Concepts of Hypothesis Testing – II
There are various methods similar to the critical value method to statistically make your decision about the hypothesis. One such method is P-Value method. This is an important method and is used more frequently in the industry.
P-Value: -
A P-Value measure the strength of evidence in support of null hypothesis. Suppose the test statistic in a hypothesis is test is equal to K. The P-Value is the probability of observing a test statistic as extreme K, assuming the null hypothesis is true. If the P-Value is less than the significance level, we reject the null hypothesis.
Higher the p-value, higher is the probability of failing to reject a null hypothesis. On the other hand, lower the p-value, higher is the probability of the null hypothesis being rejected.
After formulating the null and alternate hypotheses, the steps to follow to make a decision using the p-value method are as follows:
- Calculate the value of z-score for the sample mean point on the distribution
- Calculate the p-value from the cumulative probability for the given z-score using the z-table
- Make a decision on the basis of the p-value (multiply it by 2 for a two-tailed test) with respect to the given value of α (significance value).
To find the correct p-value from the z-score, first find the cumulative probability by simply looking at the z-table, which gives you the area under the curve till that point.
P - Value method Example
Let’s say you work at a pharmaceutical company that manufactures an antipyretic drug in tablet form, with paracetamol as the active ingredient. An antipyretic drug reduces fever. The amount of paracetamol deemed safe by the drug regulatory authorities is 500 mg. If the value of paracetamol is too low, it will make the drug ineffective and become a quality issue for your company. On the other hand, a value that is too high would become a serious regulatory issue.
There are 10 identical manufacturing lines in the pharma plant, each of which produces approximately 10,000 tablets per hour.
Your task is to take a few samples, measure the amount of paracetamol in them, and test the hypothesis that the manufacturing process is running successfully, i.e. the paracetamol content is within regulation. You have the time and resources to take about 900 sample tablets and measure the paracetamol content in each.
Upon sampling 900 tablets, you get an average content of 510 mg with a standard deviation of 110. What does the test suggest, if you set the significance level at 5%? Should you be happy with the manufacturing process or should you ask the production team to alter the process? Is it a regulatory alarm or a quality issue?
Type of Errors:
While doing hypothesis testing, there is always the possibility of making the wrong decision about your hypothesis. These instances of a wrong decision being made are referred to as errors. Let’s learn about the different types of errors during hypothesis testing.
A type I-error represented by α occurs when you reject a true null hypothesis.
A type-II error represented by β occurs when you fail to reject a false null hypothesis.