Probability distribution:

An error may also occur during a count which is not entirely due to the random nature of radioactivity but may be due to electronically or mechanical misbehaviour of the counting system causing a decrease or increase in the count rate. A single test to check the operational behaviour of a system can be made as follows.

Count the sample twice and the absolute difference |n1 - n2| may be divided by the standard deviation (σ) to obtain the value of K. Rule of Thumb is that if K > 3.5 then it indicates non-statistical behaviour and the instrument need to be checked. x² test an alternative method of checking the counter for proper operation is known as the chi- square (x²) test defined as;

 If 15 / 20 / 25 counts are recorded consecutively and x² value is calculated then it should be in the range 7.26 to 29.9, 10.8 to 31.4 and 14.6 to 37.6, respectively for 95% confidence. However, if the values are beyond these limits (smaller or greater) then the errors are not purely statistical and the instrument may not be behaving properly.

Figure: Probability distribution of activity count rate with its frequency