Question

In using statistical test of hypothesis in general and in business in particular, business practitioners face two types of errors: type I and type II error. Discuss each type of error in detail. In your opinion which type has more severe consequences in business? Support your opinion by providing an example. Also, discuss what is P-Value and its connection to type I error.

Answer 1

In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis (also known as a "false positive" finding), while a type II error is failing to reject a false null hypothesis (also known as a "false negative" finding)

Type I errors are also called:

1. Producer’s risk
2. False alarm
3. error

Type II errors are also called:

1. Consumer’s risk
2. Misdetection
3. error

Hypothesis: "Adding water to toothpaste protects against cavities."

Null hypothesis (H₀): "Adding water does not make toothpaste more effective in fighting cavities."

This null hypothesis is tested against experimental data with a view to nullifying it with evidence to the contrary.

A type I error occurs when detecting an effect (adding water to toothpaste protects against cavities) that is not present. The null hypothesis is true (i.e., it is true that adding water to toothpaste does not make it more effective in protecting against cavities), but this null hypothesis is rejected based on bad experimental data or an extreme outcome of chance alone.

Example 2

Hypothesis: "Adding fluoride to toothpaste protects against cavities."

Null hypothesis (H₀): "Adding fluoride to toothpaste has no effect on cavities."

This null hypothesis is tested against experimental data with a view to nullifying it with evidence to the contrary.

A type II error occurs when failing to detect an effect (adding fluoride to toothpaste protects against cavities) that is present. The null hypothesis is false (i.e., adding fluoride is actually effective against cavities), but the experimental data is such that the null hypothesis cannot be rejected.

part II With the Type II error, a chance to reject the null hypothesis was lost, and no conclusion is inferred from a non-rejected null. But the Type I error is more serious, because you have wrongly rejected the null hypothesis and ultimately made a claim that is not true.

Example-

Suppose you are designing a medical screening for a disease. A false positive of a Type I error may give a patient some anxiety, but this will lead to other testing procedures which will ultimately reveal the initial test was incorrect. In contrast, a false negative from a Type II error would give a patient the incorrect assurance that he or she does not have a disease when he or she in fact does.

As a result of this incorrect information, the disease would not be treated. If doctors could choose between these two options, a false positive is more desirable than a false negative.

PART III

a p-valuehelps you determine the significance of your results. ... The p-value is a number between 0 and 1 and interpreted in the following way: A small p-value (typically ? 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

The probability of a Type I error is a property of the chosen cut-off ?? and the nature of the test (in cases like the t-test when all the assumptions hold, the probability of a type I error will be exactly equal to ??). The p-value is a random variable computed from the actual observed data that can be compared to ?? as one way of performing the test).