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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