# Ordinal measures and normality

## Ordinal level measurement can become interval level with assumed normality

__and__

**ordinal outcomes****some unvalidated measures**. If you run

__statistics on the ordinal variable and its distribution__

**skewness and kurtosis****meets the**(skewness and kurtosis statistics are

__assumption of normality__**less than an absolute value of 2.0**), then you can "

**upgrade**" the variable to a

**continuous level of measurement and analyze it using more powerful parametric statistics**.

This type of thinking is the reason that the

**SAT, ACT, GRE, MCAT, LSAT, and validated psychological instruments**are perceived at a continuous level. The scores yielded from these instruments, by definition, are

**not continuous because a "true zero" does not exist**. Scores from these tests are often

**norm- or criterion-referenced**to the population so that they can be interpreted in the correct context. Therefore, with the

**subjectivity and measurement error associated with classical test theory and item response theory**, the scores are actually

**ordinal**.

With that being said, if the survey instrument or ordinal outcome is

**used in the empirical literature ofte**

**n**and it

**meets the assumption of normality as per skewness and kurtosis statistics**, treat the ordinal variable as a continuous variable and run analyses using

**parametric statistics****(t-tests, ANOVA, regression)**versus

__non-parametric statistics__(Chi-square, Mann-Whitney U, Kruskal-Wallis, McNemar's, Wicoxon, Friedman's ANOVA, logistic regression).