Abstract
Possibility of the application of the Welch test on the radioactivity measurements was discussed.
Recently, the measurements of the radioactivities in the seawater and/or marine products are often carried out by the local governments.
It is very important to compare these data and to know whether any significant differences exist between them.
The various kinds of correction must be done for all the radioactivity data, for example, background subtraction, counting efficiency, and so on, depending on the measuring places and instruments.
The test of the significance of the data must be done under the assumption that the variances of the data are different each other, although the parent means of the radioactivities can be assumed to be equal. Therefore, the Welch tests are often used for the radioactivity data.
The author has attempted Monte-Carlo simulations to know the distribution of the normalized statistic which corresponds to that for the Welch test, and concluded that the statistic was not of the t-distribution but of the normal one.
It is therefore concluded that the Welch test is not suitable to the test of the radioactivity data and involves much risks not to reject the significantly different data.
