Valdosta State University
Chapter 4: Of Tests and Testing
12 Assumptions in Psychological Testing and Assessment
* Assumption 1: Psychological traits and states exist
* Assumption 2: Psychological traits and states can be quantified and measured
* Assumption 3: Various approaches to measuring aspects of the same thing can be useful
* Assumption 4: Assessment can provide answers to some of life’s most momentous questions
* 12 Assumptions in Psychological Testing and Assessment
* Assumption 5: Assessment can pinpoint phenomena that require further attention or study.
* Assumption 6: Various sources of data enrich and are part of the assessment process.
* Assumption 7: Various sources of error are part of the assessment process.
* 12 Assumptions in Psychological Testing and Assessment
* Assumption 8: Tests and other measurement techniques have strengths and weaknesses
* Assumption 9: Test-related behavior predicts non–test-related behavior
* Assumption 10: Present-day behavior sampling predicts future behavior
* 12 Assumptions in Psychological Testing and Assessment
* Assumption 11: Testing and assessment can be conducted in a fair and unbiased manner
* Assumption 12: Testing and assessment benefit society
Most Controversial Assumption?
* Why?
What are Norms?
* Derived typical test performance of a standardization sample
* The test score distribution that provides the average or typical (normal) score level on a test
Standardization (normative) Sample
* The normative sample is a representative subset drawn from the broader target population
* Typically, a large random sample
* Sample size should be large enough to obtain stable values.
Sampling Techniques
* Randomization
* every case has an equal chance of selection
* Stratified
* representative proportions of groups
* e.g. age, socioeconomic level, ethnicity
* Incidental
* Convenience sampling
* Not a desired procedure
Types of Norms
* Developmental Norms
* Indicates developmental level attained
* Age equivalent norms (Mental Age)
* e.g., a 7 year old who scores the same mean obtained by 10 year old children has a mental age of 10.
* Grade equivalent norms
* e.g., average score of 4th graders is 23, a child with a raw score of 23 is given a 4th grade age equivalence.
Norm-Referenced (Within group) Norms
* Individual performance is evaluated in reference to a standardization group
* The same test is used to compare other groups of test-takers
* Deviation IQs
What is Correlation?
* Index of linear association between two variables (X and Y)
* Does not suggest cause and effect
* Computed value is called a coefficient
* Best example is the Pearson product-moment correlation coefficient (r)
Pearson Formula (definitional)
* Co-variation between X and Y
* Ratio of the variability between X and Y
Values of r
* Coefficient values range between -1 and + 1
* What does 0 mean?
* The closer the coefficient value is to 0, the weaker the association between two variables
* The further a coefficient moves from 0, the stronger the association between two variables
* Coefficients of -1 and +1 have the same magnitude of association
Coefficient of Determination (r2)
* Correlation coefficient squared
* The value indicates the proportion of the variation in Y scores that is a function of the X scores
* i.e., the variance in X explained by Y
Graphing Correlation
* Correlations between two variables can be displayed in a scatterplot
* Individual scores are plotted on two-dimensional axes
* X scores plotted on horizontal axis (abscissa)
* Y scores plotted on vertical axis (ordinate)
Positively Correlated
* As X increases, Y increases
Negatively Correlated
* As X increases, Y decreases
No Correlation
* No relationship between X and Y
Curvilinear Relationship
* Non-linear relationship between two variables
* The scatterplot has a significant curve
* U-shaped curve
* Umbrella-shaped curve
* S-shaped curve
Other Correlation Coefficients
* Spearman rho
* Used in rank-order correlation
* ordinal scales
* Evaluate the differences (or agreement) between rankings of two variables
* Students’ scores on a mid-term 1 and mid-term 2 are ranked from lowest to highest; the rankings are correlated
Point Biserial
* Comparison of one continuous variable and one dichotomous variable
* Dichotomous variables include Yes/No or True/False scales
* Correlation between Age (continuous) and Active Class Participation (Yes or No)
Phi
* Correlation between two dichotomous variables
* Correlation between Active Class Participation (Yes or No) and Mid-term results (Pass or Fail)
Biserial r
* Comparison of one continuous variable and one artificially dichotomized variable
* An artificially dichotomized variable is a continuous variable that is transformed to dichotomous variable
* e.g., Age in years converted to age groups
* 18-25, 26-30, 31-40, 40-50, 51-60, etc.
Tetrachoric
* Correlation between two artificially dichotomized variables
* Correlation between age groups and mid-term score
Roles of Correlations in Testing
* Test-retest reliability
* Correlation between scores on the same test at two different times
* Correlation of GRE in the Fall and Spring semesters
* Criterion (predictive) validity coefficients
* Correlation between test scores and results of an independent criterion
* Correlation between SAT and College GPA
* Convergent validity coefficients
* Correlation between scores on two conceptually similar tests
* Correlation between self-esteem and self-concept
Regression
* Degree of predictability between two variables
* Extends the concept of correlation to the prediction of a test score (Y) based on a another test score (X)
Regression Equation
Y’ = a + bX
* X = predictor (test score)
* Y’ = criterion (predicted score)
* a = y-intercept (criterion score if the predictor score is 0)
* b = slope (correlation between the predictor and criterion)
Regression Line
* Line drawn through the scatter of scores
* The regression line represents the Principle of Least Squares
* least squared deviation from the line
* The line demonstrates the best fit for all data points
Slope
* Essentially, the correlation coefficient
Y-Intercept
* Where the regression line crosses the Y-axis
* Criterion score if the predictor score is 0
a = Y – bX
* Y is the mean of the Y scores
* X is the mean of the X scores
Regression Example
Y’ = 2 + 0.67X
* What is the predicted score (Y’) if X is 10?
Regression Line
* Line drawn through the scatter of scores
* The regression line represents the Principle of Least Squares
* least squared deviation from the line
* The line demonstrates the best fit for all data points
* Regression Line Example
Residuals
* Difference between the predicted (Y’) and observed criterion (Y) values
* Y – Y’
* Principle of Least Squares
* Minimize the deviation between Y and Y’
Standard Error of Estimate
* Error in the prediction estimate
* Standard deviation of the residuals
* The square root of the residual variance
* The lower the standard deviation, the lower the degree of error in the regression equation
Inference from Measurement
* Meta-Analysis
* Statistical combination of studies
* Culture and Inference
* Individualists vs. collectivists
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