Norms & Norming Raw score: straightforward, unmodified accounting of performance Norms: test performance data of a particular group of test takers that are designed for use as a reference for interpreting individual test scores Norm group (sample): reference group whose scores are the standard of comparison for future test takers. The mean & S.D. obtained by this group are the points of comparison for standard scores.

Norms (cont.) Norm-referenced test: tests from which scores are given meaning by their relative standing compared to a particular group of test takers (norm group) Norming: the process of developing norms

Norming Norm sample should be: –Representative Stratified sampling & stratified-random sampling Purposive v. incidental/convenience samples –Large –Current –Appropriate to a particular test taker Norming procedures and sample should be described in detail in test manual

Norms Norms based on standard set of administration procedures Types of norms: –National v. local norms –Age v. grade norms Age equivalents & Grade equivalents – –Subgroup norms

Norm v. Criterion-referenced tests Norm-referenced: Individuals’ scores given meaning by comparison to normative sample –Examples: ACT, GRE, WAIS III, Iowa Tests of Basic Skills Criterion-referenced: Individuals’ scores given meaning by comparison to a standard or criterion –Index of “Mastery” How is the criterion established? –Examples: Driver’s license exam; ISAT; academic skills assessment

Correlations Definition: an expression of the degree and direction of correspondence or relationship between two variables Coefficient of correlation: numerical index of this relationship Examples: –Pearson r –Spearman rho

Correlations (cont.) Correlations & Measurement –What is the relationship between 2 types of measurement? Will scores be similar on 2 different measures? Will they vary in some relationship to each other? Are they not related at all? –Estimates of reliability & validity Relationship, not Causation –Prediction

Pearson r Formulas Average of a set of cross products Deviation Score Formula (x=X-M)(y=Y-M) Raw Score Formula

Summary Statements Correlations vary between -1 & +1 –Sign tells direction of relationship –# tells the magnitude/strength of relationship r=slope of the straight line that comes closest to describing the relationship between the scores Correlation of 0 means no linear relationship

Coefficient of Determination The square of the correlation coefficient tells what proportion of variance is explained or accounted for, or how much much variance can be predicted from one variable given knowledge of the other. –Example: If r between GPA & number of beers consumed per week is -.7, we can explain 49% of variation in grades by knowledge of how much beer consumed.

Factors Affecting Strength of Correlations Homogenous Groups v. Heterogeneous Groups –Heterogeneous groups produce higher r Restriction of range Heterogeneous groups, if there is variability, it is real variability, not attributable to error Reliability of scores –Error in one or more sets of scores causes r to be lower –Garbage in, Garbage out

Regression Analysis of relationships among variables Prediction of performance on one variable from another variable –ACT & GPA –GRE & GPA Formula

Regression (cont.) Regression to the mean –Example r xy=.8, z of x = 1 Y predicted =.8(1)=.8.8 is closer to the mean (0) than 1 –All scores contain error, no correlations are perfect, hence multiplying an obtained z score will result in a predicted z score that will be a lower absolute number (closer to the mean).

Regression (cont.) Regression line –Y =a = bX b = slope a = intercept –Example from Text Predicting GPA from entrance exam GPA = (50) = 2.3 GPA = (85)=3.7

Multiple Regression More than one predictor variable Takes into account intercorrelations among predictor variables & dependent variable Example –College GPA predicted from H.S. GPA & ACT

Accuracy of Prediction Standard Error of Estimate: Standard deviation of the difference between the observed & predicted scores; standard deviation of the errors we make in predicting Y from X –Dependent on: 1) the S.D. of y & 2) r between x & y; Larger r, the less error in prediction