Type I & Type II Errors

When you perform any hypothesis testing there are a lot of chances of getting an error in it.

So, two types of very common errors which happen, we will see them now.

First which we call as type one error, and second which we call as type two error.

 First, we will see how type one error affects our hypothesis testing.

My type one error gets created when we reject correct null hypothesis, which means when we reject any Hknot and that is okay.

We also call it as false positive error.

why? Because the event that doesn't exist, we give inferences about it by mistake.

Type one error doesn't mean at all that we have accepted the alternate hypothesis by mistake.

Always keep in mind that type one error means the already correct null hypothesis which was there, we have rejected that.

In this the risk that is there to create this error that is denoted by a significance level which we call as alpha.

That alpha value is chosen by the researchers or we chose it by ourselves.

Basically, the significance level indicates a probability that my true null hypothesis that I have rejected by mistake, what would be its probability? Suppose, we say that significance level is 0.05% in any hypothesis testing, then it means that there is a 5% probability that we have rejected one true null hypothesis.

Alpha can have any value, it can be 0.05, it can be 0.01 which means 5% or 1% chance is to reject our null hypothesis.

Because of Alfa we call type of error as level of significance.

Now we will see once that how is type two error created or what is type two error? Type two error basically is created when we fail or reject one false null hypothesis This means that if I have an incorrect null hypothesis and I'm not able to reject that incorrect null hypothesis then my type two error is created.

Because of type two error, the user is not able to reject the false null hypothesis.

Why? Because it is possible that we don't have the sufficient data that we can give the result in favour of alternate hypothesis.

We even call type two error as false negative.

Keep in mind that type one error is called as false positive.

Probability of type two error is denoted by beta.

So, the probability which is there to avoid the type two error that is called our statistical power, which means if I'm getting type two error in my system, if it is happening in any of my problem statements and I wish to avoid it.

Then we will denote it with statistical power, type two error’s inverse relationship with statistical power.

It means that as much would be my statistical power I will have that much low probability to create type two error.

Type two error’s probability is denoted by beta, where as we denote statistical power with one minus beta.

we have seen that what is type one and type two errors.

Let's understand them with few examples.

In the real time scenario, let's imagine that you have some mild symptoms and we have to test that whether we have COVID-19 or not.

So, in this situation the null hypothesis that we have created is that we have not tested COVID positive.

What would be the alternate hypothesis that you are tested COVID Positive.

Now in this situation where we have another alternate hypothesis, what is the possibility of us getting a type one error or in which situation there can be a type one error.

So, it was our null hypothesis that we don't have COVID or Coronavirus.

So, when our result says that we have Coronavirus when actually you don’t have Coronavirus.

So, this is my type one error which means you have rejected one correct null hypothesis.

So, how would be the type two error, your result is saying that you don't have Coronavirus.

But actuality you do have Coronavirus, which means what was the alternate hypothesis that you have Coronavirus which means you have tested COVID positive but what happens in this situation? We have failed to reject false null hypothesis which means we couldn't reject the incorrect null hypothesis.

So, in the same way in different scenarios, we create one null and one alternate hypothesis.

And we see in those situations what is the condition we have that a type one error can happen or type two error.

Let's see one more example.

Suppose the doctors have created the COVID vaccine, to see that the COVID vaccine that they have created.

How effective is it on COVID symptoms? So, in this situation, our null hypothesis is that COVID vaccine doesn't have any effect on our symptoms.

Okay, an alternative hypothesis we have taken that COVID vaccine is effective on our symptoms.

So, the chance of having type one error is that if my COVID vaccine is effective when actuality it is not effective.

Which means our true null hypothesis is that in actuality the COVID vaccine is not effective.

And our conclusion is that COVID vaccine is effective.

So, it will create a type one error.

How would be the type two error, if with COVID vaccine none of your symptoms are improving.

This has been concluded by the doctor but ideally with this your symptoms are getting concluded .

In type two error, we incur more loss basically.

So, if you will see in this situation where the COVID vaccine was actually effective because of which we were getting to know about our symptoms.

And COVID vaccine was helping us to recover from COVID easily.

And we told that COVID vaccine is not able to improve.

So, in this way.

Type two error becomes more difficult situation for us to handle.

Let's understand this with one more example.

Which we are also seen in the last module, suppose the charges that has been levied on a man for the murder, is he innocent or guilty.

In this situation, having a type one error means the person is innocent but still he has been proved guilty.

Which means because of this he can also get the death sentence.

So, the chance of committing a type one error that should be 1% of the probability, which means the alpha that we take in this, its probability should be 0.001.

What is the situation of type two error? The defendant is actually guilty, but he has been accepted as innocent.

This means that since the defendant is guilty, he should have ideally been in a jail but he got out of the jail now.

Like we can see in this image when the defendant was innocent, but we found him guilty.

That would be my type one error, which means that he had to go to jail for no reason.

In the second situation where the defendant was guilty, but we didn't prove him guilty so this was our time two error which was created.

In this practical case, basically the situation is more serious.

Why? Because if we let go a murderer, it is possible that he can commit more murders.

So, because of this type two error is more serious or dangerous error, that's why we must see the methods to reduce type one and type two errors.

Now we will see that how we can avoid type one errors.

It is not completely possible that we do not commit any type one error in our hypothesis testing means removing the error 100% is not possible but to some extent we can minimise the risk, which means we can reduce the risks to some extent.

How? if I minimise the significance level, which means the alpha value is chosen by the researchers or we ourselves choose it, if we take that level as less as possible, for example if I bring the significance level from 5% to 1%.

So, this tells us 1% probability to reject the null hypothesis.

How we can avoid type two errors? For that we have got two ways either we increase the sample size, simply if I increase my sample size.

Because of it whichever tests that we are performing, with it our statistical power will increase and we will not take wrong decisions.

Second if we increase the significance level, simply if we have taken the significance level from 5% to 10%, so what will happen in that we will have more chances, more probability that we are rejecting the null hypothesis.

So, in this way simply on the basis of significance level, we can avoid our errors, type one or type two.

Now we will see once, how type one and type two are related to each other and how do they influence each other.

If I keep lower significance level, which means if we reduced the significance level.

So, my type one error chances are reduced but type two error chances are increased.

But in the other scenario if I'm increasing the statistical power, then my type two error chances are reduced but on the contrary type one chances increase.

So, this means that alfa and beta work opposite to each other, if we increase the alpha then our beta increases, like we can see in this particular curve where I have drawn type one and type two errors where I have drawn one right curve and one left curve.

Left curve is my null hypothesis distribution and right curve is my alternate hypothesis distribution.

So, if my alpha value is less, this means that my beta has increased, so we will see this with criminal trial example where my left curve is innocent suspect curve and, on the right, I have criminal suspect curve.

So, if my defendant is innocent but we prove him guilty, that will be my type one error, which is shown with red.

We have taken its probability as less.

Which means in this case my alpha is low.

So, this would affect adversely my beta value like we can see here when my criminal suspect was there, but we proved him non guilty because of which it created type two error, which is shown in blue.

When alpha is low, if red is less than the blue value increases.

So, there is always a trade-off between alpha and beta.

So, we have to always keep in mind that as per our conditions and situations we have to increase the significance level or we have to reduce the significance level.

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