Interval Measurement Finance - Financial Business

Interval Measurement in Finance

Interval measurement, in the context of finance, refers to a measurement scale where the difference between two values is meaningful, but there is no true or meaningful zero point. This distinguishes it from ratio scales, which do have a true zero, and ordinal scales, which only establish order without quantifying the differences between values.

A classic example of an interval scale in finance is temperature measured in Celsius or Fahrenheit. While we can say that 20°C is 10°C warmer than 10°C, we cannot say that 20°C is “twice as hot” as 10°C. The zero point (0°C or 0°F) doesn’t represent a complete absence of temperature; it’s simply a point defined by convention.

The use of interval scales in financial analysis is less common than ratio scales, but they still appear. One area where interval scales are relevant is in some risk assessment methodologies and surveys. For example, when assessing subjective opinions using a Likert scale that uses numeric values (e.g. 1-7, where 1 = Strongly Disagree, 7 = Strongly Agree), the differences between values are meaningful, but ‘0’ may not hold specific meaning. Also, sometimes the order of the scale is more important than precise numerical values. These types of measurements are often treated as interval scales, although technically they are ordinal scales, and the treatment is acceptable if the number of steps is large enough.

Statistical analyses appropriate for interval data include calculating means, standard deviations, correlations, and performing t-tests and ANOVA. However, calculations involving ratios or multiplications are generally not meaningful with interval data because the zero point is arbitrary. For instance, it wouldn’t be appropriate to say that one investment strategy is “twice as risky” as another based solely on their numerical risk scores if those scores are derived from an interval scale measurement.

Because there is no absolute zero, caution is required when interpreting results derived from interval scale data. Comparing two interval scale measurements may lead to a different result than if a different origin or zero was used. It’s crucial to understand the limitations of the scale and interpret results within that context. While you can meaningfully compare differences between data points, calculating ratios or multiplicative relationships may not be valid.

In summary, while ratio scales dominate quantitative financial analysis, understanding interval measurement is important when dealing with subjective risk assessments or other measures lacking a true zero. Applying the appropriate statistical techniques and understanding the limitations of the scale ensures more accurate and meaningful financial interpretations.