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## Scales of Measurements The data can be categorized using different scales of measurements. Each level of measurement scale has properties that determine the various use of statistical analysis. There are four different scales of measurement. The four types of scales are: 1. **Nominal Scale**...

## Scales of Measurements The data can be categorized using different scales of measurements. Each level of measurement scale has properties that determine the various use of statistical analysis. There are four different scales of measurement. The four types of scales are: 1. **Nominal Scale** - Also called the categorical variable scale. - Defined as a scale used for labeling variables in distinct classifications and does not involve a quantitative value or order. - This scale is the simplest of the four variable measurement scales. - Calculations done on these variables will be futile as there is no numerical value of the options. - The sequence in which subgroups are listed makes no difference, as there is no relationship among subgroups. - A subgroup of nominal scale with only two categories (e.g. male/female) is called "dichotomous." - The analysis of gathered data will happened using percentages or mode. - Is often used in research surveys and questionnaires where only variable labels have significance. For instance: - "Which brand of smart phones do you prefer?" - Options: "Apple"-1, "Samsung"-2, "OnePlus"-3. - "What is your Gender?" - Options: "Male" 1, "Female"-2 - "What is your Political preference?" - Options: 1- Independent, 2- Democrat, 3- Republican 2. **Ordinal Scale** - Defined as a categorical variable measurement scale used to simply depict the order of variables and not the difference between each of the categorical variables. - These scales are generally used to depict non mathematical ideas such as frequency, satisfaction, happiness, a degree of pain etc. - It is quite straightforward to remember the implementation of this scale as 'Ordinal sounds similar to 'Order', which is exactly the purpose of this scale. - Ordinal Scale maintains descriptional qualities along with an order but is void of an origin of scale and thus, the distance between variables can't be calculated. - Origin of this scale is absent, due to which there is no fixed start or "true zero". - The analysis of gathered data will happened using percentages or median - Are generally used in market research to gather and evaluate relative feedback about product satisfaction, changing perceptions with product upgrades etc. For example, ordinal scale question such as: - "How satisfied are you with our services?" - Very Unsatisfied-1: Unsatisfied-2: Neutral-3: Satisfied-4: Very Satisfied-5 - The order of variables is of prime importance and so is the labeling. Very unsatisfied will always be worse than unsatisfied and satisfied will be worse than very satisfied. 3. **Interval Scale** - Defined as a numerical scale that allows for measurement between these variables. - Variables, which have familiar, measurable units. - Mean, median or mode can be calculated. - The only drawback of this scale is that there is an absence of a true zero. - Interval scale contains all the properties of ordinal scale and also allows for measurement of difference between variables. - The main characteristic of this scale is that the units of measurement are always equal. 80 degrees is always higher than 70 degrees, regardless of the starting point as the difference between 70 degrees and 80 degrees will always be 10 degrees. - Also, the value of 0 is arbitrary and does not reflect the absence of temperature. - Due to absence of absolute zero, it is not possible to compute ratios. - For example, you cannot say if 40 degrees Celsius is twice as hot as 20 degrees Celsius - All the techniques applicable to nominal and ordinal data can also be used in interval scale. - From those techniques, there are other techniques like variance and standard deviation, which is extensively focused on the interval scale. 4. **Ratio Scale** - Defined as a numerical scale that allows for measurement of the difference between variables, but also assumes that a true zero makes the difference between values meaningful. - It is calculated by assuming that the distance between measurement units is the same and there is a starting point of zero. - Ratio scale accommodates all the properties of the interval scale and also allows for measurement of variables, the significance of which are meaningful (i.e., the differences between variables are usually equidistant). - Because of the existence of a true zero, the origin of the scale can be established by using a ratio scale, the researcher can compare the different variables by constructing a ratio. - Ratio scale provides the researcher with the most advanced tools in statistical analysis. - The researcher can apply a wider range of statistical techniques such as variance, standard deviation, correlation, mean, median, mode, geometric mean, variation or harmonic mean. **Best examples of ratio scales:** "What is your daughter’s height?" - Less than 5 feet - 5 feet 1 inch-5 feet 5 inches - 5 feet 6 inches-6 feet - More than 6 feet ## Summary of Levels of Measurement Offers: - The sequence of variable - Mode - Median - Mean