and more of the increasing towns in the southern half. With respect to 

 criterion 2, there were only three towns in the State within the population 

 sizes stipulated that did not show some slight increase in one of the inter- 

 censal periods. Those towns with decreasing population were selected in 

 which the increase in any one decennial period was least and in which 

 net change 1920-1950 was greatest. See Table 1. 



Population and Characteristics 



The sample of increasing towns was compared with the sample of decreas- 

 ing towns, using 1950 data, to see what differences in population char- 

 acteristics, if any, existed following a 20-year history of increase or de- 

 crease respectively. 



Age-Sex Distribution 



A comparison of the 1950 age-sex distribution of the two sets of towns 

 was made by use of the Chi Square technique.* It was recognized that as 

 a measure this is relatively crude and that statistically it is not a unique 

 measure. However, if the categories for each set of towns are identical, 

 the fact that different values could be attained by different groupings of 

 classes should not affect the validity of the relation between the two arrays. 



One reason for using Chi Square is the fact that all the differences 

 cumulate, hence it is impossible for differences which might vary in opposite 

 directions to cancel one another. In this sense Chi Square becomes a con- 

 servative measure of the relationship between the two arrays. 



Using the census age categories as they appear on the photostats of the 

 Minor Civil Division count cards fO-5, 5-14, 15-20, 21-24, 25-34, 35-44, 

 45-54, 55-64, 65 and over) and further dividing the distribution by sex, 

 the Chi Square value of the relationship between increasing and decreas- 

 ing towns in 1950 was 5.42. The probability of getting a value greater 

 than this with 17 degrees of freedom is in excess of 99 percent; that is, 

 the two distributions are very much alike. 



To test further the differences between specific age and sex groups, "t" 

 scores were computed to test the significance of the difference between 

 means of the same age-sex groups of the sub-samples. f 



The highest value of "t" obtained in any of the 18 comparisons was 0.82, 

 and the probability of getting a difference as great as that by chance with 

 9 degrees of freedom is 0.55. All other probabilities, hence, were much 



* Clii Square is based on the deviation of an observed frequency from a theoretical 

 frequency. If this latter is derived from some hypothesis, the Chi Square directly 

 measures the deviation of the sample around some theoretical population. In order to 

 test the significance of a given value of Chi Square, it is necessary to know how 

 often a Chi Square of the specified size would occur by chance in the long run. Pub- 

 lished sampling distributions of Chi Square are used for this purpose, using the 

 appropriate number of degrees of freedom. 



t The "t" score is a statistic useful for comparing sample values when the number 

 of cases in the samples is small. It permits direct comparison of two different values 

 derived from two different samples, compensating at the same time for small sample 

 size. To test the significance of "t", it is necessary to know how often a "t" of 

 the specified size would occur by chance in the long run. Published sampling distri- 

 butions of "t" are used for this purpose using the appropriate number of degrees of 



freedom. Frequently this is indicated by (p = ) following the "t" value designating 



the probability of a value of "t" this large being obtained by chance. 



