Understanding Statistical Significance

Last updated 03/19/2024 by

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Summary:

Statistical significance is an important measure used in research to determine the likelihood that a result or relationship is not due to chance. There are several types of statistical significance, and the method of calculation depends on the type being tested. While statistical significance can indicate a relationship or difference between groups, it cannot prove causation on its own, and practical significance is important in determining the real-world implications of a study’s findings. By understanding the concept of statistical significance, researchers can better interpret the results of their studies and make informed decisions based on the data.

What is statistical significance?

Statistical significance is a measure of the likelihood that a result or relationship in a study is not due to chance. It is typically expressed as a p-value, which represents the probability of obtaining the observed result or relationship by chance alone. A p-value of less than 0.05 is generally considered to be statistically significant, indicating that the result is unlikely to be due to chance.

Types of statistical significance

There are several types of statistical significance, each with its own strengths and limitations. Here are the most common types:

Null hypothesis significance testing (NHST)

NHST is the most widely used method for testing statistical significance. It involves comparing the observed results of a study to a null hypothesis, which assumes that there is no difference between the groups being compared. The p-value represents the probability of obtaining results as extreme or more extreme than the observed results if the null hypothesis is true.

Pros: NHST is easy to use and widely accepted in many fields of research.

Cons: It can be prone to errors and misinterpretation, and can lead to overreliance on p-values.

Effect size

Effect size measures the magnitude of a relationship or difference between groups in a study. It provides additional information beyond statistical significance by indicating how much of an impact the intervention or treatment had on the outcome. Common measures of effect size include Cohen’s d, Pearson’s r, and odds ratios.

Importance: Effect size is important because it allows us to interpret the practical significance of a study, beyond just statistical significance.

Confidence intervals

Confidence intervals provide a range of values within which the true value of a population parameter is likely to fall. They are typically calculated at a 95% confidence level, meaning that if the study were repeated many times, 95% of the confidence intervals would include the true population value.

Interpretation: Confidence intervals provide a more nuanced interpretation of the results of a study than just a p-value. They allow us to understand the precision of the estimate and the range of possible values for the population parameter.

Practical significance

Practical significance refers to whether a result is meaningful or important in a real-world context. It takes into account factors such as the size of the effect, the cost of the intervention, and the potential benefits or harms to individuals.

Importance: Practical significance is important because it helps researchers and decision-makers to determine whether a treatment or intervention is worthwhile, beyond just statistical significance.

How to calculate statistical significance

Calculating statistical significance depends on the type of significance being tested. Here are the general steps involved in calculating statistical significance using null hypothesis significance testing, the most common method:

Define the null and alternative hypotheses: The null hypothesis is the default assumption that there is no significant difference or relationship between groups or variables, while the alternative hypothesis is the opposite. For example, the null hypothesis might be that there is no difference in test scores between a control group and an experimental group, while the alternative hypothesis might be that the experimental group scores significantly higher.
Select an appropriate test: There are many statistical tests available for different types of data and research questions, including t-tests, ANOVA, chi-square, and regression analysis. Selecting an appropriate test depends on the research question, type of data, and assumptions of the test.
Collect data: Data should be collected and organized according to the test being used, including sample size, mean, standard deviation, and other relevant variables.
Calculate the test statistic and p-value: The test statistic is a measure of how different the observed data is from what would be expected under the null hypothesis, while the p-value is the probability of obtaining a result as extreme or more extreme than the observed result, assuming the null hypothesis is true. A p-value of less than 0.05 is typically considered statistically significant.
Interpret the results: If the p-value is less than the predetermined alpha level (usually 0.05), then the null hypothesis is rejected and the alternative hypothesis is supported. If the p-value is greater than the alpha level, then the null hypothesis cannot be rejected.

Frequently asked questions

What is the difference between statistical significance and practical significance?

Statistical significance refers to the likelihood that a result is not due to chance, while practical significance refers to whether the result is meaningful or important in a real-world context.

What is the p-value and how is it related to statistical significance?

The p-value represents the probability of obtaining the observed result or relationship by chance alone. A p-value of less than 0.05 is generally considered to be statistically significant.

Can statistical significance prove causation?

No, statistical significance alone cannot prove causation. While a statistically significant result indicates that a relationship or difference exists between groups, it does not prove that one variable caused the other. Other factors, such as confounding variables, may also be at play.

Key takeaways

Statistical significance is a measure of the likelihood that a result or relationship in a study is not due to chance.
There are several types of statistical significance, including null hypothesis significance testing, effect size, confidence intervals, and practical significance.
Calculating statistical significance depends on the type of significance being tested and involves defining the null and alternative hypotheses, selecting an appropriate test, collecting data, and interpreting the results.
Statistical significance alone cannot prove causation and practical significance is important in determining the real-world implications of a study’s findings.

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