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# PSY 343 Week 3 Notes PSY 343

DePaul

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This 10 page Class Notes was uploaded by Tatum Notetaker on Friday September 23, 2016. The Class Notes belongs to PSY 343 at DePaul University taught by Douglas Cellar in Fall 2016. Since its upload, it has received 6 views. For similar materials see Intro to Psychological Measurement in Psychology at DePaul University.

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Date Created: 09/23/16

PSY 343 Ch. 3 Notes Purpose of Norms o Test norms are meant to translate the raw score into a normed score o Raw score: immediate result of an individual’s responses to the test o Normed score: the individual’s raw score is compared with scores of individuals in the norm group Also known as derived scores or scale scores The objects we study vary along each of these variables from high to low, more to less, or similar set of quantifiers Three levels of generality o Construct: verbal descriptions and definitions of the variable o We measure the variable; the operational definition of a variable o Raw data – these are the numbers that result from application of the measures Descriptive statistics: summarize or describe raw data to aid our understanding of the data Inferential statistics: help us draw conclusions about what is probably true in the populations based on what we discovered about the sample Scales o Nominal scales: distinguishes objects by tagging each with a number Least sophisticated Don’t signify more or less, bigger or smaller, etc. o Ordinal scale: objects are assigned numbers that indicate an ordering o Interval scale: places objects in order and does so with equal intervals Lacks a true zero point, has a zero but one that does not represent a complete absence of the variable o Ratio scale: places objects in order, does so with equal intervals, and has a true zero point o We need to worry about the nature of our scales in order to make meaningful statements about our measurements Frequency distribution: organizes data into groups of adjacent scores o Reveals features such as the range of scores and the area where scores are concentrated o Often converted into a graphic form such as a frequency histogram or frequency polygon Central tendency: the center around which the raw data tend to cluster o Three common measures of central tendency Mean: arithmetic average, represented by either M or X (with a bar on top, called X bar) M= ΣX N X = score or raw data N = number of scores = a summation sign 2 Median: middle score when scores are arranged in order from low to high Mode: most frequently occurring score o Variability: variation in the data Range: distance from the lowest to the highest score, simplest index of variability Standard deviation: most widely used index of variability 2 SD= (X−M) or √ N Σx2 SD= √ N When SD is calculated on a sample but is intended as an estimate of SD in a population, the “N” in the formula is replaced by “N – 1” 2 Variance: SD Interquartile range: the distance between the first and third quartiles, 25th and 75th percentiles o z-Scores: used to map out the normal curve in terms of areas under the curve X−M z= SD X = individual score or data point M = mean SD = standard deviation The distribution of z scores has a mean of 0 and SD of 1 3 Normal curve: bell curve o Distribution is unimodal or has one “mode” or “hump” o It is symmetrical about its central axis o The curves “tails” are asymptotic to the base, or they continue until infinity o Nearly all the area under to curve is contained within +/- 3 (SD) units o Distributions may “depart from normality” Kurtosis: the “peakedness” of the distribution Leptokurtic – distribution is more peaked Platykurtic – distribution is flatter than normal Skewness: where the peak tends toward, peak is not symmetrical on both sides Negative skewness, the peak is at the right of the graph, long tail to the left and bulk of scores to the right Positive skewness, the peak is at the left of the graph, long tail to the right and bulk of scores to the left Graphs are typically unimodal, but sometimes may be bimodal, trimodal, etc. Raw scores: most immediate result from scoring a test Theta : The IRT score is a function of the examinee’s responses interacting with the characteristics of the items, and that IRT score is theta o Has some properties of a raw score and some properties of a normed score 4 Types of norms o Percentile rank: the percentage of cases in the norm group falling below a given raw score One starts with a given score, then finds the percentage of cases falling below that Strengths: concept is simple, easy to calculate from a norm group Drawbacks: many confuse it with percentage- right score (used with tests in classrooms), most percentile ranks are bunched up in the middle of the distribution and spread out at the two extremes o Percentile: a point on a scale below which a specified percentage of cases falls One starts with a given percentage, then finds the raw score corresponding to this point o Standard scores: conversion of z-scores into a new system with an arbitrarily chosen mean (M) and standard deviation (SD) SDs SS=SD (X−M r) s r SS = desired standard score SD =sstandard deviation in standard score system SD =rstandard score in raw score system M =rmean in raw score system M =smean in standard score system X = raw score 5 When X is translated into z-score form, the formula is SS=z(SD)+M s s Most standard scores are linear transformations of raw scores Some standard scores are derived by a nonlinear transformation, which may be used to yield a distribution of scores that is normal, sometimes referred to as a normalized standard score T-scores: standard scores with M = 50 and SD = 10 Stanines: standard score system with M = 5 and SD = ~2 Constructed to divide the normal distribution into nine units and have the units cover equal distances on the base of the normal curve Merit of simplicity, but bad for reporting group averages Normal curve equivalent: standard score system developed so that the NCE’s are equal to percentile ranks at points 1, 50, and 99 No advantage over other standard score systems, easily confused with percentiles Multilevel test – least partially distinct tests at different age or grade levels Strengths of standard scores – provide a convenient metric for interpreting test performance in a wide variety of circumstances, avoid the problem of having 6 scores bunched up in some areas and spread out in others Drawbacks – relating them to the normal curve and z-scores has little value except when working with the cognoscenti, to make sense of a standard score one needs to be reminded of the M and SD for the systems Developmental norms: traits being measured develop systematically with time o Two commonly used: age equivalents (AE) and grade equivalents (GE) Mental Age (MA) – determined by finding the typical or median score for examinees at successive age levels Grade Equivalents (GE) – developed for administering a test to students in different grade levels; typical or median performance in each grade is then obtained o Other developmental norms Tests based on stage theories of human development Anthropometric measurements such as height and weight o Strengths – have a naturalness to their meaning, provide a basis for measuring growth across multilevel tests o Drawbacks – only applicable to variables that show clear developmental patterns, uncontrolled standard deviations, usually reserved for grade equivalents 7 Two students scoring at the 75 percentile or at a standard score of 60 did not necessarily answer the same items correctly Norm Tables o You always start with a raw score (RS), then convert it to a normed score Barnum Effect: people’s tendency to believe high-sounding statements that are probably true about everyone and contain no unique, specific information arising from the test Norm Groups o National norms: norms based on a group that is representative of the segment of the national population for whom the test is intended o International norms – based on schoolchildren drawn from groups of countries that have chosen to participate in the studies o Convenience groups: norms based on one or several groups that are “conveniently” available for testing Some tests will present several different norms based on different groups When you aspire to have a national norm but make no pretense about actually having such a norm o User norms: based on whatever groups actually took the test, usually within some specified time There is no a priori attempt to ensure that the group is representative of any well-defined population 8 o Subgroup norms: taken from the total norm group, may be provided by sex, race, socioeconomic status, occupational group, geographic region, etc. o Local norm: prepares a distribution of its own students’ scores and interprets each students’ score in relation to the scores of other students in the school o Institutional norm: based on averages for individuals within institutions o Criterion-referenced: when you compare individual scores to the test itself Think about school tests, we deem 90% satisfactory and 60% as unsatisfactory Proficiency levels, or performance standards o Norm-referenced: when you compare individual scores to the average of all individuals’ scores who have taken the test Standardization: individuals in the norm group are tested in a norming program o Stability of the norm group is determined by the size of the group (aka number of cases in the standardization program) o How to determine the representativeness of a norm group: May claim that the test is representative of a particular population May simply present the norm sample as a convenience or user group norm o Key factor is relation of the info to the trait being measured o Special issues 9 Effect of non-participation on data and interpretation Effect of motivation (faking good or social desirability) 10

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