Statistical Significance Formula – Problem Solution with Solved Example

What is Statistical Significance?

Almost everyone has participated in survey at least once in their life. The meaning of survey could be anything when the same question is asked from multiple people, it is called the survey. The most common category is formal surveys where a set of questions are asked by scientists and researchers in the form of written questions, the user can answer these questions either verbally on in written as well.

With a deep analysis of answers, they could find out about a particular thing, product, or service.  Here, the term comes statistical significance that is defined as the measure of probability not just due to the chance.

A statistically significant result can be attained when p-value is less than the significance level. Here, the final output is given in terms of alpha or also named as the Type 1 error. In simple terms, there is no formula given for the statistical significance but it can be calculated in different terms by multiple testing techniques like z testing, t testing etc.

Statistical Significance Formula

Now, you can see that there are multiple surveys or tests are conducted everyday and not all of them are useful? So, what is that? A survey can be considered useful only if it has the statistical significance, a low probability value for the hypothesis is not true. In other words, a survey is called the statistically significant only if it has the high probability for a given hypothesis that is being set true.The formula and terminologies related to this formula is given as:

\[\large Z=\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\]

Where, x¯ is the sample mean, μ is the population mean, σ is the sample standard deviation, n is the sample size.