Different levels of measurement

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 Meaning of Scales of Measurement

Scales or levels of measurement refer to the different ways in which data can be categorized and organized in the field of statistics and measurement. It describes the nature of information within the numbers assigned to a variable. It refers to the relationship among the values that are assigned to the attributes for a variable.

              

 

According to Mc Clendon (2004), “Level of measurement refers to the amount of information that the variable provides about the phenomenon being measured.”

Classification of Levels of Measurement:  

        It was developed by Stanley Smith Stevens. He proposed his theory in a science Article titled “On the theory of Scales of Measurement” in 1946. He claimed that all the measurement in science is conducted using four different types of Scales he called Nominal, Ordinal, Interval and Ratio.

 1.  Nominal Scale: 

• Nominal data represent categories or labels without any inherent order or numerical value. The data at this level are qualitative and can only be classified into distinct categories.
• There is no inherent order or value associated with these categories.
• This is the most basic/ fundamental level of measurement.
• Data are categorized into distinct, non- overlapping categories or labels.
• Nominal data only provide information about the identity or classification of items, with no inherent order or ranking.
• The values represented in these scales need not to be quantitative values.
• It is qualitative in nature.
• They are used by market researchers.
• They do not have any numeric value. Thus, they cannot be added , subtrated, divided or multiplied.
• The findings of such data can be subjected to tools like mode, average, binomial, and chi-square tests.
• Nominal scales are used to ascertain characteristics like gender, ethnicity, tastes, preferences, etc.  
• Example: Variable: City of Residence Categories: London, Manchester, Birmingham, Edinburgh, Cardiff. In this example, "City of Residence" is a nominal variable because the categories (London, Manchester, Birmingham, Edinburgh, Cardiff) are distinct labels without any inherent order. Each city is a separate and unique category, and there is no numerical value or meaningful order associated with them in the context of this variable. 

     2.     Ordinal Scale: 

• Ordinal data have categories with a meaningful order, but the intervals between the categories are not uniform or meaningful. It indicates the relative position or rank of the categories.
• In the ordinal scale, data categories have a specific order or ranking or positioning on a scale.
• It seeks to rank the responses of students on the basis of their characteristics.
• It deals with relative positioning of an item on the basis of characteristics of other items on the scale.
• The intervals between categories are not uniform and not quantifiable.
• The respondents are required to rank the objects from highest to lowest preferential order.
• Example: Variable: Educational Qualification  Categories: High School Diploma, Certificate, Diploma, Bachelor's Degree, Master's Degree, Doctorate. In this example, "Educational Qualification" is an ordinal variable because the categories represent different levels of education with a meaningful order. 
• For instance, a Master's Degree is considered a higher level of education than a Bachelor's Degree, but the intervals between these categories are not necessarily uniform. 
• The order is meaningful, indicating a progression in educational attainment, but the difference between, say, a Certificate and a Diploma may not be the same as the difference between a Diploma and a Bachelor's Degree.

 

       3.     Interval Scale: 

 

•  It is refinement over ordinal Scale. In this, absolute values are assigned to the variable.
•  Interval data have ordered categories with uniform intervals between them.
•  There is no true zero point. It means that a value of zero does not imply the absence of  the quantity being measured.
•  It provides information about the relative order, and the intervals between categories are  uniform and measurable.
• The intervals can be easily computed with the help of mean, standard deviation, etc. 
• The values on this scale can be compared in terms of differences but not in terms of ratios.
• Example: Variable: Temperature (measured in Celsius or Fahrenheit) In this example, temperature is an interval variable because the difference between each degree is consistent (uniform), but a zero temperature (e.g., 0°C or 0°F) does not represent the absence of temperature. 
• In other words, a temperature of 0°C doesn't mean there is no heat; it's just a point on the Celsius scale. Similarly, a temperature of 0°F doesn't mean there is no heat; it's a specific point on the Fahrenheit scale.
• So, while we can say that 20°C is warmer than 10°C, and the interval between 20°C and 30°C is the same as the interval between 30°C and 40°C, the concept of zero in this scale does not indicate a complete absence of temperature.

4.     Ratio Scale: 

• Ratio data have all the characteristics of interval data but with a true zero point. A true zero indicates the absence of the quantity being measured. 
• The ratio scale encompasses ordered categories with equal intervals and a true zero point.
• In ratio scale, the variables do not have a relative value but an absolute value.
• It provides the most comprehensive information, as values on this scale can be compared in terms of both differences and ratios.
• They incorporate the value for absence of a any trait in an object. It is denoted with value ‘Zero.’
• The data obtained from a ratio scale makes the outcome a meaningful and scientific interpretation.
• Example: Variable: Height (measured in centimeters) In this example, height is a ratio variable because it has a true zero point (i.e., a height of 0 cm indicates the absence of height), and the ratios between different heights are meaningful. For instance, if person A is 180 cm tall and person B is 90 cm tall, we can say that person A is twice as tall as person B. The key characteristics of a ratio scale are a true zero point, meaningful ratios, and the ability to make statements about absolute quantities and proportions. Height, weight, and income are common examples of variables measured on a ratio scale.

      Conclusion:  

Understanding the different levels of measurement—nominal, ordinal, interval, and ratio—is essential in the realm of research and data analysis. Each level brings unique characteristics that influence the types of statistical analyses that can be applied and the depth of information that can be gleaned from the data. 

Nominal measurement categorizes variables without any inherent order, while ordinal measurement introduces meaningful order. Interval measurement maintains uniform intervals but lacks a true zero point, and ratio measurement encompasses a true zero, allowing for meaningful ratios. Choosing the appropriate level of measurement is crucial for accurate interpretation and meaningful conclusions in research, ensuring that the chosen scale aligns with the nature of the variable and the objectives of the study

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