# Null hypothesis and alternate hypothesis

What should we consider the null hypothesis?

A test statistic is a statistic used to measure the plausibility of an alternative hypothesis relative to a null hypothesis. (The statistical Sleuth)

From this it can be concluded that the alternate hypothesis should be the scientific hypothesis one is trying to establish.

Now this is from a blog I'm using to understand stats

The null hypothesis, H0 is the commonly accepted fact; it is the opposite of the alternate hypothesis. Researchers work to reject, nullify or disprove the null hypothesis. Researchers come up with an alternate hypothesis, one that they think explains a phenomenon, and then work to reject the null hypothesis.

Even at my college this was taught.

But recently I have started taking help from a Stats teacher who along with a Zoology Practical book by P.K. Banerjee is of the opinion that our scientific hypothesis should be the null!

Infact I came to know that when we are not sure what we should be deducing from our data we test if it is consistent with any known theoretical data. It is then that null becomes central,i.e. the hypothesis the scientist is interested in. I found this also in wiki example.

Is this what makes the two types of assumptions different?

Discussing with a problem

A professor wants to determine whether her department should continue keeping the prerequisite for an introductory stats course that the students applying must [preferably] have college level algebra in previous curriculum. She decided to find out from an year's result of that course.

With algebra = 34 (passed) & 6 (failed)

Without algebra = 12 (passed) & 18 (failed)

Are students who had college level algebra in their previous curriculum were more likely to pass the course?

My answer:

[A chi square contingency]

Ho= The students who had college level algebra in their previous curriculum did not have a greater likelihood to pass the course over those without algebra.

Ha= They did have.

The calculated Chi-square was smaller than critical value and so the null was accepted.

Now the Stats teacher said that it would be the opposite.

• I think you might be confused about something else. The test in question should reject the null. It isn't clear what is meant by tabulated Chi-square was smaller than the critical value.' – HStamper Mar 30 '17 at 20:28
• Fixed @EricMittman Can you elaborate,The test in question should reject the null`. – Tyto alba Mar 30 '17 at 20:31
• Running chisq.test in R with the contingency table you gave: X-squared = 13.475, df = 1, p-value = 0.0002418 – HStamper Mar 30 '17 at 21:14
• The null hypothesis is usually the hypothesis you try to reject and the alternative hypothesis is usually the scientific hypothesis. – Michael Chernick Mar 31 '17 at 0:03
• "From this it can be concluded that the alternate hypothesis should be the scientific hypothesis one is trying to establish." -- usually, but not always. Typically you seek to "falsify" some position -- by showing that the position is untenable (inconsistent with data). But sometimes you're not trying to do that. So for example, in some situations you might perhaps be using equivalence tests or noninferiority tests. – Glen_b Mar 31 '17 at 9:09

## 1 Answer

It appears you are asking for clarification..

A null, Ho, essentially predicts no effect (no difference between groups, no correlation/association between variables etc), whereas an alternative/experimental, Ha or H1 predicts an effect.

So in your example, you have the gist of Ho and Ha (though the wording could be improved).

Your Chi-square test gives you a chi-square value - you need to either a) compare this with a 'critical' chi-square value b) know the p-value associated with your chi-square value and compare this with an 'alpha' p-value (typically .05 in psychology for example)

These amount to the same kind of thing For this example, if your alpha/cutoff is .05, then your 'critical' chi-square is 3.841.

NHST requires that, if your p-value is LESS than your alpha/cutoff, then you reject the null.

Here's where the confusion might arise: As chi-square values increase, associated p values decrease.

So, if your chi-square value is SMALLER than the critical, your associated p-value would be LARGER than the alpha/cutoff. If p is larger, the null is NOT rejected.

If your chi-square value is LARGER than the critical, your associated p-value would be SMALLER than the alpha/cutoff. If p is smaller, the null IS rejected.

• I have found a number of sources support the fact that a null hypothesis is not always 'not the same' hypothesis. Here are few of them wiki and an old post. – Tyto alba Mar 30 '17 at 20:44