## Bivariate analysis Example

The first thing we might do before calculating r or r2 is to produce a scatterplot of the relationship between the two variables. This is shown in Figure 10.1.

From the scatterplot we can see that there is some association between the two sets of data, although it may not be very strong. Were there to be a strong degree of association between the two variables, the graph might have appeared as shown in Figure 10.2. (Table 10.7 shows our data in tabular form.)

Notice that where there is a high degree of association, the points lie along a straight line.

The indices association r and r2 are calculated according to the formula:

r2 is obtained from r.

In this example correlation of price and alcohol r = 0.241. The significance of r can be tested using the t test:

t= 0.241^/(14 - 2) / (1 - 0.058) = 0.241 x V(12/0.942) = 0.86 tabular t = 2.179 at 0.05 level of significance, 12 degrees of freedom.

Since the computed value is less than the tabular value, the computed value of r indicates no evidence of any association.

FIGURE 10.1

Price versus alcohol content per glass - low degree of association

TABLE 10.7

Fourteen brands of cider, their price per glass and alcohol content per glass

1.20

-

X

-

2

2

1.00

-

X

'C

X

2

2 X

Q.

0.80

-

-

X

X

0.60

-j

3.0

4.0

5.0 6.0 7.0 8.0

 Brand Price (£) Alcohol content (%) 1 1.1 4.2 2 1.1 4.2 3 G.? 4.G 4 G.? 3.G 5 1.2 B.5 6 G.? B.4 y G.? 4.G B G.y 4.G ? 1.1 B.5 1G 1.1 B.5 11 G.? 7.5 12 G.? 7.5 13 G.y 7.6 14 1.G 6.G
 1.20 - X - 4 1.00 - X 01 — u - 7 ci 0.80 - X 0.60 - 3.0 4.0 5.0 6.0 7.0 8.0 Price versus alcohol content per glass - high degree of association FIGURE 10.2 Price versus alcohol content per glass - high degree of association

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