Transcript Norms & Norming

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
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•
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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
– http://alpha.fdu.edu/psychology/oat_cereal.htm
– 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)
N  xy
2
2
( x )( y )
• Raw Score Formula
N XY ( X)(Y)
N  X 2  (X 2 ) N Y 2 (Y 2)
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
ˆzy  rxy zx
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 = .82 + .03(50) = 2.3
• GPA = .82 + .03(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
Sy x  Sy 1 rxy
2