Null and Alternate Hypotheses

The first step of hypothesis testing is the formulation of the null and alternate hypotheses for a given situation. Let’s learn how to do this through different examples.

You have seen examples where you can write the null hypothesis (or status quo) easily from the claim statement, like in the last question - Flipkart claimed that its total valuation in December 2016 was $14 billion.

But in some instances, if your claim statement has words like “at least”, “at most”, “less than”, or “greater than”, you cannot formulate the null hypothesis just from the claim statement (because it’s not necessary that the claim is always about the status quo).

You can use the following rule to formulate the null and alternate hypotheses:

The null hypothesis always has the following signs:  =  OR   ≤   OR    ≥

The alternate hypothesis always has the following signs:  ≠   OR  >   OR    <

For example:  

Situation 1:  Flipkart claimed that its total valuation in December 2016 was at least $14 billion. Here, the claim contains ≥ sign (i.e. the at least sign), so the null hypothesis is the original claim.

The hypothesis in this case can be formulated as:

Situation 2:  Flipkart claimed that its total valuation in December 2016 was greater than $14 billion. Here, the claim contains > sign (i.e. the ‘more than’ sign), so the null hypothesis is the complement of the original claim. The hypothesis in this case can be formulated as:

The hypothesis in this case can be formulated as:

To summarize this, you cannot decide the status quo or formulate the null hypotheses from the claim statement, you need to take care of signs in writing the null hypothesis. Null Hypothesis never contains ≠ or > or < signs. It always has to be formulated using = or ≤ or ≥ signs.

Before you go ahead and look at some more examples of formulating null and alternate hypothesis, let us hear from Ankit Jain about how he used hypothesis testing during his time at Facebook.