LIFE HISTORY OP LAKE HERRING OF LAKE HURON 



285 



between the two means being considered significant if it is at least five times its 

 probable error. 



Table 6. — Average number of scales in the lateral line of herring collected October 26, 27 , and 29, 1921 , 

 A'oi^ember 1, 1922, and November 12, 1923, at Bay City, Mich., for each age group ' 



' The number of specimens upon which each average is based is given in parentheses. Eighteen fish of age group II, taken 

 Nov. 2, 1922, at Oscoda. Mich., about 70 miles north of Bay City, had an average scale number of 80.39, while 10 fish of this age 

 group taJien in dilTorent years and at dilferent localities on Lalie Huron had an average of 80.80. The grand average of the 28 fish 

 was 80.54. 



The two 1921 collections have been grouped together, as it is probable from a 

 study of Table 7 (containing the frequency distribution of the scales in the lateral 

 line) that both groups belong to the same population. The mean of the scale numbers 

 as well as the mode and range are virtually identical in the two collections. This 

 homogeneity is further evident when we compare statistically the two 4-year groups, 

 for example, which involve the greatest number of specimens. The difference (1.16) 

 between the two averages was computed to be 2.79 times its probable error. The 

 differences [range = 0.21 — 1.83 (2.06); average = l.ll (1.30)] of the other age groups 

 of the 1921 collections also may be accounted for by personal errors or by random 

 sampling (see Table 4, p. 283), or possibly by the persistently though trifle larger 

 average lengths (1 to 3 millimeters) of the fish taken October 29. 



It is seen from Table 6 that the grand average of the 1921 age groups, though 

 lowest in year III, does not increase consistently with each higher age group. Com- 

 putations show that the probable error of the mean of the 3-year fish is 0.3191, of 

 the 6-year group 0.3203, of the difference between the means 0.4521, and that the 

 difference, 0.9291," between the averages of these two age groups of 1921 equals 

 2.06 times its probable error and is therefore not significant. The differences between 

 the averages of the 1922 fish are even less than those of the 1921 herring. Here, also, 

 an increase in scale number can not be correlated with a higher age group. In the 

 1923 herring, however, as in the 1921 fish of October 29, the average increases slightly 

 with each older year class. As the difference between the extreme means of the 

 October 29 specimens is greater and the number of mdividuals included m these 

 means is larger than that of the 1923 fish, the averages of the 1921 herring are preferred 

 for statistical treatment. Computations show that the probable error of the mean 

 of the third and sixth age group of this collection is 0.3318 and 0.4562, respectively, 

 that the probable error of the differences between the two means is 0.5641, and that 

 the difference, 1.57, is 2.78 times its probable error. The difference between the 

 extreme averages (III and VI) of the 1923 herring is only 1.02. The footnote of 



' In the table the averages are given to the second decimal place. 



