# Null Hypothesis Statement With One-sided Tests

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• #54901

Chris Paret
Participant

So here is an interesting topic…. The Null Hypothesis Statement when conducting a one sided test.

Should it be written as a statement of equality (=)

OR

should the Null be expressed as composite (<= or >=)?

From my understanding neither is wrong. I’m just trying to figure out from this fine group what is the most common convention.

Thanks.

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#197604

Rajesh
Guest

Fundamentally the 1-sample t-test compares a sample taken from a process whose output is deemed gaussian, to a standard or constant.

Therefore, whether we use =/!=, <= or >=, depends on the context. If you’re trying to compare a sample to a standard, sometimes, you could compare to check if its mean has to be lesser than the standard, and sometimes, greater. You may also know whether or not it is okay for the mean to be equal to the standard. In such a situation, you can choose whether to use the “<=” or “>=” conditions.

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#197605

Robert Butler
Participant

Equivalence testing is not the same thing as a one sided test. Therefore = is not an acceptable choice for the null. All of my references state that, for a one sided test, the null is either <= or >= and the alternative is either > or <.

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#197607

Chris Paret
Participant

@robert – thanks for your comments. Maybe I should provide a bit more clarity. I’m more concerned about more common hypothesis tests such as 2 Means t-tests (2 Sample t), 2 Propotions, etc. Equivalence testing is its own beast. And maybe there is confusion (likely on my part) as I don’t think a 2 Means t-Test with Ho: Sample 1 = Sample 2 and Ha: Sample 1 ≠ Sample 2 is Equivalence testing.

Anyway, most software packages show the null as = even when the alternative is > or <. So theoretically the null at <= or >= is correct, but in practice and in training what is the common convention for the null.

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#197608

Robert Butler
Participant

For a two sided test the null is indeed mean1 = mean2 and the alternative is that mean1 is not equal to mean2. This is reasonable because the two sided test is checking for changes in both directions. In a one sided test you are only interested in deviations in a single direction therefore the null can’t be stated as mean1 = mean2 because you are only testing deviations in a single direction (greater than or less than)and ignoring the possibilty of changes in the untested direction.

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#197614

I have always found it useful (essential) to start the null with “there is no difference between”.. the one can proceed …”the mean of this sample and x.xx”, or “the mean of this sample and < x.xx (or >x.xx)

Minitab provides the option for greater than or less than in 1 sample T tests, something in my experience which is not often well understood.

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#197616

The null plus the alternate equals all possible outcomes.

Then, for ONE sided, if the alternate is all outcomes less than X, the null is everything else, i.e., all outcomes greater than or equal to X.

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