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:RepresentativeStratified sampling
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1. 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.
2. 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
3. Norming Norm sample should be:
Stratified sampling & stratified-random sampling
Purposive v. incidental/convenience samples
Appropriate to a particular test taker
Norming procedures and sample should be described in detail in test manual
4. Norms Norms based on standard set of administration procedures
Types of norms:
National v. local norms
Age v. grade norms
Age equivalents & Grade equivalents
5. 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
6. Correlations Definition: an expression of the degree and direction of correspondence or relationship between two variables
Coefficient of correlation: numerical index of this relationship
7. 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
8. Pearson r Formulas Average of a set of cross products
Deviation Score Formula (x=X-M)(y=Y-M)
Raw Score Formula
9. 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
10. 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.
11. 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
12. Regression Analysis of relationships among variables
Prediction of performance on one variable from another variable
ACT & GPA
GRE & GPA
13. Regression (cont.) Regression to the mean
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).
14. Regression (cont.) Regression line
Y =a = bX
b = slope
a = intercept
Example from Text
Predicting GPA from entrance exam
GPA = .82 + .03(50) = 2.3
GPA = .82 + .03(85)=3.7
15. Multiple Regression More than one predictor variable
Takes into account intercorrelations among predictor variables & dependent variable
College GPA predicted from H.S. GPA & ACT
16. 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