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Level of Significance

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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

Level of significance stands for a constant probability of incorrect abolition of null hypothesis even if it stands true. It is mainly Type I error probability which is pre-determined by the statistician even before the collection of data, along with the outcomes of error. It is the measurement of statistical significance when the null hypothesis is implicit to be established or discarded. It determines the statistical significance of the result of the null hypothesis to be false. 

For example, a significance level of 0.07 shows a 7% risk of closing that a change occurs when there is no actual change. For the rejection of the null hypothesis, one must have stronger evidence when the level of significance is low.


P-Value and Significance Level

The level of significance is the value that is represented by the Greek symbol α (alpha). We can define the level of significance as:

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 even if it is true for real, a type I error occurs. It can also be mentioned as a false positive. They can only be controlled by defining an appropriate level of significance. The 5 significance level is the most commonly determined level for research. This means that by rejecting a true null hypothesis, there is a 0.05% chance that the test may undergo Type I error. Conversely, it claims to have a 95% level of confidence that the hypothesis tests with no result to a Type I error.

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 practised.

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.


Did You Know

For a two-tailed test, the rejection region can be found in the following way: 

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The rejection region for the one-tailed test is given as follows:

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  • In the left-tailed test, the left side is shaded as the rejection region.

  • In the right-tailed test, the right side is shaded as the rejection region.

FAQ (Frequently Asked Questions)

Q1. What is the Importance of Significant Level Statistics?

Ans: The significance level statistics are represented by alpha or α. It is a measure of the potency of the verification that must be at hand in the sample before one can reject the existence of a null hypothesis and bring to a close that the effect is statistically significant. One can use significance levels during hypothesis testing to assist in representing which hypothesis the data supports. When comparing, if the p-value is less than the significance level, one can reject the null hypothesis and finalize that the effect is statistically significant. In other words, the outcome of the sample is precise enough to reject the null hypothesis at the population level.

Q2. What Do You Mean By Confidence Level?

Ans: Confidence level signifies the prospect of a factor that lies within a particular range of values, which is denoted as c. In addition, the confidence level is strongly connected to the level of significance. They can be represented as the converse of each other. The relationship between the level of significance and the confidence level is represented by:

c = 1−α.

The generally used level of significance and the analogous confidence level are given below:

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

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

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

Confidence level generally measures the extent of uncertainty or certainty in a sampling method. They are mostly designed using confidence levels of 95% or 99%.