Statistics is a branch of Mathematics. It deals with gathering, presenting, analyzing, organizing and interpreting the data, which is usually numerical. It is applied to many industrial, scientific, social and economic areas. While a researcher performs research, a hypothesis has to be set, which is known as the null hypothesis. This hypothesis is required to be tested via pre-defined statistical examinations. This process is termed as statistical hypothesis testing. The level of significance or Statistical significance is an important terminology that is quite commonly used in Statistics. In this article, we are going to discuss the level of significance in detail.
What is Statistical Significance?
In Statistics, “significance” means “not by chance” or “probably true”. We can say that if a statistician declares that some result is “highly significant”, then he indicates by stating that it might be very probably true. It does not mean that the result is highly significant, but it suggests that it is highly probable.
Level of Significance Definition
The level of significance is defined as the fixed probability of wrong elimination of null hypothesis when in fact, it is true. The level of significance is stated to be the probability of type I error and is preset by the researcher with the outcomes of error. The level of significance is the measurement of the statistical significance. It defines whether the null hypothesis is assumed to be accepted or rejected. It is expected to identify if the result is statistically significant for the null hypothesis to be false or rejected.
Level of Significance Symbol
The level of significance is denoted by the Greek symbol α (alpha). Therefore, the level of significance is defined as follows:
Significance Level = p (type I error) = α
The values or the observations are less likely when they are farther than the mean. The results are written as “significant at x%”.
Example: The value significant at 5% refers to p-value is less than 0.05 or p < 0.05. Similarly, significant at the 1% means that the p-value is less than 0.01.
The level of significance is taken at 0.05 or 5%. When the p-value is low, it means that the recognised values are significantly different from the population value that was hypothesised in the beginning. The p-value is said to be more significant if it is as low as possible. Also, the result would be highly significant if the p-value is very less. But, most generally, p-values smaller than 0.05 are known as significant, since getting a p-value less than 0.05 is quite a less practice.
How to Find the Level of Significance?
To measure the level of statistical significance of the result, the investigator first needs to calculate the p-value. It defines the probability of identifying an effect which provides that the null hypothesis is true. When the p-value is less than the level of significance (α), the null hypothesis is rejected. If the p-value so observed is not less than the significance level α, then theoretically null hypothesis is accepted. But practically, we often increase the size of the sample size and check if we reach the significance level. The general interpretation of the p-value based upon the level of significance of 10%:
- If p > 0.1, then there will be no assumption for the null hypothesis
- If p > 0.05 and p ≤ 0.1, it means that there will be a low assumption for the null hypothesis.
- If p > 0.01 and p ≤ 0.05, then there must be a strong assumption about the null hypothesis.
- If p ≤ 0.01, then a very strong assumption about the null hypothesis is indicated.
Level of Significance Example
If we obtain a p-value equal to 0.03, then it indicates that there are just 3% chances of getting a difference larger than that in our research, given that the null hypothesis exists. Now, we need to determine if this result is statistically significant enough.
We know that if the chances are 5% or less than that, then the null hypothesis is true, and we will tend to reject the null hypothesis and accept the alternative hypothesis. Here, in this case, the chances are 0.03, i.e. 3% (less than 5%), which eventually means that we will eliminate our null hypothesis and will accept an alternative hypothesis.
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Certainly! Statistics, a branch of mathematics, is my playground. Let's dive into the key concepts addressed in the article:
Statistics:
Statistics involves gathering, organizing, analyzing, and interpreting numerical data. It finds applications across various fields, from industry to science and economics.
Hypothesis and Statistical Hypothesis Testing:
In research, a null hypothesis is set and tested using statistical examinations. This process, known as statistical hypothesis testing, helps determine the likelihood of certain results being due to chance.
Level of Significance (α):
This refers to the probability of erroneously rejecting the null hypothesis when it's true. It's the probability of a type I error, typically set by the researcher before analysis. It's a measure of statistical significance and guides the acceptance or rejection of the null hypothesis.
Significance Level and p-Values:
The significance level, commonly set at 0.05 or 5%, determines if the results are statistically significant. The p-value, indicating the probability of obtaining an effect assuming the null hypothesis is true, is compared to this level. A smaller p-value indicates stronger evidence against the null hypothesis.
Interpretation of p-Values:
- p > 0.1: No significant assumption against the null hypothesis.
- 0.05 < p ≤ 0.1: A weak assumption against the null hypothesis.
- 0.01 < p ≤ 0.05: A strong assumption against the null hypothesis.
- p ≤ 0.01: A very strong assumption against the null hypothesis.
Practical Example:
If the obtained p-value is 0.03 (3%), which is less than the significance level of 0.05, it suggests that there's a 3% chance of observing a larger difference assuming the null hypothesis is true. This result is statistically significant, leading to rejecting the null hypothesis in favor of an alternative hypothesis.
The meticulous assessment of statistical significance, hypothesis testing, and interpreting p-values are integral to deriving meaningful conclusions from data analysis.
These concepts are the backbone of statistical analysis, aiding in decision-making and drawing reliable inferences from collected data.
