Surfstat.australia: an online text in introductory Statistics

# SUMMARISING AND PRESENTING DATA

## PRESENTING DATA FOR TWO CONTINUOUS MEASUREMENTS

### Introduction

So far we have considered only the presentation of results for a single variable. In practice, most studies are concerned with the association between two or more variables.

The appropriate statistical method depends on the situation.

• Two variables measured on the same subject/object (e.g. peoples' heights and weights) - are these related? Usually use correlation or regression;
• One variable measured at selected values of another variable - (e.g. children's heights at different ages) Show simple trend - usually use regression;
• One variable measured at equally spaced times (or distances) but successive values highly correlated or pattern complicated (e.g. stockmarket prices) Use methods of time series analysis.

### Scatterplots

Scatterplots are useful for illustrating the relationship between continuous variables (xi, yi), i = 1,..n

A scatterplot is constructed by marking the scales of the two variables, (x, y) along horizontal and vertical axes. Each pair of measurements is plotted with a cross at the point using the measurements as coordinates. The information from a third discrete variable can be incorporated into the plot by using different plotting symbols for each category of the third variable.

The figure below shows a scatterplot of income against age for some hypothetical data. The number 2 is used to indicate a point where two data values coincide.

#### Scatterplot of Income versus Age

Further information on sex is incorporated into this scatterplot by using diamonds for males and squares for females.

#### Example - Heights and weights of 6 female STAT101 students

The table below shows the heights and weights of 6 female STAT101 students. How closely related are the heights and the weights?

Student Height(cm) weight(kg)
1 167 60
2 170 64
3 160 57
4 152 46
5 157 55
6 160 50

First step - draw a scatter plot:

The MINITAB command for a scatter plot is:

#### Progress check

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