Biomedical Engineering Reference
In-Depth Information
large scatter
nominal scatter
small scatter
average
Figure 9.24
Demonstration of equal average but wildly variant scatter.
spread of data by giving the average and the range of the data. It is better to give an average
and the confidence limits. These are normally the 95% confidence limits (or levels); and it
literally means that you are 95% confident that the average lies within this range.
If you have 20 or more samples the equation for the confidence limits is
σ
(9.5)
95
%limits
x
2
N
where
σ
is the standard deviation and
N
is the number of samples. You should note that the
constant value, 2, is rounded up. For an infinite number of data points it is 1.96, for 20 points
it is 2.09.
Most spreadsheets have automatic functions for both average and standard deviation
calculations (as do most calculators), so it is not a difficult task to produce an equivalent
Table 9.14
for any data set. Using data set 1 as the example, this would be cited as
Average
91
.
0 137
.
(%
95
conf limits
)
9.6.6.4 The Student t-test
The t-test (as it is known) is the first port of call for most investigators trying to ascertain
whether there is any difference between two (or more) groups. Describing the mathematical
basis behind the process is beyond the scope of this text, but it is a very powerful tool that,
again, most spreadsheet packages have as an built-in function. The main aim of the t-test is to
test a hypothesis. As we saw earlier, the hypothesis is the basis for the whole investigation, so
you can imagine how important this first step into a statistical analysis has become.
To demonstrate how the analysis is performed the data in
Table 9.14
will be used, and we
shall compare data set 1 with data set 2 (i.e., the one with the least error with the one with the
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