What is a Null Hypothesis?
A null hypothesis is a type of statistical hypothesis that proposes there is no statistical significance within a set of given observations. Represented as H~0~, it serves as a starting point for hypothesis testing using sample data. Commonly known as the “null,” this hypothesis assumes that any observed differences in data are purely due to chance.
In quantitative analysis, the null hypothesis tests theories about markets, investing strategies, or broader economic conditions. By doing so, it helps researchers determine whether an idea is credible.
Key Takeaways
- A null hypothesis proposes there is no difference between specific characteristics of a population or data-generating process.
- The alternative hypothesis asserts that there is a significant difference.
- Hypothesis testing allows for rejection of the null hypothesis within a certain confidence level.
- Rejection of the null hypothesis provides support for the alternative hypothesis.
- Null hypothesis testing is fundamental to the principle of falsification in scientific research.
How a Null Hypothesis Works
A null hypothesis assumes no difference between certain characteristics of a population. Here’s a practical example: A gambler might be curious about whether a game of chance is fair. If it is, both players should have zero expected earnings per play. Collecting and analyzing earnings data from repeated plays, the gambler tests the null hypothesis that the expected earnings are zero.
If the sample results show average earnings close to zero, the null hypothesis stands. However, if earnings deviate significantly from zero, the gambler rejects the null hypothesis, adopting the alternative hypothesis—that the expected earnings differ from zero.
Analysts prefer to reject the null hypothesis because it extends stronger credence to the observed results. Conversely, failing to reject it suggests that observed variations are due to chance alone, a weaker conclusion.
The Alternative Hypothesis
We test the null hypothesis due to doubts about its credibility. The alternative hypothesis (H~1~) captures the evidence against the null hypothesis. For instance:
-
A school principal claims students score an average of seven out of ten in exams. The alternative hypothesis is that the average score is not seven.
-
The mean annual return of a mutual fund is said to be 8%. The alternative hypothesis proposes it is not exactly 8%.
In both examples, the alternative hypothesis directly contradicts the null hypothesis.
Examples of a Null Hypothesis
Consider these examples to understand better:
Example A: A school principal claims students average a score of seven out of ten. To test this, we sample 30 students and calculate their average score. We attempt to reject the null hypothesis asserting the population mean is 7.0.
Example B: The annual return on a mutual fund is claimed to be 8%. Assuming the fund has existed for 20 years, we take a random sample of five years’ returns and calculate the sample mean. We then compare this sample mean to the population mean of 8% to test the null hypothesis.
During hypothesis testing, the null hypothesis (H~0~) is temporarily accepted as true. Any observed statistic from the sample, if it falls within an acceptable range (say, the score mean range of 6.2 to 7.8), upholds this assumption. Deviations outside this range lead to the rejection of the null hypothesis.
How Null Hypothesis Testing Is Used in Investments
In the context of financial markets, consider Alice, who believes her investment strategy yields higher returns than a traditional buy-and-hold approach. The null hypothesis states no difference exists between the returns of the two strategies. Alice seeks statistical evidence to refute it.
Employing a p-value-based test, Alice finds that if the p-value is ≤ 0.05, she can reject the null hypothesis in favor of her alternative hypothesis—that her strategy indeed outperforms.
Identifying the Null Hypothesis
An analyst establishes a null hypothesis to answer a defined research question. Depending on the query—such as whether an effect exists or if two variables are the same—different forms of null hypotheses like H~0~: X = 0 or H~0~: X = Y are adopted. If the analysis shows a significant difference from zero, the null hypothesis is rejected.
Using Null Hypothesis in Finance
In finance, null hypotheses test investment strategies and market behavior. For instance, to examine if two stocks, ABC and XYZ, have a similar performance, the null hypothesis might be ABC ≠ XYZ.
Steps in Statistical Hypothesis Testing
Hypothesis testing follows a meticulous four-step process:
- State the hypotheses: Define both null and alternative hypotheses.
- Formulate an analysis plan: Detail how data will be examined.
- Analyze the sample data: Execute the analysis plan.
- Conclude: Either reject the null hypothesis or assert that differences are due to chance.
Related Terms: statistical significance, hypothesis testing, quantitative analysis, p-value, alternative hypothesis.
References
- Sage Publishing. “Chapter 8: Introduction to Hypothesis Testing”, Pages 4–7.
- Sage Publishing. “Chapter 8: Introduction to Hypothesis Testing”, Page 4.
- Sage Publishing. “Chapter 8: Introduction to Hypothesis Testing”, Page 7.
