ordinal

(adjective)

Of a number, indicating position in a sequence.

Related Terms

Examples of ordinal in the following topics:

  • Collecting and Measuring Data

    • There are four main levels of measurement: nominal, ordinal, interval, and ratio.
    • There are four main levels of measurement used in statistics: nominal, ordinal, interval, and ratio.
    • Examples of ordinal data include dichotomous values such as "sick" versus "healthy" when measuring health, "guilty" versus "innocent" when making judgments in courts, "false" versus "true", when measuring truth value.
    • Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variables, whereas ratio and interval measurements are grouped together as quantitative variables, which can be either discrete or continuous, due to their numerical nature.
    • Distinguish between the nominal, ordinal, interval and ratio methods of data measurement.

  • Types of Variables

    • Categorical variables may be further described as ordinal or nominal.
    • An ordinal variable is a categorical variable.
    • The categories associated with ordinal variables can be ranked higher or lower than another, but do not necessarily establish a numeric difference between each category.
    • Variables can be numeric or categorial, being further broken down in continuous and discrete, and nominal and ordinal variables.
    • Distinguish between quantitative and categorical, continuous and discrete, and ordinal and nominal variables.

  • Averages of Qualitative and Ranked Data

    • Stevens proposed his typology in a 1946 Science article entitled "On the Theory of Scales of Measurement. " In that article, Stevens claimed that all measurement in science was conducted using four different types of scales that he called "nominal", "ordinal", "interval" and "ratio", unifying both qualitative (which are described by his "nominal" type) and quantitative (to a different degree, all the rest of his scales).
    • The ordinal scale allows for rank order (1st, 2nd, 3rd, et cetera) by which data can be sorted, but still does not allow for relative degree of difference between them.
    • In 1946, Stevens observed that psychological measurement, such as measurement of opinions, usually operates on ordinal scales; thus means and standard deviations have no validity, but they can be used to get ideas for how to improve operationalization of variables used in questionnaires.
    • An opinion survey is an example of a non-dichotomous data set on the ordinal scale for which the central tendency can be described by the median or the mode.

  • When to Use These Tests

    • "Ranking" refers to the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted.
    • In statistics, "ranking" refers to the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted.
    • In another example, the ordinal data hot, cold, warm would be replaced by 3, 1, 2.

  • Mann-Whitney U-Test

    • The responses are ordinal (i.e., one can at least say of any two observations which is the greater).
    • a measure of the central tendencies of the two groups (means or medians; since the Mann–Whitney is an ordinal test, medians are usually recommended)
    • $U$ remains the logical choice when the data are ordinal but not interval scaled, so that the spacing between adjacent values cannot be assumed to be constant.
    • For large samples from the normal distribution, the efficiency loss compared to the $t$-test is only 5%, so one can recommend Mann-Whitney as the default test for comparing interval or ordinal measurements with similar distributions.

  • Levels of Measurement

    • This is what distinguishes ordinal from nominal scales.
    • Unlike nominal scales, ordinal scales allow comparisons of the degree to which two subjects possess the dependent variable.
    • On the other hand, ordinal scales fail to capture important information that will be present in the other scales we examine.
    • Like an ordinal scale, the objects are ordered (in terms of the ordering of the numbers).
    • However, there are extreme situations in which computing the mean of an ordinally-measured variable can be very misleading.

  • Types of variables

    • A variable with these properties is called an ordinal variable.
    • To simplify analyses, any ordinal variables in this book will be treated as categorical variables.

  • Statistical Literacy

    • Therefore, SAT is measured on either an ordinal scale or, at most, an interval scale.

  • Rank Correlation

    • A rank correlation is a statistic used to measure the relationship between rankings of ordinal variables or different rankings of the same variable.
    • A rank correlation is any of several statistics that measure the relationship between rankings of different ordinal variables or different rankings of the same variable.

  • Describing Qualitative Data

    • When the categories may be ordered, these are called ordinal variables.
    • Categorical variables that judge size (small, medium, large, etc.) are ordinal variables.
    • Attitudes (strongly disagree, disagree, neutral, agree, strongly agree) are also ordinal variables; however, we may not know which value is the best or worst of these issues.