Inferential Statistics Chapter 3 Lecture 3 Jaymie Ticknor Quantitative Methods 2317 Sect 001 24 and 29 January 2014 Z Score takes into account both standard deviation and mean of a group of scores describes a score in terms of how many standard deviations it is above or below the mean if the actual score is above the mean the z score is positive if it is below the mean the z score is negative Change raw score to z score Z X M SD raw score given X Z x SD M also known as a standard score A distribution of z scores will always have certain characteristics Mean 0 SD V 1 The shape of a distribution does not change when raw scores are converted to z scores if the distribution of raw scores is negatively skewed so will the distribution of z scores Normal Curve most variables psychologists study have distributions that are approximately normal characteristics unimodal symmetrical and bell shaped mesokurtic Shape of normal curve is standard mathematically perfect we can estimate the percentage of scores above or below a particular point 34 14 and 2 on either side total 68 28 68 28 96 4 68 28 4 99 Steps for figuring out the percentage of scores above or below a particular score Change raw score to z score Draw a picture of Normal Curve where the z score falls and then shade the area in question Sample and Population Population entire group of people to which a research intends a study to apply Sample scores of the particular group of people studied In research we usually study a sample but make inferences about a population Types of Sampling Random Selection each person in the population has an equal chance of being selected Haphazard Selection taking whoever is available biased need a system to get a representative sample Statistical Terminology Samples and Populations Population parameters Mean Standard Deviation Variance 2 Sample statistics Mean M Standard Deviation SD Variance SD2 Probability expected relative frequency of a particular outcome what you expect to happen if you ran an experiment many times Probability possible successful outcomes ALL possible outcomes Steps divide the number of successful outcomes by total all outcomes In statistics often expressed as p related to z score and normal distribution percentage probability of scores between mean and 1 standard deviation above the mean 34 0 34