Types of Data and Correlation

Four Types of Data

• Nominal

• Ordinal

• Interval

• Ratio

Continuous Data | Characteristics

• Has meaningful numerical values

• Includes interval data

• Includes ratio data

• Ordinal data can sometimes be treated as continuous

Continuous Data | Examples

• Age

• Exam Percentages

Categorical Data | Characteristics

• Places observations into categories

• Includes nominal data

• Can include ordinal data

Categorical Data | Examples

• Gender

• Ethnicity

Nominal Data | Characteristics

• Considered categorical

• No quantitative values

• No order

Nominal Data | Example

Primary language

• English

• Spanish

• German

• French

True or False: Order does not matter for ordinal data. The order of the categories does not matter and does not carry numerical meaning.

True

Can nominal data be used directly in regression?

• No, not in its raw form

• Must be converted into dummy variables

Can nominal data be used in a t-test?

• Yes

• Nominal data may define the groups being compared

Dummy variables are represented by two numbers. What are they?

0 and 1

Ordinal Data

• No quantitative values

• There is an order

• Order matters

• Numerical distance between positions is not necessarily meaningful

Ordinal Data | Example

• 1st place

• 2nd place

• 3rd place

• Place finished in a competition

What does ordinal ranking tell us?

• Order

• Provides no information about the numerical difference between positions

Order Data Treated as Continuous | Example

1 = Strongly Disagree

2 = Disagree

3 = Somewhat Disagree

4 = Neither Disagree nor Agree

5 = Somewhat Agree

6 = Agree

7 = Strongly Agree

Can ordinal data treated as continuous be used in regression?

• Yes

• We must agree on the order of the numbers

• The order must give the numbers real numeric value

Interval Data | Characteristics

• Continuous

• The “space in between” is important

• The intervals have relative value

• Can be negative

• Zero does not mean “non-existent” or “none”

Interval Data | Examples

• Temperature

• Dates/years

Ratio Data | Characteristics

• Continuous

• The “space in between” is important

• The intervals have relative value

• Cannot be negative

• Zero means “none”

Ratio Data | Examples

• Height

• Age

• Distance

• Weight

Can interval and ratio data be used in regression?

• Yes

• The numbers have numeric value

Regression

Prediction; using historical data to predict a value.

Basic Regression Formula

Y = B₁X₁ + B₂X₂ + Intercept

In the basic regression formula what does Y represent?

What we are trying to predict

In the basic regression formula, what does X represent?

Historical data used to predict it

In the basic regression formula, what does B represent?

Coefficient that tells you how much Y changes when that X changes

T-test

A comparison of the means of two groups

Example of nominal data being used with a t-test

Comparing the mean exam scores of English speakers and Spanish speakers

Covariance

The unstandardized measure of the relationship between two variables

What does positive covariance indicate?

The two variables tend to move in the same direction

Deviance

The distance each point is from the mean

Variance

The average variability in a set of data; the spread of the data

Standard Deviation

Standardized variability in a set of data; the spread of the data

Relationship between Variance and Standard Deviation

Standard Deviation = √Variance

Why is standard deviation useful?

It allows you to compare how spread out the data is between two sets

Correlation

A standardized measure of covariation between two variables

In terms of the two variables being measured, what does a positive correlation mean?

As one variable moves, the other variable tends to move in the same direction

In terms of the two variables being measured, what does a negative correlation mean?

As one variable moves, the other variable tends to move in the opposite direction

What does “standardized” mean?

The process of transforming data to a common scale

Why is correlation more meaningful than covariance?

It puts the relationship on a common scale, regardless of the measurement scales of the two variables

What two things does correlation tell us?

• Strength of the relationship

• Direction of the relationship

What does the sign of a correlation coefficient tell you?

The direction of the relationship:

• Positive = variables move in the same direction

• Negative = variables move in opposite directions

What does the magnitude of a correlation coefficient tell you?

The strength of the relationship

_________ involves only two variables, while _________ may have many predictor variables

Correlation; regression

Why might regression be needed even if we know the correlation?

Other variables may influence the relationship

Correlation tells us the strength and direction of a relationship, but cannot determine that…

One variable causes the other

True or False: Correlation determine the direction of causation.

False

What should be included when reporting a correlation?

• State what the statistics tell us

• State the strength of the relationship

• State whether the relationship is positive or negative

• Provide the correlation statistic: (r = ___)

• Explain what the relationship means

How do you describe a positive correlation in words?

As one variable moves, the other moves in similar strength and direction

How do you describe a negative correlation in words?

As one variable moves, the other moves in similar strength but in the opposite direction

Example of reporting a positive correlation

According to the data, there is a strong positive correlation between job satisfaction and happiness (r = 0.8601), such that as one variable moves, the other moves in similar strength and direction.

Example of reporting a negative correlation

Number of pets and free time are strongly and negatively correlated (r = −0.79), such that as one variable moves, the other moves in similar strength but in the opposite direction