Ch1 4 Study Guide

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PSYC 4111
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Part I of the Study Guide for Explaining Psychological Statistics Third Edition by Barry H CohenChapter 1 Introduction to Psychological StatisticsMeasurement Scales Nominal B Observations are assigned to categories that differ qualitatively but have no quantitative order eg depressed phobic obsessive etc Ordinal B The values have an order that can be represented by numbers but the numbers cannot be used mathematically because the intervals may not be equal eg assigning ranks according to the ability of gymnasts on a team Interval B One unit on this scale is the same size anywhere along the scale so values can be treated mathematically eg averaged but zero on the scale does notindicate a total absence of the variable being measured eg IQ scores Ratio B This scale has the interval property plus the zero point is not arbitrary it represents a true absence of the variable being measuredFor instance weight in pounds has this property so that if object A is measured as twice as many pounds as object B then object A has twice as much weightYou cannot say that someone ith an IQ of 120 is twice as smart as someone with an IQ of 60w The Summation Sign The uppercase Greek letter sigmais often used as a way of telling you to add your scores together it is therefore called in this context the summation sign If you follow the summation sign with a letter representing the variable you are measuring egthis is a shorthand way of telling you to add all of your scores together This notation allows us to write a very simple formula for the mean of a set of scores Xi N The subscript i associated with X is there to remind you that there is more than just one X there are a whole series of values to be added upStatistical purists would like us to put i1 under the summation sign and N above it to remind you to start adding with the first score and not to stop until you have added the Nth score but I will always useto mean add them all up so that extra notation wont be necessaryDefinitions of Key Terms Theoretical Statistics A branch of mathematics in which methods are derived for summarizing and drawing inferences about collections of numbersApplied Statistics A branch of mathematics which takes methods derived from theoretical statistics and applies them to practical problems in the analysis of dataDescriptive Statistics A branch of statistics in which the goal is to summarize a collection of numbers in a useful wayInferential Statistics A branch of statistics in which the goal is to draw inferences about a larger collection of numbers based on the information from a sampleNominal Scale A scale of measurement in which the levels can be named or numbered but the levels have no intrinsic order and the numbers would have no mathematical propertiesOrdinal Scale A scale of measurement in which the levels are ordered such as ranking paintings according to their beauty but the levels need not be equally spacedInterval Scale A measurement scale in which the levels are equally spacedthat is a unit at one part of the scale is equal to a unit at any other part of the scale However zero on the scale is not necessarily a true zero pointRatio Scale An interval scale that has a true zero pointie zero on the scale represents a total lack of the variable being measuredContinuous Variable Theoretically this is a variable that can be measured with infinite precision that is no matter how close two measurements are another one can be found between them Discrete Variable A variable whose levels are finite or countably infinite and do not have intermediate values eg the number of children in a familyPopulation Within statistics this is a usually large and sometimes infinite collection of numbers about which one is interestedSample A sample is a subset ideally random of a population that may be used for drawing inferences about the populationParameter A value that summarizes or describes a populationStatistic A value derived from the data in a sample Sample statistics are often used to estimate corresponding population parametersParametric Statistics A branch of statistics that deals with interval or ratio data and is often directed at drawing inferences about or estimating the parameters of a population distributionNonparametric Statistics A branch of statistics developed for use with ordinal or nominal data Because of the less restrictive assumptions required nonparametric statistics are sometimes preferred for dealing with intervalratio dataIndependent Variable A variable manipulated by the experimenter eg type of therapy administeredAlso a variable that has not been manipulated eg gender can be causal treated as an independent variable in statistical tests but cannot lead to conclusionsDependent Variable A variable that is measured but not directly manipulatedGenerally it is hoped that the dependent variable has been affected by one or more independent variablesRandom VariableA variable whose values depend on the outcome of random events usually probability density function these values are not equally likely but rather follow somePractice Exercises 1 For the following summation exercises the X values are 3 2 1 4 a What is the value of X 2b What is the value of X 2c What is the value of X 2d What is the value of X12 For the following summation exercises the X values are 5 1 3 2 and theY values are 1 4 2 6 a What is the value of XY b What is the value of XY c What is the value of XYChapter 2 Frequency Tables Graphs and DistributionsGuidelines for Frequency Distributions The procedure for constructing a grouped frequency distribution can be summarized in terms of the following steps and guidelinesStep 1 Choose the width i of the class intervalsFirst find the range of scores
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