210 STATISTICAL TREATMENTS 



Other statistics 



The mean is the most commonly used measure of central trend in ex- 

 perimental work. Two other measures are important in certain situations. 

 The median divides the distribution of variates into two equal halves; 

 half the values lie below the median, half above. The mode is that value 

 which occurs most frequently. In the normal curve the three measures 

 coincide. 



Several methods other than the variance exist for estimating the 

 variability of a distribution, or the "error." Experimental results are 

 frequently presented in papers as (for example) 167 ±13. The error 

 figure (±13) might have any of several meanings, and it can be inter- 

 preted by a reader only if the writer specifies how it was calculated. 



The range, a useful estimate in some cases, is the difference between 

 the largest value and the smallest. It gives quick information, and, if 

 the ranges of two samples do not overlap, the difference between the 

 samples is almost certainly significant. 



Probable error is a deviation from the mean such that ±1 PE in- 

 cludes one-half the cases. If the distribution of values is normal, ± 1 PE 

 also includes half the area under the curve; from this, PE = 0.6745cr. 



The standard error of the mean (SE) is the preferred statistic to be 

 included in tables of data. If everyone agreed with this statement, then 

 167 ± 13 above would be the mean and the standard error of the 

 mean. The standard error was calculated as cr/\/n. Radioactive decay is 

 almost perfectly random, and the number of counts determined is usually 

 large. In this case a short-cut method of computing the standard error 

 can be used. A certain number of counts (C) in a total time of X minutes 

 yields an average rate of C/t counts per minute. The standard error is 

 computed as \/C/t. This value is so near to a-/\/n that the agreement 

 between the two methods is used as a check on the randomness of the 

 counting. This relationship holds because in the normal curve cr is almost 

 equal to \/m. 



The application of statistics 



Because the use of statistical analysis depends upon a number of as- 

 sumptions, the conclusions drauoi can be no more valid than the assump- 



