Variables

Firstly, let’s view the below detailed image to learn about various forms of variables.  

 

| Image: Forms of variables | 

Variables are primarily divided into Quantitative and Qualitative. 

Quantitative variables are also called numerical variables as they can be measured in numbers. They are measured on an interval or ratio scale. The differences between two consecutive numbers carry equal significance in any part of the scale, e.g., the difference between 100 and 102 cm is the same as the difference between 176 and 178 cm. 

For more information on the difference between interval and ratio scales, please click here. 

Quantitative variables are further divided into Continuous and Discrete.  

Discrete variables are restricted to certain values and are often the results of counting. An example is the number of children in the family. 

Continuous variables are ones that may take on any values within a given range. Examples are age, weight, height, temperature. 

Qualitative variables are defined by a characteristic therefore are referred to as categorical. 

These are further divided into Nominal and Ordinal. 

Ordinal variables are those which can be logically ordered or ranked such as academic grades (A+, A, B+, B, etc.) 

Nominal variables are those who can’t be ranked or follow an order, such as a person’s gender, eye colour, etc. 

Statistical methods can only be used with certain data types: 

• Nominal: frequency / proportion 
• Ordinal: percentiles
• Continuous: histograms, box plot

Types of Variables 

 

 

| Image: Types of variables | 

Variables can also be divided into two types: 

• Dependent, meaning depending on other factors, for example an exam score. 
• Independent, that is, not changed by other variables, for example hours of study/sleep. 

In a causal relationship, the cause is the independent variable, and the effect is the dependent variable.  

There are also extraneous variables that may alter dependent or independent variables, and in experimentation should be controlled/monitored. 

In the list above, we can see synonyms of dependent and independent variables. Labelling variables as explanatory and response does not guarantee that the relationship between the two is actually causal, even if there is an association identified between the two variables. (Explanatory variable might affect explained variable). We use these labels only to keep track of which variable we suspect affects the other (correlation does not imply causation). 

Let’s observe the below chart. Does there appear to be a relationship between the hours of study per week and the GPA of a student? Can you spot anything unusual about any of the data points? 

 

| Image: Scatter plot: relationship between the hours of study per week and the GPA of a student | 

There is one student with GPA > 4.0, this is likely a data error. 

In general, scatter plots are useful for visualising the relationship between two numerical variables. 

Possums: True/False? 

Let’s see if you've got it! The below scatter plot shows the relationship between the skull width and the head length of possums. Which one of the below sentences (a to d) is correct? 

 

| Image: Scatter plot: relationship between the skull width and the head length of a possum | 

(a) There is no relationship between 'head length' and 'skull width', i.e. the variables are independent. 

(b) 'Head length' and 'skull width' are positively associated. 

(c) 'Skull width' and 'head length' are negatively associated. 

(d) A longer head causes the skull to be wider. 

(e) A wider skull causes the head to be longer. 

Select the next lecture to find out the correct answer!