9597

• UCREFRP Catalog Number: 9597
• Author: U.S. Environmental Protection Agency.
• Title: Biological Field and Laboratory Methods for Measuring the Quality of Surface Waters and Effluents.
• USFW Year: 1973.
• USFW - Doc Type: Cincinnati, OH.
• Copyright Material: NO

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right of the last place to be retained. If this
number is greater than 5, the last place to be
retained is rounded up by 1; if it is less than 5,
do not change the last place - merely drop the
extra places. To round to 2 decimal places:

Unrounded
1. 239
28.5849

Rounded
1.24
28.58

. If the digit to the right of the last place to
be retained is 5, then look at the second digit to
the right of the last place to be kept, provided
that the unrounded number is recorded with
that digit as a significant digit. If the second
digit to the right is greater than 0, then round
the number up by 1 in the last place to be kept;
if the second digit is 0, then look at the third
digit, etc. To round to 1 place:

Unrounded
13.251
13.25001

Rounded
13.3
13.3

. If the number is recorded to only one place
to the right of the last place to be kept, and that
digit is 0, or if the significant digits two or more
places beyond the last place to be kept are all 0,
a special rule (odd-even rule) is followed to en-
sure that upward rounding occurs as frequently
as downward rounding. The rule is: if the digit
to the right of the last place to be kept is 5, and
is the last digit of significance, or if all following
significant digits are 0, round up when the last
digit to be retained is odd and drop the 5 when
the last digit to be retained is even. To round to
1 place:

Unrounded
13.2500
13.3500

Rounded
13.2
13.4

.

Caution: all rounding must be made in 1 step
to avoid introducing bias. For example the
number 5.451 rounded to a whole number is
clearly 5, but if the rounding were done in two
steps it would first be rounded to 5.5 then to 6.

BIOMETRICS - TESTS OF HYPOTHESES

Retaining Significant Figures

Retention of significant figures in statistical
computations can be summarized in three rules:
. Never use more significance for a raw data
value than is warranted.
. During intermediate computations keep all
significant figures for each data value, and carry
the computations out in full.
. Round the final result to the accuracy set
by the least accurate data value.

5.0 TESTS OF HYPOTHESES

Often in biological field studies some aspect
of the study is directed to answering a hypothet-
ical question about a population. If the hy-
pothesis is quantifiable, such as: "At the time of
sampling, the standing crop of plankton biomass
per liter in lake A was the same as the standing
crop per liter in lake B," then the hypothesis can
be tested statistically. The question of drawing a
sample in such a way that there is freedom from
bias, so that such a test may be made, was dis-
cussed in the section on sampling (2.0).
Three standard types of tests of hypotheses
will be described: the "t-test," the "X2 -test,"
and the "F-test."

5.1 T-test

The t-test is used to compare a sample statistic
(such as the mean) with some value for the
purpose of making a judgment about the popula-
tion as indicated by the sample. The comparison
value may be the mean of another sample (in
which case we are using the two samples to judge
whether the two populations are the same). The
form of the t-statistic is

t=o-e
So (26)

where a = some sample statistic; Sa = the
standard deviation of the sample statistic; and
e = the value to which the sample statistic is
compared (the value of the null hypothesis).

The use of the t-test requires the use of
t-tables. The t-table is a two-way table usually
arranged wi th the column headings being the
probability, lX, of rejecting the null hypothesis
when it is true, and the row headings being the
degrees of freedom. Entry of the table at the

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