Statistics for Beginners (Part 3) | Levels of Measurement | Statistics for the Social Sciences

Introduction

In this video, the presenter introduces important statistical terminology and concepts. The focus of this particular video is on the different levels of measurement.

Levels of Measurement

• Any variable can be categorized as either nominal, ordinal, interval, or ratio.

• A categorical variable is in nominal level or scale if the values of that variable cannot be ranked or ordered because there is no basis for doing so. Examples include sex and eye color.

• A categorical variable is an ordinal scale or level if we can find a basis for identifying which value comes first, next, or last. These are variables whose values are ranked or ordered.

• A numerical variable is either interval or ratio. It is interval if zero is not absolute; we say that zero is not absolute if the variable still exists even if its value is zero. An example of this would be temperature measured in degrees Celsius where at zero degrees Celsius there is still a temperature present.

• If zero is absolute for a numerical value meaning a zero value implies that the variable does not exist then the level for that variable is ratio. Examples include hair length and number of people measured from an area where having a zero value means it does not exist at all such as floor area with 0 square meters means there's no floor at all.

Identifying Level of Measurement

• To identify whether a variable's level of measurement falls under nominal or ordinal scales, think about whether its values can be ranked or ordered.

• For numerical variables, to determine whether it falls under interval or ratio scales consider whether 0 represents an absence of the attribute being measured.

Examples

Racial Origin

• Racial origin cannot be ranked making it nominal.

Monthly Electric Bill

• Monthly electric bill is numerical because it is associated with numbers. It cannot be nominal or ordinal because these variables are categorical not numerical.

• To determine whether it falls under interval or ratio scales, consider whether 0 represents an absence of the attribute being measured. A zero electric bill means that you do not have a bill at all, making it a ratio variable.

Military Rank

• Military rank is categorical and can be ranked making it ordinal.

IQ

• IQ values are numerical and can't be nominal or ordinal.

• To determine whether it falls under interval or ratio scales, consider whether 0 represents an absence of the attribute being measured. A score of 0 in an IQ test does not mean that you do not have an IQ at all, making it an interval variable.

Categorical and Numerical Variables

In this section, the speaker discusses the different types of variables and how to categorize them.

Types of Variables

• Categories can be nominal or ordinal. Stages of cancer is an example of an ordinal variable.

• Floor area is a numerical variable that can be measured in meters squared, kilometers squared, or inches squared. It is a ratio variable because it has an absolute zero value.

• Growth of a chai measured in centimeters is also a numerical variable but it cannot be nominal or ordinal because it has an actual baseline measurement (zero centimeters). Therefore, it is a ratio variable.

Conclusion

The speaker concludes that there are two main types of variables: categorical and numerical. Categorical variables can be further classified as nominal or ordinal while numerical variables can be interval or ratio. The type of variable depends on the nature of the data being collected and how it will be used in analysis.