Bivariate Data

The Statistical Investigation Process

Identify a problem, Pose a statistical question, Collect or obtain data, Analyse Data, Communicate Results

Univariate Data

Data which involves one variable

Bivariate Data

Data which involves two variables. Bivariate data analysis looks at whether there is a relationship between two variables.

Association

A general term used to describe the relationship between two (or more) variables.

Correlation

Used interchangeably with the term association. Correlation tends to be used when referring to the strength of a linear relationship between two numerical variables.

Explanatory Variable (EV)

Variable used to explain or predict a difference in the RV.

Response Variable (RV)

What happens in response to the EV.

Example of EV and RV

When investigating the relationship between the temperature of a loaf of bread and the time it has spent in the oven, the temperature is the response variable and time is the explanatory variable. 

Displaying Categorical Bivariate Data

Two-way table, Side by side column graph, Segmented column graph

Displaying Numerical Bivariate Data

Scattergraphs

Does EV go on x axis or y axis?

x axis

Does RV go on x axis or y axis

y axis

When do you use a column percentage table?

If the explanatory variable is at the top of the frequency table.

When do you use a row percentage table?

If the explanatory variable is on the side of the frequency table.

Words to use when commenting on trend

In general, tend to, seems to be

Rule for line of best fit

Line that joins as many points as possible but leaves the same amount of unconnected points on either side of the line.

Reliability of prediction can be affected by…

Form of scattergraph, number of points on scattergraph, how closely the points form a straight line, predicting between the given EV values or beyond given EV values.

Interpolation

Predicting between given values (Reliable)

Extrapolation

Predicting beyond given values (Unreliable)

When interpreting a graph comment on

Form, direction, strength of association

Form

Linear, non-linear, no relationship/random

Direction (if linear)

Positive, negative

Positive direction

As the explanatory variable increases, the response variable increases.

Negative direction

As the explanatory variable increases, the response variable decreases.

Strength

Strong relationship, moderate relationship, weak relationship

Equation of least squares regression line

y hat = ax + b

Interpreting the gradient (a)

The RV increases/decreases by a units for every one unit increase in the EV

Interpreting y intercept (b)

The RV is b units when the EV is zero (not always relevant)

Weak range Pearson’s correlation coefficient

0-0.35

Moderate range Pearson’s correlation coefficient

0.35-0.75

Strong range Pearson’s correlation coefficient

0.75-1

Commenting on r

r = xxxx which suggest strong/moderate/weak positive/negative correlation. As the EV increases/decreases, the RV increases/decreases.

Commenting on causation

Although there is a strong/moderate/weak positive/negative correlation between the variables, a correlation does not imply causation. There might be a coincidence or a lurking variable such as…

Commenting on coefficient of determination

xx% of the variation in the RV can be explained by the variation in the EV.