Physics and Engineering of Radiation Detection

554 Chapter 9. Essential Statistics for Data Analysis

generally given for different degrees of freedom and levels of significance. The total
degrees of freedom for the dataset are given by

ν =(N 1 −1) + (N 2 −1)

= N 1 +N 2 − 2. (9.6.5)

The choice of level of significance depends on the level of confidence one intends to
have on the analysis. If one chooses a value of 0.05 and the calculatedtvalue turns
out to be less than the tabulated one, then one could say with 95% confidence that
the means are not significantly different.

Example:

An ionization chamber is used to measure the intensity of x-rays from an

x-ray machine. The experiment is performed at two different times and yield

the following values (arbitrary units).

Measurement-1: 380, 398, 420, 405, 378

Measurement-2: 370, 385, 400, 419, 415, 375

Perform Student’sttest at 95% and 99% confidence levels to see if the means

of the two measurements are significantly different from each other.

Solution:

First we compute the means of the two datasets.

x ̄ 1 =

∑N^1

i=1

x 1 ,i

N 1

= 396. 2

x ̄ 2 =

∑N^2

i=1

x 2 ,i

N 2

= 394

Next we determine the standard deviations of the two means.

σ 1 =

1

N 1 − 1

∑N^1

i=1

(x 1 ,i−x ̄ 1 )^2

=17. 61

σ 2 =

1

N 2 − 1

∑N^2

i=1

(x 2 ,i−x ̄ 2 )^2

=20. 59