14Arelatedvariables

= 14A Related Pairs of Variables =

Bivariate statistics involves investigating the relationships between two variables.
 * sometimes the relationship is direct and obvious like the connection between the length of a taxi ride and the cost
 * sometimes the relationship is only revealed by studying the statistics, like the connection between cigarettes and cancer


 * Classifying Variables **

Recall that data generally comes in two forms
 * ** Numerical ** (sometimes called __**quantitative**__)
 * numbers
 * numerical data can be either
 * __**continuous**__ (usually resulting from measuring, eg distance, time, temperature, weight)
 * __**discrete**__ (a limited number of separate possible values, usually resulting from counting)
 * ** Categorical ** (sometimes called __**qualitative**__)
 * categories (descriptive words)
 * categorical data can be either
 * __**ordinal**__ (the descriptions have a natural order, eg letter grades on assignments, pizza sizes)
 * __**nominal**__ (the descriptions don't have a natural order, eg brands of cars, hair colour)


 * Dependent and Independent Variables **

When investigating the relationship between two variables, we can often identify the following:
 * one of the variables will be ** independent **
 * takes on values according to the circumstances
 * is not controlled by the other variable
 * the other variable will be ** dependent ** on the first
 * changes value __**depending**__ on whatever happens to the other variable
 * value of the dependent variable is controlled by the value of the other variable


 * Example 1 **

Identify the dependent and independent variables in each of the following.
 * 1) cost of a taxi ride and the distance travelled
 * 2) age of a child and their reading ability
 * 3) height of a child and their shoe size
 * 4) y = 2x + 3


 * Solution:**

.... .... ** 1. ** .. the cost of a taxi ride depends on the distance travelled
 * distance travelled is independent
 * cost is dependent

... ... ** 2. ** .. a child's reading ability generally increases as they grow older
 * age is independent
 * reading ability is dependent

... ... ** 3. ** .. generally speaking, the shoe size increases as a the height of a child increases
 * height is independent
 * shoe size is dependent

... ... ** 4. ** .. y = 2x + 3 -- the value of y is controlled by the value of x
 * x is independent
 * y is dependent


 * Note: **
 * the situation will not always be as clear cut
 * there are many situations where one variable does not obviously depend on the other
 * the two variables may feed back on each other (eg a person's weight and the amount of food they eat)
 * the two variables may both depend on a third variable (eg a person's shoe size and shirt size)
 * there might not be an obvious relationship between the two variables


 * Graphing Pairs of Variables **


 * When graphing a pair of variables
 * the independent variable should go on the horizontal (x) axis
 * the dependent variable should go on the vertical (y) axis


 * Analysing Pairs of Variables **


 * When analysing a pair of variables for the relationship between them, the options are:
 * a strong relationship
 * a moderate relationship
 * a weak relationship
 * no relationship
 * If a relationship exists it might be
 * positive (an __**increase**__ in the independent variable results in an __**increase**__ in the other)
 * negative (an __**increase**__ in the independent variable results in a __**decrease**__ in the other)
 * think positive and negative gradients of a straight line

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