally distributed. 2. A distribution of mean is less variable than a distribution of individual scores.  Distribution of means: a distribution composed of many means that are calculated from all possible samples of a given size, all taken from the same population.  The mean of the sample means will be the same as the mean.  Standard error: the name for the standard deviation of a distribution of means.  The standard error measures (roughly) the average difference between M and μ that should occur by random sampling alone (i.e., roughly, the average value for M - µ).  Formula for standard error: s s M = n You can find sample means from z-scores using: M = µ + (z)(σ ) M Chapter 7: Hypothesis Testing with z Tests Hypothesis Testing with Z Tests  Z test: a hypothesis test in which we compare data from one sample to a population for which we know the mean and the standard deviation. Given a score, Find a proportion a) Finding Proportions and Probabilities Step 1 – Sketch the normal distribution and shade the target area Step 2 – Choose the appropriate z-table column Step 3 – Convert X (raw score) to a Z-score Step 4 – Use the z-table to find the proportion (probability) of your raw score (X) 2 Statistics Midterm 2 Review Stephanie Oliveira Raw scores, z Scores, and Percentages  The z table allows us to translate the standardized z distribution into percentages and individual z scores into percentile ranks.  We can determine the percentage associated with a given z statistic by following two steps. o Step 1: Convert raw score into a z score. o Step 2: Look up a given z score on the z table to find the percentage of scores between the mean and that z score.  Steps to finding percentages: o Step 1: Convert the raw score to a z score o Step 2: Look up the z score on the z table to find the associated percentage between the mean and the z score. o Once we know that the associated percentage is 33.65%, we can determine a number of percentages related to the z score.  Calculating the percentile for a positive z score: We add 50% to the percentage between the mean and that z score to get the total percentage below that z score.  Calculating the percentage above a positive z score: We subtract the percentage between the mean and that z score from 50% to get the percentage above that z score.  Calculating the percentage at least as extreme as our z score: For a positive z score, we double the percentage above that z score to get the percentage of scores that are at least as extreme  Calculating a score from a percentile: We can convert a percentile to a raw score by calculating the percentage between the mean and the z score, and looking up that percentage on the z table to find the associated z score. We would then convert the z score to a raw score using the formu The Assumptions of Hypothesis Testing  Assumption: A characteristic that we ideally require the population from which we are sampling to have so that we can make accurate inferences.  Parametric Test: an inferential statistical analysis based on a set of assumptions about the population.  Nonparametric test: an inferential statistical analysis that is not based on a set of assumptions about the population.
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