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Tests of correlation



Types of data, nominal data, ordinal data, interval data

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[In this article the equations have had to be omitted. Download the whole article in its original format.] There can be three types of data: Nominal Data: This is data in the form of frequencies fitting discrete, distinct categories. For example, we can count the number of boys and girls in a class. Each individual is either a boy or a girl and there is no sense in which the boys and the girls can be placed into a rank order. Ordinal Data: Ordinal data are measures of physical quantities that can be ranked. For example, the variable X could measure the number of days individuals have been subject to a special diet; the variable Y could measure the position of those individuals in a race. Here, it is meaningful to ask how does the position of an individual, that is his rank, in terms of values of X correlate with his position, or rank, in terms of Y. Interval Data: Data is said to be at interval level when there is a meaningful continuous scale of measurement such that equal differences between values in the scale genuinely correspond to real differences between the physical quantities that the scale measures. An example of a set of interval level data would be a collection of measurements of height. Here it is meaningful to say that the difference of height between a person who is 1.80m and one who is 1.70m tall is equal to the difference of height between a person who is 1.90m and one who is 1.80m tall. Equal differences in the scale correspond to equal differences in the physical quantities they measure. All interval level data can be placed in rank order; in other words, interval level data can be "reduced" to ordinal level data. Ordinal level data cannot necessarily be promoted to interval level data. Interval level data contain more information than ordinal level data.
Contents of
Tests of correlation

1 Scatter diagrams
2 Tests of Correlation
3 Types of data, nominal data, ordinal data, interval data
4 Correlation and data types
5 Pearson's product moment correlation coefficient - testing correlation at interval level
6 Spearman's Coefficient of Rank Correlation

Related articles: (1) Graphical presentation of data, (2) Tests of correlation