Statistical Methods for Dichotomous Variables

Types of Tests

• A performance test measures a person's observable activity.
• A speed test measures a person's ability to perform a task quickly.
• An aptitude test measures a person's potential for learning or acquiring skills.

Test Characteristics

• A power test presents a smaller number of items, but more complex as compared to speed tests.

Key Figures

• Romanes is regarded as the Father of Comparative Psychology.
• Galton is considered the founder of the Mental Testing Movement.

Psychological Laws

• Weber's Law states that the just-noticeable difference (JND) is proportional to the intensity of the stimulus.

Correlation Coefficients

• The phi coefficient (φ) is used when both variables are dichotomous and at least one of them is a true dichotomous variable.
• The coefficient of determination (r^2) tells us the proportion of variance in the dependent variable that is predictable from the independent variable.
• The coefficient of non-determination (1 - r^2) is the measure of non-association between two variables.
• Multiple regression is appropriate when there are multiple independent variables.

Statistical Tests

• The correlation coefficient (rho) is used when both data are ordinal.
• The point-biserial correlation coefficient is used when one datum is nominal and the other is at the interval level.
• The McNemar test is used on paired nominal data.
• The chi-square test is used to evaluate the relationship between two variables in the population using frequency data from a sample.

z-Scores and Regression

• The formula to convert a raw score into a Z-score is: z = (X - μ) / σ
• The formula for the regression line or the line of best fit is: Y' = a + bX
• The principle of least squares in regression analysis is to minimize the sum of the squared errors.

Intelligence Quotient (IQ)

• The formula for the Pearson Product Moment Correlation Coefficient is: r = Σ[(xi - μx)(yi - μy)] / sqrt[Σ(xi - μx)^2 * Σ(yi - μy)^2]
• The Wechsler-Bellevue Intelligence Scale was developed by David Wechsler.
• The formula for calculating IQ is: IQ = (MA / CA) * 100, where MA is mental age and CA is chronological age.

Scales and Measurement

• The purpose of a nominal scale is to categorize or classify data into distinct groups.
• Factor analysis is a data reduction technique.
• Lord is known as the Father of Classical Test Theory.
• Classical Test Theory assumes that errors of measurement are random and independent.
• The standard error of measurement (SEM) tells us the amount of error in the measurement of a person's true score.