Physics and Engineering of Radiation Detection

560 Chapter 9. Essential Statistics for Data Analysis

Example:

The following data are obtained in an experiment.

x={102, 154, 200, 220, 267, 263, 352, 361, 423, 449, 512, 598, 601, 701, 711}

y={28, 98, 132, 98, 129, 202, 265, 243, 291, 324, 376, 412, 524, 511, 560}

Determine if the data are well correlated.

Solution:

A plot of the data together with a regression fit is shown in Fig.9.8.2. It is

evident that the data are very well correlated. To quantify our confidence we

calculate the correlation coefficient. To do that we can use equation 9.8.1 to

compute the correlation coefficient. To simplify the computations, we create a

table with the needed terms computed individually. The correlation coefficient

is then given by

r =

(15)(2113232)−(5914)(4193)

√[

(15)(2875604)−(5914)^2

][

(15)(1574209)−(4193)^2

]

=0. 98.

Hence we can say with high confidence that the variables are very well corre-

lated.

x

100 200 300 400 500 600 700

y

0

100

200

300

400

500

600

Figure 9.8.2: Plot of the data given in the example above

together with a straight line fit.