[Maths Class Notes] on Level of Significance Pdf for Exam

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.