Tag Archives: Failing to reject the null hypothesis

The Null Hypothesis: Why it can never be accepted

One of the commonest uses of Biostatistics is null hypothesis significance testing.

This involves the following steps:

1. State the null hypothesis (H0)

2. State the alternative hypothesis (Ha) (one sided or two sided)

3. Choose a test of significance

4. Set the level of significance

5. Make observations and collect data

6. Run the test of significance

7. Take a decision regarding the null hypothesis.

Often, the last step is the trickiest- how does one interpret the test statistic? Does one reject the null hypothesis?

In common usage, when one does not reject something, one is accepting it. This seems logical since accept and reject are antonyms (opposites).

However, in null hypothesis significance testing, one can never accept the null hypothesis. Here’s why:

Let us assume that a 4 year old asked you, “Why do men have larger hands than women?”

You don’t know the answer to that question, but you start wondering if all women have smaller hands than men. Being of a scientific bent of mind, you decide to find out for yourself.

Accordingly, you follow the steps outlined above:

Null hypothesis (H0): The hands of men are the same size as those of women

Alternative hypothesis (Two sided): Men and women do not have the same hand size

You decide to use the Chi-square test to test significance, and set the significance level at 5% (p= 0.05).

You then go around requesting men and women to provide an outline of their hands (on paper). To keep things simple, if you first encountered a woman, you’d then go looking for a man, and vice-versa. For the purpose of the study, it has been decided that a difference of 10% or more in size would qualify as being larger or smaller than the preceding/ succeeding hand.

After spending weeks, you do not find any difference in hand size between men and women (as per definition).

It’s time to conclude the study, you think to yourself.

What would you conclude at this point?

Since you failed to find a significantly larger or smaller hand, would you conclude that the null hypothesis was true and accept it?

Chances are, you’d say, “I’m not sure. Maybe it’s because of the way I collected the data; Maybe it is true in this location, but we’re talking about men and women in general;…”

You decide to obtain one last set of prints before finally concluding the study.

This time the man has a much larger hand than the woman. Point proven. Case closed.

Now what would you conclude?

The null hypothesis has been proven to be false, so it can be rejected.

From the above example we understand the following:

1. It is easier to reject the null hypothesis (because even a single observation to the contrary will disprove it)

2. Numerous factors influence the ability to disprove the null hypothesis

3. Due to this, there is uncertainty about the truth

4. Therefore, it is risky to conclude that the null hypothesis is true merely because we did not find evidence to reject it

5. It is always possible that investigators elsewhere might be able to disprove the null hypothesis. However, in order that they can do this, we must not accept the null hypothesis as true- there is no question of testing something that has already been proven.

6. It is safer (and preferable) to state that we failed to reject the null hypothesis (and leave it to others to test the null hypothesis subsequently), than accepting the null hypothesis as true and making a Type I error.

For these reasons, in null hypothesis significance testing, one can either reject the null hypothesis, or fail to reject it, but can never accept it. 


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