What it means
Think of a court case in which the defendant is presumed innocent until proven guilty. The null hypothesis plays the same role: it assumes that nothing special is happening, such as a new pricing strategy having no effect on sales or a fund manager having no skill.
The analyst then collects data to see whether the evidence is too unlikely under that assumption. The competing claim is called the alternative hypothesis, and it states that there is an effect or a difference.
A hypothesis test calculates how likely the observed data would be if the null were true. If that likelihood, known as the p-value, falls below a chosen threshold such as 5%, the analyst rejects the null hypothesis.
An important point is that failing to reject the null is not the same as proving it true. It means the data did not give strong enough evidence against it, which could simply reflect a small sample or noisy data.
Equally, rejecting the null does not prove the alternative with certainty, since there is always a chance of error. Two kinds of error are possible.
A Type I error means rejecting a null that is actually true, a false alarm, and its probability is the significance level the analyst selects. A Type II error means failing to reject a null that is actually false, a missed discovery, and it becomes more likely with small samples.
In business, null hypotheses appear in A/B testing, quality control, audit sampling, investment analysis and market research. Whenever someone asks whether a difference is real or just random variation, a null hypothesis is working in the background.
Getting comfortable with it helps managers question numbers rather than accept them at face value.
In practice
Real-world examples.
Example
A retailer tests a new website layout against the old one. The null hypothesis is that conversion rates are the same, and after two weeks of data the difference is large enough that the team rejects the null and adopts the new layout.
Example
An auditor samples 100 expense claims from a total of 10,000. The null hypothesis is that the error rate is within the acceptable limit, and the sample shows too many errors, so the auditor extends testing.
Example
An investment committee assesses a fund manager who claims to beat the market. The null hypothesis is that the manager has no skill, and the analysis shows the three-year outperformance is well within what luck could produce, so the committee does not reject it.
Formula
Calculation
Test statistic (z) = (Sample mean - Hypothesised mean) / (Sample standard deviation / Square root of sample size)
Suppose a company's historical average invoice is $500 (the null hypothesis), and a sample of 64 recent invoices has an average of $540 with a standard deviation of $160. Standard error = $160 / square root of 64 = $160 / 8 = $20. z = ($540 - $500) / $20 = 2.0. At a 5% significance level with a two-sided test, the critical value is about 1.96, and since 2.0 is larger than 1.96 the company rejects the null hypothesis and concludes that average invoice size has probably changed.Case study
Seen in the real world.
Summit Foods is a fictional company that trialled a new loyalty scheme in 20 of its 200 stores. The marketing director excitedly reported that trial stores had sales 3% higher than the others. The finance analyst asked what the null hypothesis was and whether the difference could be down to chance.
She set the null hypothesis that the loyalty scheme had no effect on sales per store and ran a test. The p-value came out at 22%, well above the usual 5% threshold, so the null could not be rejected. The variation between stores was so large that a 3% gap could easily have appeared by luck.
In this illustrative story, the company extended the trial to 60 stores for six months. The larger sample showed a smaller but consistent effect, and the company launched the scheme with realistic expectations of the return rather than an inflated one.
Watch out
Common mistakes.
- Saying the null hypothesis has been proven true. A failure to reject it only means the evidence was not strong enough against it.
- Treating the p-value as the probability that the null is true. It is the probability of seeing data at least this extreme if the null were true.
- Testing many things and reporting only the significant one. Repeated testing increases the chance of false findings.
Questions
People also ask.
Why start with a null that says nothing is happening?
It gives a clear benchmark, and requires the evidence to be convincing before a change is accepted.
What significance level should I use?
Many fields use 5%, but riskier decisions may justify a stricter level such as 1%.
Is the null hypothesis always about zero difference?
Usually, but it can also state a specific value, such as an average invoice of $500.
From the founder's library
Take it further with the book.
Build your financial confidence beyond this definition. Shihan's full-length guide, Accounting Fundamentals, takes the same plain-English approach and turns it into a complete, practical playbook for non-finance managers, business owners and students - with chapter-end quiz answers and presentation slides included.
25% off with code MMHQ25, applied at checkout. Priced in USD - checkout may show the equivalent in your local currency.
View the book and save 25%Related