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# Statistical Significance

## Definition

Statistical significance, in the financial field, refers to the likelihood that the relationship between two or more variables is caused by something other than random chance. It is a mathematical tool used to infer whether an event or a set of observations differs significantly from a standard or expected pattern. A result is considered statistically significant if it is unlikely to have occurred by chance alone, according to a pre-determined threshold value, usually a p-value of 0.05.

### Phonetic

The phonetics for the keyword “Statistical Significance” would be /stəˈtɪstɪkəl sɪɡˈnɪfɪkəns/.

## Key Takeaways

1. Level of Confidence: Statistical significance is the level of confidence that the results found in a study would hold up in the general population. When a result is considered statistically significant, it means that we are very sure that the result is not due to chance.

2. Correlation vs Causation: Statistical significance can help to establish a correlation between two variables, but it doesn’t necessarily imply a cause and effect relationship. Correlation simply indicates that two variables move in relation to each other, but it doesn’t tell us if one variable causes the other to move.

3. P-value: The p-value is a fundamental part of statistical significance. It represents the probability that the results observed occurred by chance. In most research studies, a p-value of 0.05 is often used as the cutoff: if the p-value is less than or equal to 0.05, the results are considered statistically significant.

## Importance

Statistical significance in business and finance is crucial as it helps decision-makers determine if a particular outcome is the result of chance or due to specific actions or factors. It involves using statistical methods to assess whether any differences observed between groups, trends, strategies or investments are ‘real’ or if they could have happened by chance. This quantifies the risk involved in deciding whether to consider the observed changes as noteworthy to act upon. For this reason, understanding the degree of statistical significance aids businesses and investors in making confident, data-driven decisions, minimize risk, and maximize gains. It’s a critical tool used to validate the effectiveness of business strategies, marketing campaigns, investment decisions and more.

## Explanation

Statistical significance plays a pivotal role in decision-making processes within a variety of industries, particularly in finance and business. It is a mathematical tool used mainly to determine whether outcomes from certain operations or activities are a result of specific factors or merely due to chance. In finance and business, it is often used in hypothesis testing to make judgements about populations based on sample data. For instance, analysts may use it to ascertain if changes in a specific economic indicator have a significant impact on stock market performance.One of the most common applications of statistical significance in finance is in the field of investment analysis. This could involve testing the performance of different stocks or investment strategies. For example, an investor might want to know whether the average return of a particular stock is statistically different from that of the market. This helps in making informed decisions on whether an investment strategy is effective or not. In the business arena, statistical significance might be used to understand consumer behaviour, such as determining whether a change in pricing has a significant effect on sales. In conclusion, despite its complexities, the concept of statistical significance remains a relevant tool in drawing meaningful conclusions and shaping sound financial and business decisions.

## Examples

1. Market Research: A company may launch a new product, and they conduct market research surveys to get responses. They receive feedback from 1000 people out of which 60% said they liked the new product. Now, whether 60% is statistically significant or not depends on the context. The company would measure the statistical significance to conclude whether a majority of their potential or existing customers are likely to accept the new product or not.2. Portfolio Investment: An investor has a portfolio of semi-annual return stocks over the last 20 years. He uses t-tests to select a subset of stocks to predict if they will have higher returns in the next year than the rest. If the p-value is less than 0.05, then the results are statistically significant at the 5% level and the investor can conclude with 95% certainty that this subset of stocks can provide higher returns.3. A/B Testing in Marketing: Companies often do A/B testing in which a small change is introduced in the website or marketing technique, and user responses are observed. One group is exposed to the new idea (test group) and the other remains unchanged (control group). Statistical significance is then tested to decide whether the observed difference between the two groups was due to chance or due to the implemented changes. If the results are statistically significant, the company may decide to roll out the change to all users.

## Frequently Asked Questions(FAQ)

What is statistical significance in finance?

Statistical significance is a mathematical tool used in finance and other fields to determine the likelihood that a certain result or outcome is not due to random chance but is instead significant and indicative of a specific event or trend.

How is statistical significance measured in finance?

In finance, statistical significance is usually measured using a p-value. A p-value is calculated using statistical tests and can then be compared to a significance level with the latter most often being 0.01, 0.05, or 0.10. If the p-value is less than or equal to this selected level, it is said to be statistically significant.

Why is statistical significance important in financial analysis?

It’s crucial because it helps to make decisions based on a set of observed data. For instance, through statistical significance, we can determine whether a particular investment result was due to managerial skill or sheer luck.

What’s the role of hypothesis testing in statistical significance?

This forms the basis of statistical significance. A null hypothesis is developed which assumes no significant difference in the observed result. If this can be rejected through statistical tests, it means the result holds statistical significance.

How can statistical significance be misleading in finance?

Sometimes a result may appear statistically significant simply due to a large sample size, even if the effect observed is actually small and of no practical importance. Also, statistical significance doesn’t consider the economic value or the cost-benefit analysis of a decision.

What is the difference between statistical significance and practical significance in finance?

Statistical significance deals with whether an investment result or phenomenon is unlikely to have occurred by chance, based on a specific confidence level (e.g., 95% or 99%). Practical significance, on the other hand, refers to whether the result is of practical or economic importance in decision-making.

Can a result be statistically significant but not practically significant?

Yes, a result can be statistically significant but have little to no practical significance. This usually means the result has passed the threshold for significance in a statistical model, but its impact on real-world decisions or results isn’t substantial or meaningful.

Can a statistically insignificant result still matter in finance?

Sometimes, yes. While a result may not pass the threshold for statistical significance, it could still indicate a trend or effect that is worth paying attention to in a business or finance setting. It all depends on the specific context, the size of the effect in question, and the associated risks and rewards.

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