Explain the difference between (a) ordinal and cardinal scales, and (b) interval scales and rati

step 1 The nominal scale defines the identity property of data. This scale has certain characteristics,

Explain the difference between (a) ordinal and cardinal...

Key Concepts

Interval Scale

An interval scale is a numerical scale in which the difference between values is meaningful and consistent, allowing for the measurement of the degree of difference between items. However, it lacks a true zero point, which means that ratios between numbers are not inherently meaningful. For example, while the difference in temperature between two values is calculable, stating that one temperature is 'twice as hot' is not valid.

Ordinal Scale

An ordinal scale refers to a level of measurement where the values can be ranked or ordered based on some criterion, but the exact differences between the ranks are not necessarily uniform or known. This type of scale is useful for identifying relative positions (such as first, second, third) but it does not provide information about the magnitude of difference between the ranks.

Cardinal Scale

A cardinal scale, in contrast, deals with numerical values that represent quantities where not only the order is known but also the actual magnitudes. This allows for mathematical operations such as addition, subtraction, comparison of differences, and, in some cases, multiplication and division, meaning that both the order and the size of the intervals between values are significant.

Ratio Scale

A ratio scale is the highest level of measurement which not only provides consistent and meaningful differences between values but also includes a true zero point, enabling the meaningful statement of ratios. This means that both differences and multiplications are valid; for instance, one can legitimately say that one weight is twice the other because the zero point truly signifies an absence of the measured quantity.

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