Ch 4 definitions: Measurement Scales, Distributions, and Standard Scores

Flashcards covering levels of measurement, distributions, and standard scores based on the provided lecture notes.

What is the concept of level of measurement and which scales are typically included?

The relationship among the numbers assigned to data; the common scales are nominal, ordinal, interval, and ratio.

What is nominal data?

Data consisting of labels or categories without intrinsic order; used for frequency counts, mode, and chi-square tests.

What is ordinal data?

Data with a meaningful order but unknown or non-constant distances between categories; used for rank ordering, median, and percentiles.

What is interval data?

Ordered data with equal intervals between values but no true zero point; allows addition, subtraction, and calculation of mean and standard deviation.

What is ratio data?

Interval data with a true zero; allows multiplication and division; supports all statistical operations (e.g., height, weight).

What is a frequency distribution?

A summary showing how many observations fall into each category or score range.

What is a class interval?

A range of scores used to group data for frequency distributions and histograms.

What is the normal distribution?

A theoretical, bell-shaped, symmetric distribution where most scores cluster around the mean.

What is the mean?

The arithmetic average: sum of all scores divided by the number of observations.

What is the median?

The middle value when the data are ordered.

What is the mode?

The most frequently occurring value in the data set.

What is a percentile?

A value below which a specified percentage of observations fall.

What is standard deviation?

A measure of variability representing the average distance of scores from the mean; the most commonly used measure of dispersion.

What are descriptive statistics?

Statistics that summarize central tendency and variability of a data set.

What is the correlation coefficient (r)?

A statistic describing the strength and direction of the linear relationship between two variables; Pearson's r is the common method.

What is a z-score?

A standard score indicating how many standard deviations a value is from the mean, computed as (X - mean)/SD.

What is a T-score?

A standardized score with a mean of 50 and a standard deviation of 10; always nonnegative.

What is a Stanine score?

A nine-point standard-score scale used to describe a distribution in nine qualitative bands (e.g., below average to above average).

What is a linear transformation?

A transformation that changes the scale by multiplying by a constant and/or adding a constant; it does not alter the underlying relationships.

What is a nonlinear (data) transformation?

A transformation that changes the distribution shape or variance non-proportionally (e.g., log, square root) to normalize data.

What are raw scores?

The original, untransformed scores obtained on a test.

What is a proportion?

A part-to-whole ratio expressed as a value between 0 and 1 (or 0% to 100%).

What is a probability distribution?

A function that describes the likelihood of different outcomes; the normal distribution is a common example.