In this session, we will discuss about Zinnanti this so for.
First of all, let us understand about some important films.
So the P value, p value is the value of probability, which is obtained from the Z value or B value.
When we look these values on the Z or B, B, but now this probability is the probability of obtaining
a particular sample mean is less than the alpha value, then it is going to be falling in the B or also
known as a critical region.
So let us have a look at the DiGRA.
So this is their dytham.
And we are checking that we have a particular mean value.
And we want to compare a different mean and we want to check if the machine is actually falling in the
same distribution or not, that is let us see the example of the beat so the children would have the
mean value.
The population mean value for the children's teeth was one point four.
So one point four beats, one missing for the children.
The average value missing was one point for.
Now, we want to check that if the average value of the missing teeth is one point, which is somewhat
higher, then is this value significantly different from this one point four or not?
So if the value is not significantly different, if the value is not significantly different, then
it will fall in this region, only then it will be the part of the distributionally.
But if the value was not one point two, but the value was actually us is zero point five.
If the value was zero point five, then maybe the value would have fallen here.
Then what would happen is that the value is actually falling into the value or elfatih Jim.
So when the value is falling in this region, which is the region, this is the Lord and this is the
Upworthy, if the value is, let's say, zero point five zero point zero, then it will fall in the
Lordi.
If the value is three or four, then the value will lie in the Upworthy.
So if the value is falling in that region, then we will see that the meaning of the new new scenario,
then we have some kind of illness in the children.
And because of the illness, the number of falling teeth is actually changed.
The usually the children have one point four missing teeth.
But now in this scenario, because the children are ill, they are having less number of these or they
have more number of falling.
So now the population has entirely changed, so in this case, the mean of the population of nine of
the children, all of the children, the deed is actually different from this one point.
For now, the mean is some other value.
So if the value is significantly different, then it should fall in the regions.
So this is what we are taking in the case of the best or the best, basically, in case of hypothesis
testing, if the value which we are checking, if the hypothesis which we are checking is significantly
different from this data or it is just by chance, if the value is significantly different, this means
that it is not by chance what actually there is something which is different in the scenarios or in
the samples, which is the reason why these means are coming out with different.
If the means are not coming out to be significantly different, that will mean that it is just by chance.
The value comes out to be something here or something new and not something very not exactly the mean
value.
So if the Z score or this school is greater than the critical level, that is when the P value is less
than the critical alpha value, then it is said that the mean is significantly different than the population
mean, hence pointing out that the population is entirely different.
That is what we just said, that if the value of the value of the new machine is significantly different
and is lying in this region.
This critical region, then it means that these two samples are belonging to the different population,
one population is one healthy kids.
For them, the missing teeth number is one point for and for the unhealthy.
They the missing teeth value is either four or five, which means that this is belonging to a local
population, which has a completely different number of missing deep.
So this means that the illness has actually changed the population with illness, thus children have
different demographic and without illness, the children have different.
So this is what we can prove using the speed that this.
So this means that there was no impact from the treatment on the existing population, does the null
hypothesis is rejected.
Now, if there is no significant difference between the populations, that means and the population
are completely.
And there is no difference, there is no impact of the treatment on the existing population.
The population is just laid back and the null hypothesis can be rejected.
And also.
We cannot accept the null hypothesis.
We can only reject the null hypothesis on the basis of the evidence.
We cannot say that the null hypothesis is correct.
We can only say that the null hypothesis is incorrect.
Now, let us have a look at one example.
So on the twenty five point five, the scheme men and women differed by about five points.
The means for men and women were eighteen point seventy five belonging to men.
I'm twenty three point five belonging to women now.
They were not identical, but how likely is five point difference to occur just by chance?
So here what we are trying to say is that there was a sort of scaling system and there was a satisfaction
scale which was set up and men said that they were satisfied eighteen point seven, five times out of
twenty five points, they give eighteen point seven five and women give twenty three point five.
Now, again, these two values are two different means, belonging to two different datasets.
Now, out of these two different data sets, we want to find out that are these two belonging to the
same population or it is actually different for men and women?
Is the satisfaction criteria different for men and women?
So we will check.
So we will find out if these populations are similar or different.
So an analysis was conducted, I'm the P-value value for the gender comparison was found out to be point
one one.
Which means that the probability was find out to be 11 percent.
Thus there was about 11 percent chance that this data, the five point difference would occur by chance.
So there was an 11 percent chance that this would occur by chance.
Now the P value is greater than point five.
So we would fail to reject the null.
That is the.
That is this is not a significant difference, thus there is no evidence that the male and female differ
in their satisfaction if the probability was lower than zero point five.
If the probability was lower than zero point five or zero point five, that is, there was about five
percent chance that this would occur by a chance that this is occurring by chance, then we would have
rejected the null hypothesis that these populations are safe.
We would see that these populations are actually different and they have different satisfaction levels.
Let us look at another example.
So we are comparing how means and females differ with respect to how likely they would be recommended
on an online course.
OK, so.
Measurement is on a five point gain, so the measurement is five point scale.
The men have given four point one and the men have given three point one here.
Men have given four point to the rating and women have given three point one rating.
Now, the null hypothesis states.
Then there is no difference between men and women in the recommendation of an online course, which
is men and women will equally recommend an online course, it is not like if we are target men, then
they will recommend more of online courses and women will not recommend online courses.
So we just want to check if this is a scenario or not.
So the hypothesis is that they are saying they are no different.
Now, on a five point satisfaction scale, they differ by one point, men give four point three and
women give three point one recommendation of value.
Now, these values are not identical, but we want to find out how much is the chance that this one
point differences by chance.
We want to find out if these two populations are actually different, if men and women will give different
amount of recommendations, or that it is just by chance that the samples which we were taking and the
people which we were targeting, they give different answers.
So for this analysis was conducted and the P-value for the gender comparison, give point three point
zero three, this means that this was a three percent chance that this would occur by chance.
This means that the value is less than zero point five, the P value zero point five.
So we will reject the null hypothesis that the results are actually significant.
There is a significant difference between four point three and three point one.
That is why we are rejecting this hypothesis that both had equal goodwill equally.
So now what we will do, we will target men for recommending our course.
Thus, there is evidence that male and female differ in their recommendations.
So now you can understand how we are doing this, we will be basically having to type of data sets and
based on these two mean values, we are just trying to find out the difference between these values.
Is it actually significant or not?
So if the difference is significant enough, if it is significant enough, then we will see that they
are belonging to the two different population and that is it is not occurring by chance.
And if it is not different enough, then we will see that this is just Biogen's and this is calculated
on the basis of this probability value.
And this is something which we will have to decide.
So this is different significance level, so we decide on different significance level, there is a
zero point zero one zero point zero five and zero point one as significance level.
So this are these are the Z school values which define the significance levels.
Ideally, the significance level, which is chosen is zero point zero five.
So these Xcode value is one point ninety six, if the Z value is greater than one point ninety six,
then it is significantly different.
If it is not greater than one point ninety six, then it does not significantly different.
That is what we define here.
And these are the values.
So we can directly calculate this on the basis of the Z values or.
So let us get back.
So this is what we have for now and we will discuss about the different types of errors and what is
the meaning of significance and discuss about this in the next session.