1.1 Overview
1.1: Overview
1.1.1: Collecting and Measuring Data
There are four main levels of measurement: nominal, ordinal, interval, and ratio.
Learning Objective
Distinguish between the nominal, ordinal, interval and ratio methods of data measurement.
Key Takeaways
Key Points
- Ratio measurements provide the greatest flexibility in statistical methods that can be used for analyzing the data.
- Interval data allows for the degree of difference between items, but not the ratio between them.
- Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values.
- Variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, they are often grouped together as categorical variables.
- Ratio and interval measurements are grouped together as quantitative variables.
- Nominal measurements have no meaningful rank order among values.
Key Terms
- sampling
- the process or technique of obtaining a representative sample
- population
- a group of units (persons, objects, or other items) enumerated in a census or from which a sample is drawn
Example
An example of an observational study is one that explores the correlation between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case, the researchers would collect observations of both smokers and non-smokers, perhaps through a case-control study, and then look for the number of cases of lung cancer in each group.
There are four main levels of measurement used in statistics: nominal, ordinal, interval, and ratio. Each of these have different degrees of usefulness in statistical research. Data is collected about a population by random sampling .
Nominal measurements have no meaningful rank order among values. Nominal data differentiates between items or subjects based only on qualitative classifications they belong to. Examples include gender, nationality, ethnicity, language, genre, style, biological species, visual pattern, etc.
Defining a population
In applying statistics to a scientific, industrial, or societal problem, it is necessary to begin with a population or process to be studied. Populations can be diverse topics such as “all persons living in a country” or “all stamps produced in the year 1943”.
Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values. Ordinal data allows for rank order (1st, 2nd, 3rd, etc) by which data can be sorted, but it still does not allow for relative degree of difference between them. Examples of ordinal data include dichotomous values such as “sick” versus “healthy” when measuring health, “guilty” versus “innocent” when making judgments in courts, “false” versus “true”, when measuring truth value. Examples also include non-dichotomous data consisting of a spectrum of values, such as “completely agree”,