What Is Statistical Significance?

Statistical significance is a conclusion that a set of data is not the result of chance but can✨ instead be attributed to a specific cause. Statistical significance is vital for professionals in any field that relies on the analysis of data, including economics, finance, investing, medicine, physics, and biology.

Statistical significance can be considered strong or weak. Strong statistical s🐻ignificance supports the conclusion that the results are real and not caused by luck or chance.

Understanding Statistical Significance

Researchers are usually working with samples of larger populations, not entire populations. The samples must be representative of the✅ population to ꦛavoid bias in the results.

In most sciences, including economics, a result may be considered statistically significant if it has a 澳洲幸运5官方开奖结果体彩网:confidence level of 95% (or sometimes 99%).

The calculation of statistical significance, called significance testing, is subject to a certain degree of error. Even if data appear to have a strong relationship, researchers must account for the possibility that an apparent correlation arose due to random chance or a 澳洲幸运5官方开奖结果体彩网:sampling error.

Sample size is an important component of statistical significance. Larger samples are less prone to flukes. Only randomly chosen, 澳洲幸运5官方开奖结果体彩网:representative samples should be used in significance testing.

The level at which one can accept whether an event is 澳洲幸运5官方开奖结果体彩网:statistically significant is known as the significance level.

Measuring P-Value

Researchers use a measurement known as the p-value, or probability value, to determine statistica𒈔l significance.

꧒ If the p-value falls below the significance level, the result is statistically significant.

The p-value is a function of the means and standard deviations of the data samples. It indicates the probability under which the given statistical result occurred, assuming chance alonﷺe is responsible for the result. If this probability is small, the researcher can conclude that some other factor could be responsible for the observed data.

The opposite of the significance level, calculated as 1 minus the significance level, is the confidence level. It indicates the degree of confiden🐭ce that the statistical result did not occur by chance or by sampling error.

The customary 澳洲幸运5官方开奖结果体彩网:confidence level in many statistical tests is 95%, leading to a customary significance level or p-value of 5%.

Special Considerations

Statistical significance does not always indicate p⭕ractical significance, meaning the reꦗsults cannot necessarily be applied to the real world.

Moreover, the fact that a result is statistically significant does not imply that it is not the result🧸 of chance, just that this is ⛎less likely to be the case.

Just because two data series hold a strong correlation with one another does not imply causation. For example, the number of movies in which actor Nicolas Cage stars in a given year may be very highly correlated with the number of accidental drownings in swimming pools. The correlation is spurious since no theoretical causal claim can be made.

Relying on the Past

Pa🔴st data—whether statistically significant or not—may not reliab🦂ly predict future conditions.

The problem is clear in investment analysis. A pricing model based on a stock's past performance may be used to predict movements within the selected time range. It may break down when faced with later events.

As a standard, statistical significance can ♌help an investor choose one asset pricing model over others.

Types of Statistical Significance Tests

Several types of significance tests are used depending on the resear♊ch being conducted. For example, tests can be employed for one, two, or more data samples of various sizes for averages, variances, proportions, paired or unpaired data, or different data distributions.

There are also different approaches to significance testing depending on the type of data that is available. Ronald Fisher is credited with formulating one of the most flexible approaches, as well as setting the norm for significance at p < 0.05.

Because most of the work can be done after the data have already been collected, this method remains popular for short-term or ad-hoc research projects.

Seeking to build on Fisher’s method, Jerzy Neyman and Egon Pearson ended up developing an alternative approach. This method requires more work before the data are collected, but it allows researchers to design their study in a way that controls the probability of reaching false conclusions.

Null Hypothesis Testing

Statistical significance is used in 澳洲幸运5官方开奖结果体彩网:null hypothesis testing, in which researchers attempt to support their theories by rejecting other explanations. Although the method is sometimes misunderstood, it remains the most popular method of data testing in medicine, psychology, and other fields.

The most common null hypothesis is that the parameter in question is equal to zero (typically indicating♕ that a variable has zero effect on the outcome of interest).

If researchers reject the null hypothesis with a confidence of 95% or better, they can claim that an observed relationship is statistically significant. Null hypotheses can also be tested for the equality of effect for two or more alternative treatments.

Rejection of the null hypothesis, even if a very high degree of statistical significance can never prove something, can only add support to an existing hypothesis. On the other hand, failure to reject☂ a null hypothesis is often grounds to dismiss a hypothesis.

Additionally, an effect can be statistically significant but have only a v♑ery small impact. For example, it may be statistically significant tha🌳t companies that use two-ply toilet paper in their bathrooms have more productive employees, but the improvement in the absolute productivity of each worker is likely to be minuscule.

The Bottom Line

Statistical significance is used to assess the possibility that an observed relationship could be the result of random chance. When an observation shows a weak relationship🎀 between two variables or has a small number of data points, it is said to be statistically insignif🅘icant. However, when there are more data points showing a more consistent relationship, that correlation is said to be statistically significant.

Researchers use statistical significance to assess the likelihood that two variables might share a causal relationship.