Can you state three alternative hypotheses?The three possible alternatives are:
- H 1 :P≠π (LEA proportion of statements is not equal to (≠) the proportion in England and
Wales) - H 1 :P>π (LEA proportion of statements is greater than (>) the proportion in England and
Wales) - H 1 :P<π (LEA proportion of statements is less than (<) the proportion in England and
Wales)
The first alternative hypothesis reflects the situation when a researcher is interested in
testing whether the proportion of referrals is different from the national proportion, either
less than or greater than. This is a two-tailed test because consideration is given to
proportions both less than 0.130 (π) and greater than 0.130.
This last alternative reflects the teachers’ opinions; they were concerned about the
LEA proportion of referrals being less than the proportion in England and Wales. If the
researcher were to just consider this possibility, P<0.130, this would represent a one-
tailed test since there would be no interest in values of P>0.130.
Generally it is this author’s advice not to use one-tailed tests unless there are
compelling reasons to do so. The reason is that it is easy to introduce bias by making a
choice prior to testing a hypothesis. The intention of hypothesis testing is not to test what
is expected but to identify what is plausibly not true.
The idea of hypothesis testing is so important in quantitative research design and
analysis that at this point it is helpful to pause and to recap the logic underpinning this
approach. The idea is that we test for a statistically significant difference between two or
more population parameters. Sample statistics are used as estimators and this explains
why a null hypothesis may be stated as, ‘there is no difference between sample A and
sample B’ or ‘treatment C and treatment D are equally effective’ or ‘the proportion for
the LEA is no different from the proportion for England and Wales’. Although we may
be comparing sample statistics or a sample statistic with a known population parameter
you should remember that a null hypothesis is a hypothesis about the situation in the
population hence the importance of statistical inference, probability and sampling
distributions.
In summary, the general approach to hypothesis testing is based on inference and is a
way of deciding whether data are consistent with a null hypothesis. The usual steps in
testing a statistical hypothesis are:
1 State the null and alternative hypotheses.
2 Decide whether a one- or two-sided (tailed) test is appropriate and state the significance
level, alpha, of the test. Alpha is the level of probability for rejection of the null
hypothesis, usually in social sciences p≤.05). A one-sided test means that you are only
concerned with one tail of the sampling distribution.
3 Calculate a test statistic and confidence interval from the data obtained in a sample.
4 Report whether the selected confidence interval excludes zero and compare the
probability value associated with the test statistic with the chosen alpha level (e.g.,
p≤.05). If the obtained p-value for the test statistic is less than or equal to alpha then
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