CH 2: Basic Statistics of Measurement

Measurement scale

System describing the mathematical properties of measurement.

Nominal scale

Categories used only as labels; no meaningful order.

Ordinal scale

Categories have an order, but intervals are not necessarily equal.

Interval scale

Equal intervals but no meaningful absolute zero.

Ratio scale

Equal intervals and a meaningful absolute zero.

Distribution

Collection of scores and how those scores are distributed.

Frequency distribution

Shows how often each score occurs.

Frequency

Number of times a score occurs.

Relative frequency

Proportion or percentage represented by a score/category.

Central tendency

Statistics describing the center/typical value of scores.

Mean

Arithmetic average of scores.

Median

Middle score when scores are ordered.

Mode

Most frequently occurring score.

Variability

Degree to which scores differ or spread out.

Range

Difference between highest and lowest score.

Variance

Average squared deviation from the mean.

Standard deviation (SD)

Typical amount scores differ from the mean.

Normal distribution

Symmetrical, bell-shaped distribution where mean = median = mode.

Positive skew

Distribution with a tail toward higher scores (right).

Negative skew

Distribution with a tail toward lower scores (left).

z score

Number of standard deviations a score is from the mean.

Correlation

Relationship between two variables.

Correlation coefficient

Number describing strength and direction of a relationship.

Positive correlation

Variables tend to increase/decrease together.

Negative correlation

One variable increases as the other decreases.

Zero correlation

No linear relationship between variables.

Perfect positive correlation

r = +1.00

Perfect negative correlation

r = −1.00

Magnitude

Absolute strength of a correlation.

Pearson correlation

Measures the linear relationship between two quantitative variables.

Scatterplot

Graph displaying paired scores for two variables.

Restricted range

Limited variability in scores; can reduce correlations.

Outlier

Extreme observation that can strongly affect statistics.

Linear regression

Procedure for predicting one variable from another.

Predictor variable

Variable used to make a prediction.

Criterion variable

Variable being predicted.

Regression equation

Equation used to predict criterion scores.

Predicted score

Score estimated using a regression equation.

Residual/error

Difference between actual and predicted score.

Standard error of estimate (SEE)

Amount of error associated with predicted scores.