Why does the scale of measurement matter? The scale of measurement of our variables determine the mathematical operations that are permitted for those variables. In turn, these mathematical operations, determine which statistics can be applied to the data.
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The chart below lists the scales of measurement that we have reviewed in this exercise and the types of statistics that can be applied to variables created using these scales of measurement. |
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Scale of Measurement
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Nominal
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Ordinal
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Interval
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Ratio
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Approximately Interval
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| Properties |
Identity
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Identity Magnitude |
Identity Magnitude Equal Interval |
Identity Magnitude Equal Interval True Zero |
Identity Magnitude *Treated as Equal Interval |
| Mathematical Operations |
Count
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Rank Order
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Addition Subtraction |
Addition Subtraction Multiplication Division |
Addition Subtraction |
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Statistical Applications
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Nominal
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Ordinal
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Interval
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Ratio
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Approximately Interval
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Descriptive Statistics
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Mode |
Mode Median Range Statistics |
Mode Median Mean Range Statistics Variance Standard Deviation |
Mode Median Mean Range Statistics Variance Standard Deviation |
Mode Median Mean Range Statistics Variance Standard Deviation |
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Inferential Statistics
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Non-Parametric Chi-Square |
Non-Parametric Mann-Whitney U Kruskal-Wallis H Friedman ANOVA Spearman Correlation |
Parametric t-test ANOVA Pearson Correlation |
Parametric t-test ANOVA Pearson Correlation |
Parametric t-test ANOVA Pearson Correlation |
