Hypothesis Testing

This week in our CRE Test Prep class/webinar we covered the Advance Statistics section of the CRE Primer, and I felt great that we stayed an hour more going over these though topics.

One of the topics was Hypothesis Testing.

Let me share some of the questions that arose during that section.

Question:  What is meant by Testing a Hypothesis?

Answer:  Testing a Hypothesis refers to the acceptance or rejection of an assumption made about an unknown characteristic of a population, such as a parameter or the shape or form of the population distribution.  The first step in testing a hypothesis is to make an assumption about the unknown population characteristic.  A random sample is then taken from the population, and on the basis of the corresponding sample characteristic, we accept or reject they hypothesis with a particular degree of confidence.

We can make two types of errors in testing a hypothesis:

• Type I error
• Type II error

Question:  What is meant by Type I and Type II error?

Answer:  Type I error refers to the rejection of a true hypothesis; while, Type II error refers to the acceptance of a false hypothesis.

In statistical analysis, we can control or determine the probability of Type II or Type II errors.  The probability of Type I error is usually given by the Greek letter alpha (α), while the probability of Type II error is represented by Beta (β).  By specifying a smaller Type I error, we increase the probability of a Type II error.  The only way to reduce both α and β is to increase the sample size.

Question:  What is meant by the level of significance?  The level of confidence?

Answer:  The level of significance refers to the probability of rejecting a true hypothesis or committing a Type I error (α).  The level of confidence (given by 1 -α) refers to the probability of accepting a true hypothesis.  In statistical work, the level of significance, α, is usually set at 5%, so that the level of confidence, 1-α, is 95%.

Looking forward to next weeks class, when we cover Reliability in Design and Development!!!

Related:

Hypothesis Test Selection (article)

Hypothesis Test Sample Size (article)

Degradation Hypothesis (article)