## Introduction to Statistical Hypotheses:

Whenever we want to apply some statistical test to evaluate
experimental data, we need to frame our question in an statistical
appropriate form. In other words, we need to state a *hypothesis*
from which conclusions can be drawn. Some
common questions have already
been outlined; in this section, we will see how to formulate these into
hypotheses that can then be subjected to statistical evaluation.

Suppose, for example, that we have two sets of replicate data obtained for the same sample. This could be as a result of an analyst repeating the determination on different occasions, or having two different analysts perform the same determination on the same sample. We might want to know several things about the two sets of data:

- Did the two sets of measurements yield the same result?
- Is one set of measurements more or less precise than the other?
- Is one set of results more or less accurate than the other?

Remember that any set of measurements represents a
sample from the
population of all possible results; there will *always*
be some inherent variation in the mean and standard deviation for each set
of replicate measurements. What we therefore need to establish is whether
or not our two sets of measurements are drawn from the *same*, or
*different* populations. In statistical terms, we might therefore
propose a hypothesis statement (* H*) that:

** H:** “two sets of data (1 and 2)
with sample means

*m*

_{1}and

*m*

_{2}, are both part of the same population such that their population means

*μ*

_{1}and

*μ*

_{2}are equal (

*μ*

_{1}=

*μ*

_{2})”