Level of Significance

Dhristi JEE 2022-24

P-value Significance Level

In statistics, p-value and significance level are very important concepts in hypothesis testing. In the case of research, the researcher has to set a hypothesis in order to start with the analysis. This hypothesis is called the null hypothesis. The null hypothesis has to go through statistical hypothesis testing on the basis of pre-defined statistical examinations. When a statistician determines that some outcome is highly significant, that shows that the outcome has a high probability of being true. 

 

Significance Level Definition

The level of significance refers to a constant probability of incorrect abolition of the null hypothesis.  It is mainly a Type I error probability that is predetermined by the statistician before the collection of data, together with the outcomes of error. It refers to the measurement of statistical significance when the null hypothesis is implicit to be established or discarded. The level of significance helps to determine the statistical significance of the result of the null hypothesis to be false. For the rejection of the null hypothesis, there should be stronger evidence when the level of significance is low.


P-Value and Significance Level

The level of significance can be said to be the value which is represented by the Greek symbol α (alpha). Here, Level of significance = p (type I error) = α 


The less likely values of the observations are always farther from the mean value. The results are claimed to be “significant at x%”.


p-values are the probability of procuring an effect no less than as intense as the one in the test data, assuming the null hypothesis to be true.


For example, the significant value at 7% signifies that the p-values are less than 0.07 or p < 0.07. Correspondingly, when a result is significant at 2%, it means that p < 0.01.


When the null hypothesis is rejected, a type I error occurs. It can be a false positive too, and they can be controlled only by defining an appropriate level of significance. For research purposes,  the 5 significance level is the most commonly determined level.


Lower p-value means a significant difference in the considered values from the population value that was hypothesized in the beginning. The results are highly significant if the p-value is very less, i.e. 0.05 as it is rarely practiced.


When measuring the level of statistical significance of the result, the researcher first needs to evaluate the p-value. It defines the probability of isolating an outcome which shows that the null hypothesis is true. If the p-value is less than the level of significance (α), the null hypothesis is declined. If the p-value observed is equal to or greater than the significance level α, then hypothetically, the null hypothesis is made customary. When in real practice, the sample size is increased to check whether the significance level is reached. In general practice, we consider p-value based upon the level of significance of 10%. As per the above assumption,


  • If p > 0.1, the null hypothesis will not be considered as an assumption

  • If p > 0.05 and ≤ 0.1, the null hypothesis has a chance of low assumption.

  • If p > 0.01 and ≤ 0.05, the null hypothesis is strongly assumed

  • If p ≤ 0.01, the null hypothesis is very significantly assumed.


The rejection rule of the null hypothesis is as follows:


  • If p < α, then one must reject the null hypothesis

  • If p > α, then one should not reject the null hypothesis


Rejection Region

The values of test static for which the null hypothesis is rejected is considered to be the rejection region.


Non-Rejection Region

The set of all potential outcomes for which the null hypothesis is not rejected is called the non-rejection region.

FAQs on Level of Significance

1. What is the Importance of a Significant Level of Statistics?

The significant level statistics are usually represented by alpha or α, and is a measure of the potency of the verification which must be at hand in the sample before one is able to reject the existence of a null hypothesis and bring to a close that the effect is statistically significant. The significance levels can be used during hypothesis testing in order to assist in representing which hypothesis the data supports. If the p-value of reduced significance level, then the null hypothesis can be rejected and finalized that the effect is statistically significant. This means that the outcome of the sample is precise enough to reject the null hypothesis at the population level.

2. What is the Confidence Level?

Confidence level refers to the prospect of a factor that lies within a particular range of values, and which is denoted as c. Here, the confidence level is strongly connected to the level of significance and they can be represented as the converse of one other. This relationship between the level of significance and the confidence level is represented by:

c = 1−α.


The level of significance and the analogous confidence level are:

  • When the level of significance is 0.10, there is a 90% confidence level.

  • When the level of significance is 0.05, there is a 95% confidence level.

  • When the level of significance is 0.01, there is a 99% confidence level.

3. Mention some important points of the Level of Significance.

The level of significance is expressed by the Greek symbol α (alpha), and the level of significance can be defined as the values or the observations which are less likely when they are farther away than the mean. The results can be written as “significant at x%”. 


The significance level is said to be the measure of the strength of the evidence which must be present in the sample before you reject the null hypothesis .

4. Explain Level of Significance?

The level of significance can be defined as the fixed probability of the wrong elimination of the null hypothesis, which is, in fact, true. The level of significance is described as the measurement of statistical significance, and it says whether the null hypothesis is assumed to be accepted or rejected levels of Significance helps to identify whether the result is statistically significant for the null hypothesis to be false or rejected.

5.  Where can I get study material on the P-value significance level?

Math is a subject of utmost importance. The online portal, Vedantu.com offers important questions along with answers and other very helpful study material on ‘Level of Significance’, which have been formulated in a  well structured, well researched, and easy to understand manner. These study materials and solutions are all important and are very easily accessible from Vedantu.com and can be downloaded for free. 

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