Quantitative Methods

Variables and the three levels of measurement

変数と計測レベル

2016

Keiko Ono, Ph.D.

More Key Terms in Quantitative Methods

• Unit of Analysis 分析単位 • Observations, cases, records (in rows) 観察・観測対象となるもの

• Variables (in columns) 変数 – Values – Levels of measurement

• Measures of association

– Chi square χ2 カイ2乗 – Compare means test T検定 – Correlation 相関関係

A variable: an empirical property of an observation that can take on two or more different values.

Remember the “favorite color” data set?

There are 59 cases/observations in total. What do they represent? In other words, what is the unit of analysis? How many “empirical properties” (variables) are recorded for the observations?

A variable must vary (by definition). The gender variable could take one of the two values: girl or boy. The favorite color variable could take one of several values: pink, blue, white, yellow, white…etc. The age variable could take one of several values: 17-24.

Three levels of measurement for variables • Nominal (or “Categorical”) Values communicate differences b/w subjects on the

characteristic being measured. Variable “color”: each value (pink, white, blue…) represents

a different category of color. Cannot be ordered. • Ordinal Values communicate relative differences b/w subjects on the characteristic being measured. Can be ordered. -ordered ranking -ordered categories (cloudy---partly cloudy---sunny) • Interval (or “Scale”) Values communicate exact differences b/w subjects on the

measured characteristics. Variable “age” : each value (17, 18, 19…) represents the

student’s age in years. Can be ordered.

Three levels of measurement for variables in the Color dataset

• Nominal (or “Categorical”) Variable “color”: pink, white. Variable “gender”: boy, girl. • Ordinal • Interval (or “Scale”) Variable “age” : each value (17, 18, 19…)

An

oth

er examp

le

Men’s individual 400m medley

Men’s individual 400m medley Ordinal

Nominal Interval

Yet another sport example.

Yomiuri (巨人) and Soft Bank (ソフトバンク) both came in second (2位）。 But were they equally successful in winning games?

http://baseball.yahoo.co.jp/npb/standings/

Summary Statistics and Levels of Measurement

Categorical

(or “nominal”)

Ordinal Interval

(or “scale”)

Frequency ☺ ☺ ☺

Mode ☺ ☺ ☺

Mean X X ☺

Median X ☺ ☺

Variance and σ X X ☺

Minimum X ☺ ☺

Maximum X ☺ ☺

Range X X ☺