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.

Scatterplot of Income versus Age Classified by Sex 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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