Data Levels and Measurement
All research needs particular data levels and measurement. There are many procedures in statistics which need different types of data levels, and all data contain assumptions for particular procedures.
Broadly, four types of data levels and measurement are used in every type of research:
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A nominal scale is one in which numbers are only used as labels. For example, if we want to categorize male and female respondents, we could use a nominal scale of 1 for male, and 2 for female, but 1 and 2 in this case do not represent any order or distance. They are simply used as labels. We can use a nominal scale to show the categories of a variable as a numeric value. Nominally, scaled variables cannot be used to perform many statistical computations such as mean and standard deviation, because such statistics do not have any meaning when used with nominal scale variables.
However, nominal scale variables can be used to do cross tabulations. The chi-square test can be performed on a cross-tabulation of nominal scale data.
Ordinal scale variables have a meaningful order to them. We can assign order to the variable or respondent. For example, we can assign rank 1, which is higher than rank 2, and 2 is higher than 3 etc. Instead of rank 1, 2, 3, we can use any other number which preserves the same order. This is because we do not know for sure what the distance between 1 and 2 is, or what the distance between 2 and 3 is.
We can use statistics median various percentiles such as the quartile, and the rank correlation on ordinal data. In addition to this statistic, we can use frequency tables and cross tabulations on ordinal data. Arithmetic mean should not be calculated on the ordinal scale variables.
An interval scale variable can be used to compute the commonly used statistical measures such as the average standard deviation and the Pearson correlation coefficient. Many other advanced statistical tests and techniques also require interval scaled or ratio scaled data.
Most of the behavioral measurement scales are used to measure attitudes of respondents on a scale of 1 to 5, or 1 to 7, or 1 to 10. These can be treated as interval scales. These types of scales are also known as rating scales and they are very commonly used in marketing research.
The difference between an interval scale and an ordinal scale variable is that the distance between ordinal data is the same, but in ordinal data the distance is not fixed.
All arithmetic operations are possible on a ratio scaled variable. These include computation of geometric mean, harmonic mean, and all other statistic-like averages such as standard deviation and Pearson correlation. Additionally, the tests such as the t-test, F-test, correlation and regression are also included with ratio-level variables. An example of ratio scale data would be the sales of a company, the expenditure of a company, the income of a company, etc. We can do any mathematical procedure with ratio scale data that is not possible with nominal, ordinal, and interval scale data.