The nominal significance level, also known as the alpha level, is a measure of the probability of making a Type I error in statistical analysis. A Type I error occurs when a statistical test rejects the null hypothesis, when in fact it is true. The nominal significance level is the probability that a Type I error will be made, and is usually set at 0.05 or 0.01.

For example, suppose a researcher is conducting a study to determine whether a new medication is effective in reducing blood pressure. The null hypothesis is that the medication has no effect on blood pressure, and the alternative hypothesis is that the medication does have an effect. The researcher conducts a statistical test and finds that the medication is effective at a significance level of 0.05. This means that there is a 5% chance that the result was due to chance and the medication does not actually have an effect on blood pressure.

Another example is a study examining the relationship between education level and income. The null hypothesis is that there is no relationship between education level and income, and the alternative hypothesis is that there is a relationship. The researcher conducts a statistical test and finds that there is a significant relationship at a significance level of 0.01. This means that there is a 1% chance that the result was due to chance and there is no actual relationship between education level and income.

It is important to note that the nominal significance level is not the same as the probability that the null hypothesis is true or false. The probability that the null hypothesis is true or false is known as the p-value, which is calculated based on the data collected in the study. The nominal significance level is simply the probability that a Type I error will be made.

In conclusion, the nominal significance level is a measure of the probability of making a Type I error in statistical analysis. It is usually set at 0.05 or 0.01, and is not the same as the probability that the null hypothesis is true or false. Understanding the concept of nominal significance level is important in evaluating the results of statistical tests and making informed decisions based on the data.