**Scale of measurement** is the classification that describes the nature of input we take in a survey/questionnaire. It helps us identify the right scale in each context, helping us simplify the analysis.

### Nominal Scale

Nominal or quantitative data involves differentiating between items based on their names. Each item in the scale may be associate with a number, but the number will not have a significance.

**Example**: What is your gender? a) Male b) Female c) Others

Which is your favourite statistical package? a) SPSS b) JASP c) R-programming

Note that we cannot associate a number with these options which has a significance to them. Hence, only possible mathematical operation possible is to check whether two options are equal or not.

We will soon discuss about a descriptive statistical tool called ‘central tendencies’ and note that only possible central tendency we can measure from a nominal data is mode.

Due to the restrictions in mathematically manipulating nominal data, analysis becomes hard when you have a lot of nominal input.

### Ordinal Scale

The ordinal type allows for rank order (1st, 2nd, 3rd, etc.) by which data can be sorted, but still does not allow for relative degree of difference between them.

**Example**: Are you guilty or not guilty? a) Guilty b) Not-guilty.

How do you feel today? a) Very happy b) Happy c) OK d) Unhappy e) Very Unhappy

Ordinal scale helps us decide whether two options are ‘greater than’ or ‘lesser than’ but not measure how greater it is. A typical example is ranking in a class. Suppose Aso is ranked 16 and Ben is ranked 18 in the class. It associates a sensible number to each name based on some criteria, but we cannot conclude that Aso is ‘two times’ better than Ben.

Most favoured central tendency in ordinal scale is Median. Mode can also be used. Using mean as central tendency is not allowed.

### Interval

Interval scales overcome the weakness of ordinal scale: it brings in a degree of comparison between two items. We can be definite about the difference between two choices.

**Example**: What is the temperature in your town now? a) 25°C b) 30°C c) 35°C

Date of birth?

In case of intervals, ratios are not meaningful. We cannot multiply/divide two data points either. It lacks an absolute zero measure: for example, if you take temperature, we have 0°C – but in Fahrenheit, the same temperature is 32°F.

This is more powerful because we can use mean, media and mode alike to measure central tendencies.

### Ratio

Ratio scales has all properties of interval scale mentioned above, along with a definite zero. That makes ratio scales the most friendly to statistical analysis.

**Example**: Height of a person, weight of a person etc.

All mathematical tools can be used on ratio scales, including mean, media, mode and we can also use all measures of dispersion with ratio scale.

## Summary

Nominal | Ordinal | Interval | Ratio | |
---|---|---|---|---|

The “order” of values is known | | ✓ | ✓ | ✓ |

Labelled | ✓ | ✓ | ✓ | ✓ |

Mode | ✓ | ✓ | ✓ | ✓ |

Median | | ✓ | ✓ | ✓ |

Mean | | | ✓ | ✓ |

Can quantify difference between each value | | | ✓ | ✓ |

Can add/subtract values | | | ✓ | ✓ |

Can multiply and divide values | | | | ✓ |

Has a ‘true’ zero | | | | ✓ |

**Related Lecture Video**: Video 1

## Puzzles

- Which scale does marks scored in a particular exam belong to?
- You did a survey to know the current status of your school friends. Which scale will the following questions belong to? Justify your choice.
- Are you studying now?
- What is your field of study?
- Annual income.

- Suppose you are studying the positive impact joining for higher education had on your school classmates. Which scale will the following questions belong to? Justify your choice.
- Are you studying now?
- What is your field of study?

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