Why is a null hypothesis required?
Do you know why the null hypothesis is tested, instead of the working or alternative hypotheses?
In this Chalk Talk episode that continues our series on statistics,
we’ll explain what the null hypothesis is and the advantages of its use
when comparing against an alternative hypothesis using a fictitious example.
In general, statistical studies test a statement or claim known as a hypothesis.
Let’s assume that a pharmaceutical company develops a bronchodilator that can be used
in the treatment of asthma. Now, the drug's efficacy needs to be assessed in a clinical trial.
To do so, we need to first establish a working hypothesis, which is a preliminary assumption
and represents a starting point from which other more precise hypotheses can be developed.
Let's start by using the company’s expected outcome as the hypothesis:
"The new drug induces bronchodilation in subjects with asthma." However, this hypothesis isn’t
suitable for conducting a study because it’s too general and, therefore, harder to test.
So, which variables should be used to assess the drug’s success, and what should the study measure?
Now, the pharmaceutical company decides to perform pulmonary function tests to assess potential
bronchodilation. Specifically, they decide to use the change in forced expiratory volume in 1
second, abbreviated as FEV1, before and 30 minutes after taking the drug.
From the difference between these two values, the change in the volume of air forcibly expired in one second is measured and,
therefore, can indicate a potential decrease in obstruction and effective bronchodilation.
If you’d like to find out more about pulmonary function tests, check out our Chalk Talk episode
on spirometry, where we explain what the FEV1 value is and how to determine it.
Now, the working hypothesis can be formulated more specifically: "In test subjects with asthma,
the amount of air expired in one second changes 30 minutes after administration of the drug".
With this alternative hypothesis, we have an assumption of what to observe in the study and
what outcome to expect.
However, the alternative hypothesis is still non-specific because it doesn’t specify the size of the expected change, nor does it rule out a decrease in FEV1, although
it’s unlikely.
Without detailed prior knowledge, a more specific hypothesis can’t be formulated.
To avoid the predicament of a lack of prior knowledge, a strategy derived from the philosophy
of critical rationalism can be applied: in other words, acquiring knowledge through contradiction.
In this approach, which can be traced back to the scientific philosopher Karl Popper,
it’s assumed that hypotheses can never really be proven true, only be proven false.
In this theory, the validity of a hypothesis is demonstrated by showing its opposite is false.
So, instead of the alternative hypothesis, the null hypothesis is tested in statistics.
The null hypothesis is mutually exclusive to the alternative hypothesis.
So, in our example, the null hypothesis would be: "In test subjects with asthma, the amount of air expired in one second
doesn’t change 30 minutes after administration of the drug", or, in other words: "There’s no
observable difference in FEV1 on administration of the drug in test subjects with asthma".
Because both hypotheses can’t be correct at the same time, the working hypothesis is the “alternative” to the
null hypothesis.
By the way, there’s also an abbreviation for the null hypothesis:
H0 and for the alternative hypothesis H1.
If a study’s conducted using the null hypothesis, the result should ideally show that the observations are incompatible with the null
hypothesis.
So, the study should falsify the null hypothesis.
According to Popper’s theory, the alternative hypothesis is assumed to be true without it needing to be analyzed.
Does indirect verification seem somewhat odd?
In fact, you probably know this procedure from another application, namely in criminal trials.
In court cases, the alternative hypothesis is: The defendant is guilty.
Accordingly, the null hypothesis is: The defendant is not guilty.
Court proceedings should prove that the null hypothesis is false.
Courts are required to consider the defendant as innocent until proven guilty with a significant amount of evidence.
In statistics, the same approach applies: The null hypothesis is considered true until the
sample data shows otherwise.
In this case, the null hypothesis is rejected and its mutually exclusive alternative hypothesis accepted.
This indirect approach via the null hypothesis can be initially confusing, especially because study data is usually published as though the
alternative hypothesis was analyzed, not the null hypothesis.
Often the null hypothesis isn’t mentioned in publications.
In clinical studies, clinical evidence usually indicates that a drug leads to substantial improvements.
However, the study actually only provides evidence that the drug alters the measured variable.
Whether there’s a positive or negative effect is initially not so important.
Theoretically, a study can also be considered significant if the drug demonstrates a clear disadvantage for the participant.
Now, how is a null hypothesis correctly formulated?
First, it’s important to know what the term: “The null hypothesis is mutually exclusive to the alternative hypothesis” means:
The null hypothesis doesn’t claim any alternative facts and also doesn’t provide any additional
information to the alternative hypothesis.
Hypotheses that don’t follow these rules are known as competing hypotheses.
Why don’t we use a simple example to illustrate the difference?:
Let’s assume that there are red and green balls in a jar.
Our alternative hypothesis is: "The majority of balls in the jar are green."
So, the null hypothesis would be: "The majority of balls in the jar aren’t green."
The hypothesis: "The majority of balls in the jar are red" would be a competing hypothesis, abbreviated as H2.
Well, that wraps it up for the theoretical aspects.
If you’d like to practice formulating the null hypothesis, try the quiz on the next slide.