Statistical significance, number samples needed

The use of statistical tests to analyze and quantify the significance of sample data is widespread in the study of biological systems where precise physical models are not readily available. Statistical tests are used in conjunction with measured data as an aid to understanding the significance of a result. Their aid in data analysis fills a need to answer the question of whether or not the inferences drawn from the data set are probable and statistically relevant. The statistical tests go further than a mere qualitative description of relevance. They are designed to provide a quantitative number for the probability that the stated hypothesis about the data is either true or false. In addition, they allow for the assessment of whether there are enough data to make a reasonable assumption about the system. 

The o of a Poisson distribution can be shown to be equal to (N)1 2 where N Is the number of particles counted. An experimental standard deviation (S) for counts In all channels less than or equal to a, was chosen as the criterion for number of samples to Indicate that the error was due to counting statistics rather than any other experimental parameter. The results are presented In Table I and a channel size Identification In Table II. It can be seen that the above criterion was met when the number of samples was at least 6. It should be understood that when the total number of particles Is small. Increased counting times and number of samples are needed to attain statistical significance. 

The number of samples needed to obtain an experimental standard deviation less than or equal to the Poisson standard deviation was found to be six when particle counts were 2000 particles/ft or greater. If the particle concentration Is lower. Increased counting times and number of samples will be required to attain the same level of statistical significance. 

Massive stars are less numerous than low mass stars implying a smaller number of progenitors and the need to survey large areas in the sky to build statistically significant samples. 

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