Insights into Concept of Hypothesis Testing (Part 13)

Decreasing Type I Error Increases Type II Error

Decreasing alpha increases beta

Population 1= {1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5}

Population Mean = 3 and Population variance = 1.263

Population 2 = {3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6 }

Population Mean = 4.944, Population Variance = 1.719

The probability of rejecting a true null hypothesis is denoted by α (alpha) . Rejection of a true null hypothesis is called Type I Error. In the adjacent figure we see that alpha is the area of the region where sample coming from a parent population with mean 3 is still rejected and it is falsely concluded that it comes from a parent population with mean 4.944. Committing Type I error disturbs the status quo. So minimize this error and minimize alpha. But when we try to minimize alpha we increase beta, as seen from the area of alpha and beta shown above.