How to State the Null Hypothesis in Statistics: Part One

Hypothesis Testing 12 Comments

You’ll be asked to convert a word problem into a hypothesis statement in statistics that will include a null hypothesis and an alternate hypothesis. Breaking your problem into a few small steps makes these problems much easier to handle.
Sample Problem: A researcher thinks that if knee surgery patients go to physical therapy twice a week (instead of 3 times), their recovery period will be longer. Average recovery times for knee surgery patients is 8.2 weeks. 

Step 1: Figure out the hypothesis from the problem. The hypothesis is usually hidden in a word problem, and is sometimes a statement of what you expect to happen in the experiment. The hypothesis in the above question is “I expect the average recovery period to be greater than 8.2 weeks.”

Step 2: Convert the hypothesis to math. Remember that the average is sometimes written as  μ.

H1: μ > 8.2

Broken down into (somewhat) English, that’s H1 (The  hypothesis): μ (the average) > (is greater than) 8.2
Step 3: State what will happen if the hypothesis doesn’t come true. If the recovery time isn’t greater than 8.2 weeks, there are only two possibilities, that the recovery time is equal to 8.2 weeks or less than 8.2 weeks.

H0: μ ≤ 8.2

Broken down again into English, that’s H0 (The null hypothesis): μ (the average) ≤ (is less than or equal to) 8.2

That’s it!

But what if the researcher doesn’t have any idea what will happen? See part two of Stating the Null and Alternate Hypothesis

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12 Responses to “How to State the Null Hypothesis in Statistics: Part One”

  1. Angie Widdows said:

    Oct 15, 09 at 9:44 am

    This was a good example. It is the next step that I often have problems with. This example helps because it (like others) lists out the meaning of the symbols. Very helpful

  2. How to Do Everything Statistics » How to State the Null Hypothesis in Statistics: Part Two said:

    Oct 17, 09 at 5:29 am

    [...] the previous post on How to State the Null Hypothesis, I explained how to convert a word problem into a hypothesis statement if you have an idea about [...]

  3. How to Do Everything Statistics » How to Support or Reject a Null Hypothesis (Using a P-Value) said:

    Oct 17, 09 at 5:42 am

    [...] Deciding to support or reject a null hypothesis in statistics can seem like an overwhelming task at first. The question will state that a researcher made a claim; your task is to decide whether the evidence supports the claim. If you have a P-value, or are asked to find a P-value, follow these instructions. If you do not have a P-Value, follow Reject/Support the Null Hypothesis instead. Step 1: State the null hypothesis and the alternate hypothesis (”the claim”). If you aren’t sure how to do this, follow this link for How To State the Null and Alternate Hypothesis. [...]

  4. How to Do Everything Statistics » How to Support or Reject a Null Hypothesis said:

    Oct 17, 09 at 5:45 am

    [...] the alternate hypothesis (”the claim”). If you aren’t sure how to do this, follow this link for How To State the Null and Alternate Hypothesis. Step 2: Find the critical value. You should have already covered that topic by this point, but [...]

  5. How to Do Everything Statistics » How to Support or Reject a Null Hypothesis (for a Proportion) said:

    Oct 17, 09 at 10:02 am

    [...] Sometimes, you’ll be given a proportion of the population or a percentage and asked to reject or support the researcher’s claim. For example, a researcher claims that 40% of the population support Obama, or claims that 12% of the population are vegetarians. In this case you can’t compute a test value by calculating a z-score (you need actual numbers for that), so we use a slightly different technique. Sample question: A researcher claims that 16% of vegetarians are actually vegans. In a recent survey, 19 out of 100 vegetarians stated they were vegan. Is there enough evidence at α=0.05 to support this claim? Step 1: State the null hypothesis and the alternate hypothesis (”the claim”). Ho:p=0.16 (claim); H1 If you aren’t sure how to do this, follow this link for How To State the Null and Alternate Hypothesis. [...]

  6. Lisa Barcomb said:

    Oct 18, 09 at 10:36 am

    Understanding the null hypothesis is much easier now because when you go to convert it to math it makes a lot more sense in figuring out the formulas that you are suppose to be working with. I think I put more into these problems then I really need to.

  7. Vanessa DuBarry said:

    Oct 27, 09 at 9:39 am

    This example really helped me, because it explains how to put it into english, and at first it was kind of hard knowing what sign goes were, but this really helped.

  8. Donna Allen said:

    Oct 27, 09 at 2:17 pm

    At first, I was a little intimidated by this. But, after going over your instructions, it seems fairly easy. Thanks!

  9. Bill Bryan said:

    Nov 03, 09 at 1:45 pm

    I was starting to get that sinking feeling until I read this, love the matter of fact approch to discribing the steps.

  10. How to Do Everything Statistics » How to Support or Reject a Null Hypothesis (for a Proportion: P-Value Method) said:

    Nov 18, 09 at 5:02 am

    [...] There are four main ways you’ll compute test values and reject or support a hypothesis: two ways are with proportions (i.e. percentages) and two are without (if you do not have a proportion, check out how to support/reject a null hypothesis). This how to shows you the steps to deciding whether to support or reject a null hypothesis, using the P-Value method. Sample question: A researcher claims that more than 23% of community members go to church regularly. In a recent survey, 126 out of 420 people stated they went to church regularly. Is there enough evidence at α=0.05 to support this claim? Use the P-Value method. Step 1: State the null hypothesis and the alternate hypothesis (”the claim”). Ho:p ≤ 0.23; H1:p>0.23 (claim) If you aren’t sure how to do this, follow this link for How To State the Null and Alternate Hypothesis. [...]

  11. 10.1 Statistical Hypotheses « MS in OR said:

    Jan 09, 12 at 8:11 pm

    [...] http://www.statisticshowto.com/articles/how-to-state-the-null-hypothesis-in-statistics/ Share this:TwitterFacebookLike this:LikeBe the first to like this post. [...]

  12. What Does it Mean to Reject the Null Hypothesis? | said:

    Nov 09, 12 at 9:04 am

    [...] hypothesis first, because that’s the researcher’s thoughts about the experiment. Check out this article if you want to learn how to state the null hypothesis. Step 2: Support or reject the null hypothesis. Several methods exist for supporting or rejecting [...]