Data Analysis for LEL - Week 5

Statistical variables

Stefano Coretta

University of Edinburgh

Sample \(y\)

When we ask a research question, we collect a sample \(y\) from a population.

Sample \(y\)

\(y\) is a sample of values (\(y_1, y_2, y_3, ..., y_n\)).

Sample of values can be e.g.:

  • Number of telic and atelic verbs in a historical corpus of Sanskrit.

  • Voice Onset Time of stops from 50 speakers Mapudungun.

  • Friendliness ratings of synthetic speech as indicated by 300 participants.

  • …

Sample \(y\)

\(y\) is a sample of values (\(y_1, y_2, y_3, ..., y_n\)).

We say that the values in the sample \(y\) were generated by a (random) variable \(Y\).

Variable \(Y\)

\(Y\) is a (random) variable that generates the values in the sample \(y\).

A (statistical) variable is any characteristics, number, or quantity that can be measured or counted

  • When you observe or measure something, you are taking note of the values generated by the variable.

  • It’s called variable because it varies (ha!).

  • The opposite of a variable is a constant.

Sample \(y\)

\(Y\) is a (random) variable that generates the values in the sample \(y\).

Variables can be e.g.:

  • Token number of telic verbs and atelic verbs in written Sanskrit.

  • Voice Onset Time of stops in Mapudungun.

  • Friendliness ratings of synthetic speech.

  • …

Types of variables

Types of variables

Types of variables

Numeric continuous variable: between any two values there is an infinite number of values.

  • The variable can take on any positive and negative number, including 0.

  • The variable can take on any positive number only.

  • Proportions and percentages: The variable can take on any number between 0 and 1.

Numeric discrete variable: between any two consecutive values there are no other values.

  • Counts: The variable can take only on any positive integer number.

Types of variables

Categorical (discrete) variable.

  • Binary or dichotomous: The variable can take only one of two values.

  • The variable can take any of three of more values.

  • Ordinal: The variable can take any of three of more values and the values have a natural order.

Operationalisation

We can operationalise something as a numeric or a categorical variable.

Think of ways to operationalise the following:

  • Voice Onset Time.

  • Friendliness of speech.

  • Lexical frequency.

  • …

Operationalisation

Summary

  • The sample \(y\) is generated by a (random) variable \(Y\).

  • A (statistical) variable is any characteristics, number, or quantity that can be measured or counted.

  • Variables can be numeric or categorical.

    • Numeric variables can be continuous or discrete.
    • Categorical variables are only discrete.

  • We operationalise a measure/observation as a numeric or a categorical variable.