# Null Hypothesis – Application in Trading, Investing, and Finance

Written By
Written By
Dan Buckley
Dan Buckley is an US-based trader, consultant, and part-time writer with a background in macroeconomics and mathematical finance. He trades and writes about a variety of asset classes, including equities, fixed income, commodities, currencies, and interest rates. As a writer, his goal is to explain trading and finance concepts in levels of detail that could appeal to a range of audiences, from novice traders to those with more experienced backgrounds.
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## What is a Null Hypothesis?

The null hypothesis is a hypothesis that states there is no difference between two groups, two investments, two economies, or two of anything.

It is usually denoted by H0. For example, let’s say you are testing the effect of a new medication on blood pressure.

The null hypothesis would be that there is no difference in blood pressure between those who take the medication and those who don’t.

Null hypotheses are important because they help us to focus our research.

By starting with the assumption that there is no difference between two groups, we can then design experiments to try to disprove the null hypothesis.

If we are unable to disprove it, then we can say that the null hypothesis is supported by our data.

## How a Null Hypothesis Works

In order to understand how a null hypothesis works, it’s important to understand what a p-value is.

The p-value is the probability that you would have seen your results, or something more extreme, if the null hypothesis were true.

## Null Hypothesis Example

For example, let’s say you are testing the effect of a new medication on blood pressure.

You give the medication to 100 people and measure their blood pressure before and after taking the medication.

You find that the average blood pressure decreases by 10 points after taking the medication.

The null hypothesis would be that there is no difference in blood pressure between those who take the medication and those who don’t.

To calculate the p-value, you would compare your results to what you would expect if the null hypothesis were true.

If the null hypothesis were true, you would expect that 50 people would have a decrease in blood pressure and 50 people would have no change.

Based on this, you can calculate that the likelihood of seeing a result as extreme as 10 point decrease in blood pressure is very low.

This means that the null hypothesis is probably not true.

The p-value helps us to understand how likely it is that our results are due to chance.

A p-value of 0.05 means that there is a 5 percent chance that you would have seen your results if the null hypothesis were true.

This is often used as a cutoff for deciding whether or not to reject the null hypothesis.

If the p-value is less than 0.05, we can say that the null hypothesis is probably not true.

If the p-value is greater than 0.05, we can say that the null hypothesis is supported by our data.

## How Null Hypothesis Testing Is Used in Investments and Trading

For example, let’s say you are testing the effect of a new stock market trading system.

The null hypothesis would be that there is no difference in the performance of the system compared to a buy-and-hold strategy.

To test this, you would backtest the system against historical data.

You would then compare the results of the system to what you would expect if the null hypothesis were true.

If the null hypothesis were true, you would expect that the system would perform no better or worse than a buy-and-hold strategy.

## Null Hypothesis vs. Alternate Hypothesis

It’s important to understand the difference between the null hypothesis and the alternate hypothesis.

The null hypothesis is the hypothesis that there is no difference between two groups.

The alternate hypothesis is the hypothesis that there is a difference between two groups.

If you’re testing the effect of a new medication on blood pressure, the null hypothesis would be that there is no difference in blood pressure between those who take the medication and those who don’t.

The alternate hypothesis would be that there is a difference in blood pressure between those who take the medication and those who don’t.

In order to test these hypotheses, you would need to design an experiment and collect data.

You would then use statistical tests to compare the two groups and see if there is a significant difference.

If you find a significant difference, you can reject the null hypothesis and say that the alternate hypothesis is supported by your data.

## Null Hypothesis Testing Is Not Perfect

Null hypothesis testing is not perfect and there are some limitations to consider.

First, null hypothesis testing can only be used to test for differences between two groups.

It can’t be used to test for more than two groups at a time.

Second, null hypothesis testing can only be used to test for differences in means.

It can’t be used to test for other types of differences, such as differences in proportions or variances.

Third, null hypothesis testing assumes that your data is normally distributed.

If your data is not normally distributed, the results of null hypothesis testing may not be accurate.

Fourth, null hypothesis testing relies on the p-value to make decisions about whether or not to reject the null hypothesis.

As we mentioned before, the p-value is the probability of seeing your results if the null hypothesis were true.

A p-value of 0.05 means that there is a 5 percent chance that you would have seen your results if the null hypothesis were true.

This means that there is a 95 percent chance that your results are due to something other than chance.

While this is often used as a cutoff for deciding whether or not to reject the null hypothesis, it’s important to understand that there is always a chance that your results are due to chance.

Even if you have a p-value of 0.001, there is still a 0.1 percent chance that your results are due to chance.

This is why null hypothesis testing should be used in conjunction with other methods, such as replication, to make sure that your results are not due to chance.

Null hypothesis testing is a useful tool for making decisions about investments and trading strategies, but it’s important to understand the limitations of null hypothesis testing.

## How Is the Null Hypothesis Identified?

The null hypothesis is usually identified by looking at the research question.

In the blood pressure medication example, this can be written as:

H0: There is no difference in blood pressure between those who take the medication and those who don’t.

Ha: There is a difference in blood pressure between those who take the medication and those who don’t.

The null hypothesis is usually the status quo, or what is currently believed to be true.

The alternative hypothesis is what you are testing for.

In this example, the null hypothesis is that there is no difference in blood pressure between those who take the medication and those who don’t.

The alternative hypothesis is that there is a difference in blood pressure between those who take the medication and those who don’t.

This difference could be that the medication decreases blood pressure, or that it doesn’t have any effect on blood pressure.

It’s important to note that the null hypothesis and alternative hypothesis are not always mutually exclusive.

## Null Hypothesis – FAQs

### How Is Null Hypothesis Used in Finance?

A null hypothesis is used to assess the premise of a trading or investing strategy or an economy to determine if it is true or false.

For example, an analyst may want to see if two economies, such as the United States and China, are closely correlated.

The null hypothesis would be Growth (US) ≠ Growth (China).

If the null hypothesis is false, it means that the two economies are closely correlated.

The null hypothesis is also used in evaluating trading strategies.

A null hypothesis for a trading strategy would be that there is no relationship between the variables being tested, such as buy and hold (i.e., investing) vs. day trading.

If the null hypothesis is false, it means that there is a relationship between the variables being tested.

### What Type of Data Is Used for Null Hypothesis Testing?

Null hypothesis testing can be used with any type of data, but it is most commonly used with numerical data.

This data can be continuous (such as height or weight) or discrete (such as number of siblings).

Null hypothesis testing can also be used with categorical data, such as gender or hair color.

### Is the Null Hypothesis Always False?

No, the null hypothesis is not always false.

The null hypothesis is only false if the alternative hypothesis is true.

For example, if the null hypothesis is that there is no difference in blood pressure between those who take the medication and those who don’t, and the alternative hypothesis is that there is a difference in blood pressure between those who take the medication and those who don’t, then the null hypothesis would be false if there is a difference in blood pressure between those who take the medication and those who don’t.

However, if there is no difference in blood pressure between those who take the medication and those who don’t, then the null hypothesis would be true.

### What Are the Limitations of Null Hypothesis Testing?

Null hypothesis testing is a useful tool for making decisions, but it’s important to understand the limitations of null hypothesis testing.

One limitation is that null hypothesis testing can only be used to make decisions about investments and trading strategies if the data is normally distributed.

Another limitation is that null hypothesis testing can only be used to make decisions if the data is largely free of outliers that might heavily distort the data.

Finally, null hypothesis testing can be subject to Type I and Type II errors.

Type I errors occur when the null hypothesis is rejected even though it is true.

Type II errors occur when the null hypothesis is accepted even though it is false.

Despite these limitations, null hypothesis testing can still be a helpful tool for making investment and trading decisions.

However, it’s important to understand the limitations before using this technique.

## Summary – Null Hypothesis

The null hypothesis is a statement that there is no difference between two groups or no relationship between two variables.

Null hypothesis testing is used to assess the premise of a trading or investing strategy or an economy to determine if it is true or false.

Null hypothesis testing can be used with any type of data, but it is most commonly used with numerical data.

Null hypothesis testing can only be used to make decisions about investments and trading strategies if the data is normally distributed and mostly free of outliers.

Finally, null hypothesis testing can be subject to Type I and Type II errors.

Despite these limitations, null hypothesis testing can still be a helpful tool for making investment and trading decisions.