Level of measurement

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Level of measurement (LoM) is an important characteristic of data. The LoM determines what types of descriptive, graphical, and inferential statistical analyses can be used. There are four levels of measurement:

Levels of measurement

1. Categorical/nominal
2. Ordinal
3. Interval
4. Ratio

It is possible to recode a variable into a lower level of measurement, but not the other way around. So, data can be simplified, but not complexified.

Non-parametric statistics are appropriate for categorical and ordinal data. Parametric statistics are appropriate for interval and ratio data.

However, social science researchers often treat composite scores based on multiple items measured using ordinal scales (e.g,. using verbal frequency scales) as continuous for the purposes of parametric analyses.

## Categorical/nominal

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* The simplest type of variable is dichotomous (or binary, e.g., 0 = male/ 1 = female; 0 = black/ 1= white; 0 = yes/ 1 = no).
* Categorical or nominal variables simply provide numerical labels (or names) for two or more categories e.g., 0 = red/ 1 = blue/ 2 = green / 3 = yellow; 0 = car; 1 = bus; 2 = bicycle; 3 = aeroplane; 4 = train.

## Ordinal

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1. When categorical variables can be meaningfully ordered, they become ordinal variables
2. The distance between the ordered categories may vary
3. e.g., 1 = 1st, 2 = 2nd, 3 = 3rd in a race; verbal frequency scale (0 = never, 1 = sometimes, 2 = often, 3 = always)

## Interval

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1. Ordered categories (discrete values) which have equal distances (e.g., Strongly Disagree - Disagree - Neither Agree or Disagree - Agree - Strongly Agree)
2. Allows use of parametrics statistics (which assume a normal distribution)

## Ratio

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1. Continuous (not discrete) - values can take on (in theory) infinite decimal points
2. Has a meaningful 0 (e.g., the 0 point isn't arbitrary), which allows ratio comparisons (e.g,. according to the sample of participants, males are, on average, 20% taller than females).

## See also

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* Level of measurement (Wikipedia)
* Psychological statistics
* Response formats
* Units of measurement

## External links

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* Summary of univariate descriptive statistics and graphs for the four levels of measurement (pdf)