math kms

Bar chart

A graph where the length or height of a bar represents values.

Class interval

A fixed range of values, used in the creation of a frequency distribution.

Difference score

The result of subtracting the mean in a distribution from a single score. Difference scores can be positive or negative.

Frequency distribution

A method for illustrating how often each score or group of scores occurs in a distribution.

Frequency polygon

A graphical representation of a frequency distribution that uses a continuous line to show the number of values that fall within a class interval.

Histogram

A graphical representation of a frequency distribution that uses bars of different heights or lengths to show the number of values that fall within each class interval.

Interval level of measurement

A level of measurement that places a variable’s values into categories that are equidistant from each other, as when points are evenly spaced along a scale.

Levels of measurement

The four ways that numbers can have meaning when used as scores—nominal, ordinal, interval and ratio. The level of measurement determines the methods that can reasonably be used to summarize scores mathematically.

Line chart

A graph where the height of a line represents values.

Measurement

A procedure that assigns scores to the values of a variable in a meaningful way.

Midpoint

The central point in a class interval.

Nominal level of measurement

A low level of measurement that involves using numbers only as names for categories, not as quantities.

Ordinal level of measurement

A level of measurement that places a variable’s value into a category and assigns that category an order with respect to other categories.

Pie chart

A circular graph that resembles a pie with various slices. Each slice shows the percentage of things that are in each category of a nominal-level variable. The percentages add up to 100%.

Range

The difference between the highest and lowest score in a distribution.

Ratio level of measurement

A level of measurement defined by the presence of an absolute zero on the scale.

Standard deviation

The average amount of variability in a set of scores or the scores’ average distance from the mean.

Variability

How much scores differ from one another. The amount of spread or dispersion in a set of scores.

Variance

The standard deviation squared.

Classical test theory

A framework for conceptualizing score reliability that defines a score as being a function of a true score (the average score an individual would get on a measure) and a random error score that moves the true score higher or lower than it would typically be.

Concurrent criterion validity

How well a test’s scores correlate with a criterion that exists in the present.

Construct-based validity

How well a test score reflects an abstract hard-to-observe concept, such as intelligence or aggression.

Content-based validity

A characteristic of items on a test that are a fair representation of the items that could be on the test.

Criterion-based validity

A type of validity that examines how well a test correlates with an external criterion that exists in either the present (concurrent) or the future (predictive).

Cronbach’s alpha

A coefficient of reliability that estimates internal consistency among the items on a measure. It generally ranges from .00 to 1.00.

Dependent variable

The outcome variable in a research study, or the variable that a researcher believes is affected by some other variable (the independent variable).

Error score

The part of a test score that is random and contributes to the unreliability of a test.

Independent variable

The causal variable in a research study, or the variable that a researcher believes affects some other variable (the dependent variable).

Internal consistency reliability

A type of reliability that reflects how well items on a single test correlate with each other.

Interrater reliability

A type of reliability that reflects how well two different human scorers agree.

Observed score

The score that an individual gets on a test or measure.

Predictive criterion validity

How well a test’s scores correlate with a criterion that will exist in the future.

Reliability

The degree to which scores from a measure are random.

Test–retest reliability

A type of reliability that examines a test’s consistency over time.

True score

The average score an individual would get if they took the same test or measure an infinite number of times.

Validity

The degree to which scores from a measure represent the intended construct.

Phi coefficient

X-Nominal (college major)

Y- Nominal (biological sex, such as male or female).

The correlation between college major and sex

Rank biserial coefficient

X-Nominal (college major)

Y-Ordinal (rank in high school graduating class)

The correlation between college major and rank in high school

Point biserial coefficient

X- Nominal (family configuration, such as two-parent or single-parent)

Y-Interval (grade point average)

The correlation between family configuration and grade point average

Spearman rank coefficient

X-Ordinal (rank in high school graduating class)

Y-Ordinal (rank in high school graduating class)

The correlation between high school rank and medical school rank

Pearson correlation coefficient

X-Interval (number of math problems solved)

Y-Interval (IQ intelligence)

The correlation between number of math problems solved and intelligence