Choosing the Significant Level (alpha):
- What are the consequences of rejecting the null hypothesis?
- Are you conducting a preliminary study?—if so, you may want a larger
alpha-level so that you will be less likely to miss an interesting result.
- There are no “sharp” cutoffs: 4.9% vs. 5.1%, for example.
- It is the order of magnitude of the p-value that matters: “somewhat
significant”, “significant”, or “very significant.”
Cautions about Significance Tests:
- Statistical significance only says whether the effect observed is likely to be
due to chance along because of random sampling.
- Statistical significance may NOT be practically important because statistical
significance doesn’t tell you about the magnitude of the event, only that
there is one.
- An effect could be too small to be relevant.
- With large sample sizes, significance can be reached even for the tiniest
- Having no proof of something does not imply that the action was not done.
- There is no consensus on how big an effect has to be in order to be
considered meaningful. In some cases, effects that may appear to be trivial
can be very important. Always think about the context. Try to plot the
results and compare them with a baseline or results from other studies.
- Type I Error: if we reject H0 when H0 is TRUE.
o The probability of a Type I Error is the probability of rejecting H0
when it is actually true.
o The significance level � of any fixed-level test is the probability of a
Type I Error. That is, � is the probability that the rest will reject the
null hypothesis when it Is actually try.
- Type II Error: if we FAIL to reject H0 when H0 is FALSE.
o There are many values of the parameter that satisfy the alternative
hypothesis, so we need to concentrate on one value.
o The probability that a test does reject H0 when H1 is TRUE is called
the power of the test.
o Power refers to testing against a specific alternative is the
probability that the test will reject the null hypothesis at a chosen
significance level when the specified alternative value of the
parameter is true.
- If you want a smaller significance level (i.e. 1%), take a larger sample. A
smaller significance level requires stronger evidence to reject H0.
- If you want higher power (i.e. 99%), take a larger sample. Higher power
gives a better chance of detecting a difference when it is really there.
- At any significance level / desired power, detecting a small difference
requires a larger sample than detecting a large difference.