### What is a P-test?

A P-test is a statistical method that tests the validity of the null hypothesis which states a commonly accepted claim about a population. Though the term null is a bit misleading, the objective is to test accepted fact by attempting to disprove, or nullify, it. The P-test can provide the evidence that can either reject or fail to reject (statistics speak for 'inconclusive') a widely accepted claim.

### Key Takeaways

- A P-test is a statistical method that tests the validity of the null hypothesis which states a commonly accepted claim about a population.
- The smaller the p-value, the stronger the evidence that the null hypothesis should be rejected and that the alternate hypothesis might be more credible.
- The P-test statistic typically follows a standard normal distribution when large sample sizes are used.

### Understanding P-test

A P-test calculates a value which enables the researcher to determine the credibility of the accepted claim. The corresponding p-value is compared to a statistically significant level (confidence level), alpha (α), that the researcher has chosen to gauge the randomness of the results. The P-test statistic typically follows a standard normal distribution when large sample sizes are used.

Researchers will usually choose alpha levels of 5% or lower which translates to confidence levels of 95% or greater. In other words, a p-value less than a 5% alpha level means that there is greater than 95% chance that your results are *not random, *thus enhancing the significance of your results. This is the evidence that would allow the researcher to reject the null hypothesis.

- The smaller the p-value (p-value < alpha), the stronger the evidence that the null hypothesis should be rejected and that the alternate hypothesis might be more credible.
- The larger the p-value (p-value > alpha), the weaker the evidence against the null hypothesis meaning that it cannot be rejected which makes the test inconclusive.

When conducting a hypothesis test to validate a claim, the researcher postulates two hypotheses - null (H_{0}) and alternate (H_{1}). Formulating the null and alternate hypotheses is key to the usefulness that a P-test can offer the researcher.

The null hypothesis states a commonly held belief or premise which the researcher tests to see if they can reject it. The key point to grasp is that the researcher wants to always reject the null hypothesis and the P-test aids them in achieving this goal. Another point to note is that if the P-test fails to reject the null hypothesis then the test is deemed to be inconclusive and is in no way meant to be an affirmation of the null hypothesis.

The alternate hypothesis is the different explanation posited by the researcher to better explain the phenomenon being investigated. As such, it needs to be the only, or the best, possible alternative explanation. This way, if the p-value validates a rejection of the null hypothesis then the alternate hypothesis can be viewed as being credible.

### Z-test and T-test

A common and simplistic type of statistical testing is a z-test, which tests the statistical significance of a sample mean to the hypothesized population mean but requires that the standard deviation of the population be known, which is often not possible. The t-test is a more realistic type of test in that it requires only the standard deviation of the sample as opposed to the population's standard deviation.

Understanding how statistics can impact product development, especially in biotechnology, can be quite useful in guiding investors to make more informed investment decisions. For example, a basic understanding of the statistical results for a promising drug's clinical trial can be invaluable in assessing a biotech stock's potential returns.