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Department

Statistics

Course Code

STAT 3005

Professor

H C Tavera

Lecture

8

Daniel T. Eisert STAT-3005

1

8.2 – Consequences of Testing

Chapter VIII: Using Inference

Consequences of

Testing

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

effect.

- 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.

Power:

- 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.

Sample Size:

- 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.

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