View report page

Diagram I.
For each group the odds are a thousand to one that any subsequent average taken from the
same material will fall within the limits of the original average A + 3 σ/N, σ being the standard
deviation and N the number of observations in the original group. For each group of schools and for
each age and sex these limits have been calculated both for stature and weight. The ordinates
represent statures in centimetres and the abscissae weights in kilograms. They are shown in the charts
for the three groups, A, B, and C schools for each year of age, and for boys and girls separately.
12
Thus the average stature of boys of 11 years old was for 635 boys in the schools of Group B
equal to 135'82 cm., ascertained as shown above, and for 386 boys in schools of Group C 132.54 cm. To
test the significance of this difference. A2— A2. = 135.82 — 132.54 = 3.28 cm., and from the table
and σ2 are found, then
but the difference of the averages ( A2 — A2) is about seven times as great, i.e,.,3.28 /.4673 = 7.1, and the odds
are many millions to 1 against random difference, so that some definite factor must be acting.
So, too, with groups A and B. The difference between the averages is about six times as great,
again meaning millions to one against chance or random sampling, but between groups A and C, it
is found
Group A. Average height A2 133 4 Number 440 σ =6.1500.
Group C. Average height A2 13254 Number 386 σ=7.5352.
Now .86/.48 = 1.8 so that the odds are only thirty to one against random selection, and this is
not enough to establish a real difference between them, or allow any definite conclusion to be drawn
from their difference.
The probable error of a series of observations is that divergence from their mean on either side
within which exactly half the observations lie.
The co-efficient of variation is the figure obtained by dividing the standard deviation of a
group, multiplied by one hundred, by the arithmetical mean. It gives a value for the variation of a
series independent of the unit employed. Roughly speaking, the amount of variation in groups, in
which a sufficiently large number of measurements has been made increases with age. These three
groups will serve as standards with which any subsequent averages may be compared.
The results may perhaps be more clearly shown graphically in diagrams I., II., III.