# Hypothesis Testing: 4 Steps and Example

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*Hypothesis testing can be used various fields such as economics, business decision-making, scientific research, and quality control. — Investopedia / Jessica Olah*

> **Definition**
>
> Hypothesis testing is a procedure designed to measure the strength of a hypothesis based on sample data.

## What Is Hypothesis Testing?

Hypothesis testing is a method of testing an assumption regarding a population by examining data from a sample. The process is sometimes called significance testing,

Hypothesis testing begins when a researcher observes a pattern in a set of data. The test determines whether the pattern can be explained by coincidence or other variables.

The methodology used depends on the nature of the data and the reason for the analysis.

### Key Takeaways

*   The four steps of hypothesis testing include stating the hypotheses, formulating an analysis plan, analyzing the sample data, and interpreting the results.
*   The test provides evidence concerning the plausibility of the hypothesis, given the data.
*   Statistical analysts test a hypothesis by measuring and examining a sample of the population being analyzed.

## How Hypothesis Testing Works

In hypothesis testing, an [analyst](https://www.investopedia.com/terms/a/analyst.asp) tests a statistical sample, intending to provide evidence on the plausibility of the null hypothesis. Statistical analysts measure and examine a random sample of the population being analyzed. All analysts use a random population sample to test two different hypotheses: the [null hypothesis](https://www.investopedia.com/terms/n/null_hypothesis.asp) and the alternative hypothesis.

The null hypothesis is usually a hypothesis of equality between population parameters; e.g., a null hypothesis may state that the population mean return is equal to zero. The alternative hypothesis is effectively the opposite of a null hypothesis. Thus, they are [mutually exclusive](https://www.investopedia.com/terms/m/mutuallyexclusive.asp), and only one can be true. However, one of the two hypotheses will always be true.

> **Important**
>
> The null hypothesis is a statement about the data that is assumed to be true.

## 4-Step Process

The steps in hypothesis testing are:

1.  State the hypotheses.
2.  Formulate an analysis plan, which outlines how the data will be evaluated.
3.  Carry out the plan and analyze the sample data.
4.  Interpret the results and either reject the null hypothesis, or state that the null hypothesis is plausible, given the data.

## Example of Hypothesis Testing

If a researcher wants to test if a penny is fair, the null hypothesis would state that the probability of landing on heads is exactly 50%. The alternative hypothesis would assert that the probability of landing on heads is not 50%. Mathematically, these would be represented as follows:

*   Null hypothesis (Ho): P = 0.5
*   Alternate hypothesis (Ha): P≠0.5

A random sample of 100 coin flips is taken, and the results are recorded. If it is found that the outcomes were 40 heads and 60 tails, the analyst might infer that the penny does not have a 50% chance of landing on heads.

Further statistical testing, such as [p-testing](https://www.investopedia.com/terms/p/p-value.asp), might be performed to determine the likelihood of a fair coin landing heads up 40 times out of 100. If that likelihood is very low, the researcher would reject the null hypothesis and accept the alternative hypothesis.

If there were 48 heads and 52 tails, then it is plausible that the coin could be fair and still produce such a result. When the null hypothesis is "accepted," the analyst states that the difference between the expected results (50 heads and 50 tails) and the observed results (48 heads and 52 tails) is "explainable by chance alone."

## Explain Like I'm Five

When scientists and researchers notice patterns in data, they need a way to make sure those patterns cannot be explained by coincidence or other variables. Hypothesis testing is a way of comparing different theories to find the best explanation for a pattern.

To perform hypothesis testing, the researcher lists different hypotheses about the relationships between the data they are looking at. Then they make a series of observations. The theory that does the best job of explaining their observations is considered the strongest hypothesis.

## When Did Hypothesis Testing Begin?

Some statisticians attribute the first hypothesis tests to satirical writer John Arbuthnot in 1710, who studied male and female births in England after observing that in nearly every year, male births exceeded female births by a slight proportion. Arbuthnot calculated that the probability of this happening by chance was small, and therefore it was due to “divine providence.”

## What are the Benefits of Hypothesis Testing?

Hypothesis testing helps assess the accuracy of new ideas or theories by testing them against data. This allows researchers to determine whether the evidence supports their hypothesis, helping to avoid false claims and conclusions. Hypothesis testing also provides a framework for decision-making based on data rather than personal opinions or biases. By relying on statistical analysis, hypothesis testing helps to reduce the effects of chance and confounding variables, providing a robust framework for making informed conclusions.

## What are the Limitations of Hypothesis Testing?

Hypothesis testing relies exclusively on data and doesn’t provide a comprehensive understanding of the subject being studied. Additionally, the accuracy of the results depends on the quality of the available data and the statistical methods used. Inaccurate data or inappropriate hypothesis formulation may lead to incorrect conclusions or failed tests.

Hypothesis testing can also lead to errors, such as analysts either accepting or rejecting a null hypothesis when they shouldn’t have. These errors may result in false conclusions or missed opportunities to identify significant patterns or relationships in the data.

## The Bottom Line

Hypothesis testing is a statistical process that helps researchers determine the strength of a hypothesis. By using a well-formulated hypothesis and set of statistical tests, individuals or businesses can make inferences about the population that they are studying and draw conclusions based on the data presented.

All hypothesis testing methods have the same four-step process, which includes stating the hypotheses, formulating an analysis plan, analyzing the sample data, and interpreting the results.

> **Article Sources**
>
> 1.  Sage. "[Introduction to Hypothesis Testing](https://www.sagepub.com/sites/default/files/upm-binaries/40007_Chapter8.pdf)," Page 4.
>     
> 2.  Elder Research. "[Who Invented the Null Hypothesis?](https://www.elderresearch.com/blog/who-invented-the-null-hypothesis/)"
>     
> 3.  Formplus. "[Hypothesis Testing: Definition, Uses, Limitations and Examples](https://www.formpl.us/blog/hypothesis-testing#:~:text=The%20most%20significant%20benefit%20of,%E2%80%9Cis%20or%20is%20not%E2%80%9D.)."