Question

Identify the given scenario as either a potential Type I or Type II error. Explain your decision by referring to the definitions of Type I and Type II errors.

Silicon breast implants have been popular for many years for purposes of breast reconstruction and breast enlargement. Since no evidence had been collected by the drug manufacturing company nor the public, it was incorrectly assumed that they presented no harm to public health (i.e., failure to reject the null hypothesis). Currently, due to reports of serious complications from thousands of women who elected to have this surgery, silicon implants are no longer being produced by major drug manufacturers.

Answer 1

First, let’s understand the type-1 and type-2 errors.

Type-1 error: This error occurs when we reject the null hypothesis when we should have retained it. That means that we believe we found a genuine effect when in reality there is not one. The probability of a type I error occurring is represented by α and as a convention the threshold is set at 0.05 (also known as significance level at 5%). When setting a threshold at 0.05 we are accepting that there is a 5% probability of identifying an effect when actually there is not one.

Type-2 error: This error occurs when we fail to reject the null hypothesis. In other words, we believe that there is not a genuine effect when actually there is one. The probability of a Type II error is represented as β and this is related to the power of the test (power = 1- β). The max. Probability of β is assumed to be roughly 20%.

Null Hypothesis: It is simply an assumption or simple notion about anything, which we assume to be true.

Altenative Hypothesis: complementary of null hypothesis.

Now in the given scenario, we see that is has type-1 error. Because here null assumption is that “silicon breast implant has no harm” but we assumed it incorrectly (i.e. it is harmful actually). so we have to reject our null hypothesis (hence by definition it is type-1 error)

That’s why thousands of women who elected to have this surgery are now avoiding it and silicon implants are no longer being produced by major drug manufacturers. So it supports our decision about type-1 error.