Understanding Statistical Significance

Statistical significance is the measure of whether differences observed between a sample outcome and a population parameter are real or have occurred by chance. The sample can be a group of people who were assigned “control” in a randomized experiment or organizations with different characteristics than the rest. If you are in need of statistical significance help in research, our expert data analysts offer personalized solutions such as statistical power calculation, sample size calculation, or hypothesis testing to help you gain meaningful insights from determining the statistical significance.

Statistical significance is attained after statistical hypothesis testing whenever the observed p-value of a test statistic is less than the significance level defined for the research. The p-value is the probability of obtaining results at least as extreme as those observed, given that the null hypothesis, H₀, is true. The significance level, a, is the probability of rejecting the null hypothesis given that it’s true.

In this article, we give a detailed guide to how to determine statistical significance, distinguish terms such as statistical and practical significance, effect size, and statistical significance, and provide practical examples at the end.

What is Statistical Significance in Research?

Statistical significance in research is a measurement of how likely it is that the difference between two variables under research occurred by chance or relate to each other. It signals that a finding is worth investigating further. The minimal sample size for statistical significance depends on the research study but at least 30 data points should be collected in each group. For large sample sizes, Pearson's Chi-square, Z-tests, and G-tests are usually used to test hypothesis.

How to Determine Statistical Significance

Step 1: Set the Null Hypothesis (H₀) and Alternative Hypothesis (H₁)

The null hypothesis is whereby the researcher wants to reject while the alternative hypothesis is which the investigator wants to accept that the statement is true. The alternative hypothesis is a negation of the null hypothesis because it will state if there is a statistically significant relationship between your data sets. For example, if H₀= 0.5, then H₁ ≠ 0.5, meaning that it is not just a coincidence.

Step 2: Calculate the Test Statistic

The test statistic is the number calculated from a statistical study to find out if your data could have occurred under the null hypothesis. In a binomial test, either the number of desired outcomes or the sample proportion can be used as a test statistic. Methods used to calculate statistical hypothesis include Chi-square, ANOVA, G-test, and t-tests.

Step 3: Calculate the p-value from the Sampling Distribution

After calculating the test statistic, we now evaluate its probability. The p-value is the probability, under the assumption that the null hypothesis is true, that the test statistic in the sampling distribution takes on a value as extreme as the number calculated from the data.

Step 4: Reject or Accept the Null Hypothesis (H₀)

The fourth and last step involves either rejecting or accepting the null hypothesis. If the p-value is small and an unlikely fact is observed, then we conclude that the assumption that the null hypothesis is true is incorrect. Generally, the null hypothesis is rejected or accepted based on the significance level, which is normally denoted as α. 0.05 is normally used as the significance level.

Effect Size Vs. Statistical Significance

While the effect size is the magnitude of the difference between two groups, statistical significance is defined as the probability that the observed difference between two groups is due to chance. While the p-value statistical significance informs the reader whether an effect exists, it does not reveal its size. To calculate the effect size, find the standardized mean difference that is given by:

Mean (group 1)- mean (group 2) ⁄  Standard deviation

Statistical Significance Vs. Practical Significance

Statistical significance and practical significance are two terms in statistics that are often misunderstood. Practical significance refers to the relevance of a statistical result. It identifies whether or not the observed relationship has any practical implications.

So, while statistical significance shows that an effect exists through null hypothesis testing, practical significance shows that the effect is large enough to be meaningful. Below are examples to distinguish the two concepts:

Statistical Significance Example

A researcher conducted a study to examine the relationship between exercising and blood pressure. They discovered a statistically significant relationship between the two factors, with those who exercise more having lower blood pressure than those who don’t. However, the difference in blood pressure between the two groups is minimal, i.e., 3 mm Hg. This translates to statistically significant results that are practically insignificant because the correlation is unlikely to have occurred by chance, and the small size of the effect demonstrates the impracticality of the observation.

Practical Significance Example

Research is conducted to evaluate the relationship between dieting and weight loss. The researcher discovered that there is no statistically significant relationship between the two variables, with those who diet losing more weight than those who did not. Additionally, the size of the effect was large, i.e. 20 kilograms. In this case, the findings are statistically insignificant but practically significant since the observed relationship has practical consequences and a large effect size.

Practical Applications of Statistical Significance

(1). A/B Testing

A/B testing is comparing two versions of a web page or app to identify which one performs better. For instance, assume that you run a business website and want to evaluate the effectiveness and credibility of two checkout page designs. So, you run an A/B test and find a 6% conversion rate of A more than B, but before deciding to use A as your official site, you need to establish whether the rate is random or statistically significant.

(2). Marketing

Another application of statistical significance is in marketing, where a marketer can test various features such as attractive email templates, track metrics, and subject lines to discover which methods gain the most click-through rates. Confirming statistical significance can help marketers make evidence-based decisions that contribute to better results.

Summary

Statistical significance is the probability that the observed difference between two groups is due to chance. To determine this significance, a researcher should follow four crucial steps which are setting the null and alternative hypotheses, calculating the test statistic and the p-value from the sampling distribution, and finally rejecting or accepting the null hypothesis. Statistical significance is applied in various applications to gain insights from data sets, such as in clinical variations, marketing, and A/B testing. Apply statistical significance to your data today by hiring our expert analysts! Our services are available and accessible 24/7, and we comply with all the necessary terms agreed upon with the client. Contact us or join our live chat today to make inquiries for prompt responses.