Question

10.  What is the true state of the population and what decision was made in a Type 1 error.  Give a concrete example.

Answer 1

What is error?

Error (statistical error) defines the distinction between a value got from an information accumulation process and the 'genuine' esteem for the populace. The more noteworthy the mistake, the less agent the information are of the populace.

Type I Error (False Positive Error) :

A type I error happens when the null hypothesis is true, but it was rejected. Let me tell about  this again, a type I error happens when the null hypothesis is actually true, but was rejected as false by the checking.

A type I error, or false positive, is attesting something as true when it is really false. This false positive error is basically a “false alert” – a result that demonstrates a given condition has been fulfilled when it actually has not been fulfilled (i.e., erroneously a positive result has been assumed).

Let’s use a shepherd and wolf example. Let’s say that our null hypothesis is that there is “no wolf present.” A type I error (or false positive) would be “crying wolf” when there is no wolf present. That is, the actual condition was that there was no wolf present; however, the shepherd wrongly indicated there was a wolf present by calling “Wolf! Wolf!” This is a type I error or false positive error.

A tabular relationship between truthfulness/falseness of the null hypothesis and outcomes of the test can be seen in the table below:

	Null Hypothesis is true
Reject null hypothesis	Type I Error False Positive
Fail to reject null hypothesis	Correct out come True Negative

Examples

Let’s walk through a few examples and use a simple form to help us to understand the potential cost ramifications of type I and type II errors. Let’s start with our shepherd/wolf example.

Null Hypothesis	Type I Error / False Positive
Wolf is not present	Shepherd thinks wolf is present (shepherd cries wolf) when no wolf is actually present
Cost Assessment	Costs (actual costs + shepherd credibility) associated with scrambling the townsfolk to kill the non-existing wolf

Note: I added a row called “Cost Assessment.” Since it can not be universally stated that a type I or type II error is worse (as it is highly dependent upon the statement of the null hypothesis), I’ve added this cost assessment to help me understand which error is more “costly” and for which I might want to do more testing.

Example :2

Null Hypothesis	Type I Error / False Positive
Person is not guilty of the crime	Person is judged as guilty when the person actually did not commit the crime (convicting an innocent person)
Cost Assessment	Social costs of sending an innocent person to prison and denying them their personal freedoms (which in our society, is considered an almost unbearable cost)