In this session, we will discuss about hypothesis testing.
They know we have discussed about a normal distribution and we have discussed how we can actually locate
a particular point on a normal distribution and find out the probability of that point occurring and
the probability of anything occurring below a particular point or a percentage of a value of cutting
percentage of values occurring below a particular point.
And we found out how we can find out the confidence interval at a particular confidence level.
Now, hypothesis testing is defined in Boredoms.
So in case of hypothesis testing, we will have to doms one will be the null hypothesis and another
will be the alternate hypothesis.
The null hypothesis will be the sample statistic will be equal to the.
Population cycliste.
So, for example, the null hypothesis, for one example, would be that the average marks after extra
class are same as before the class.
So let's say we have a problem.
We have a situation where we have certain students and these students are being given some sessions,
some extra some classes, and they obtain some marks.
The students are scoring some months after an exam.
So we're trying to come forward if the students will score just the same after some extra classes are
given to the students or not.
OK, so the null hypothesis will be that the student will remain just the same, even after we provide
an extra cost to the string.
So the treatment which we are providing here.
So the null hypothesis always says that we are providing some treatment to the sample.
We are doing something to the sample.
But still, the sample does not show any response.
The sample does not show any change.
So the treatment here is we are providing an extra class.
Still the.
Metric, which we are checking, the value which we are checking, that is the average mass, that average
marks remain just the same.
So this is the null hypothesis, null hypothesis is that whatever we were seeing was happening earlier
before a particular there was a plane that is still applicable even after providing a.
And alternative hypothesis is that even after we have provided an extra class, then there will be a
significant difference of the marks, the average marks in comparison to the marks which were given
before the extra class.
So basically, we are trying to say here is the null hypothesis states that something is just the same
even after a treatment has been provided.
An alternate hypothesis is that there will be a significantly different.
Now, when we say significant difference.
So if I am saying that initially the students marks were to see 15 marks out of 20, so initially students
were scoring 15 months and now students are scoring 16.
So this 16 is not a significant difference, change of a very small value is not a significant difference.
This difference can anyhow be present with the change in the sample or with the confidence interval.
The change we might need, even if we have a confidence in double the value, could be present in the
confidence interval.
So a small change is not a significant change.
A significant change will be if the confidence interval entirely changes, if we are able to say that
in the population with the sample was earlier, representing is now not the same population.
The new machine which we have the new value of the average mean is now let's say 18, so now or 19.
So now the population itself has changed.
So now the population mean has also changed after the treatment which we have provided.
So this is the difference between null hypothesis, an alternate hypothesis that is null hypothesis
that I used to negate a treatment, that the treatment has not impacted anything.
While the alternate hypothesis is to say that the treatment has actually made a significant.
Now, let us look for the how hypothesis distinguished, so hypothesis testing is an infringement procedure
that uses the sample data to evaluate the credibility of hypotheses about a population.
So in this scenario, we will be, first of all, Stoebe, a particular statement and then we will try
to evaluate if that particular statement is correct or not.
Now, remember why we are creating this and why we are evaluating this.
We cannot see a hypothesis is correct.
We can only reject the null hypothesis.
That is, we can only say that the statement is incorrect on the basis of evidence.
We cannot say that the statement is correct in this scenario.
Now, hypothesis is an educated guess about something in the world around you.
It should be testable in nature, either by experiment or by observation.
For example, a new medicine that you think might work or a way of teaching, you might be better on
a possible location of a new species or legacy.
We want to find out if a particular way of we introduce music is not learning.
And we introduce some music in the videos of the beginning.
And will that improve your learning or not?
So obviously, to administer the test or anything which we can put on this can be of hypothesis.
Now, what is hypothesised statement now is we I'm going to propose a hypothesis, it is important to
write the statement.
The statement will look like if I do something, then something may happen to the dependent variable.
That is, if we do something to an independent variable, then something will happen to the dependent
variable.
For example, if I decrease the amount of water given to the hops, then the hopes will increase in
size.
So here the amount of water is the independent variable, while the size of the hub is the dependent
variable, which is increasing with the amount of water which we are giving to it.
Similarly, if I give patients counselling in addition to the medication, then their overall depression
scale will decrease.
Or if I give exam at noon instead of seven, then the students that could be improved so we can have
these kind of different statements created.
Now, a good hypothesis when we always have a if and then statement, and it will include both independent
and dependent variable, and this has to be testable by experiment or survey or any other scientifically
sound.
Now, here we have seen this go before.
Now, we used to.
Analyze this particular plot for finding out the critical region or for finding out the confidence interval,
but now we will be using this to test a hypothesis so we will have a particular significance level.
This significance level will see how significant the value is.
Different from the original value?
How much significant difference is present in the value and the original value?
So in this scene, what happens is we will have a mean value.
We will have some value which is present inside this gold.
We will have some value which is present in this distribution.
So let us say we want to say that we have a student, we have those group of students who were learning
was studying for an average three hours.
So the average three hours that the students were learning, where was the mean value?
So are student loans for three hours in average, so the mean value becomes three here.
Now we want to find out if the change in the learning pattern, if we want to change the learning pattern
of those students and introduce us to a scenario where we will train students by converting the lectures
into music, so we will convert the content of the lectures into a music form.
And then we want to check if the average learning time of the students, which they learn continuously
changes or not.
So what we can do is we can we will have the original data where the mean of the average learning time
will be three years and we provide treatment.
But just we change the learning process by introducing music in the lectures.
And we check that if the mean of the new students, the new mean of the learning time of the students
has changed or not.
So now let's see.
The new game is actually three point five hours now.
The student loan for three point five hours instead of three years.
So.
How we accept and how we reject this hypothesis is actually depending on if this three point five hours
actually falls in this significant region or not.
And this, again, is defined by the.
Confidence which we want to have by the significant difference which we want to have, the full value
which you want to set.
So if the percentage value we want to have a zero point zero five, then it should fall in this particular
region.
If we want to have the confidence of zero point zero one info value, then it will fall in this particular
region.
And if you want to have even less in confidence, then it will fall in this region.
So based on that, we will have different values.
So let us check for the.
Now, the general structure of hypothesis testing, so all this hypothesis testing will have null hypothesis,
alternate hypotheses on the data, which we will have, the null hypothesis again will be a statement
about the population barometer, which we want to prove is wrong.
And alternate hypothesis is a general statement about the population barometer, which is opposed to
this null hypothesis.
So the null hypothesis and the alternate hypothesis have to be opposite statements.
These statements should be contradicting in nature and null hypothesis is something which we want to
actually evaluate and we want to prove wrong.
So we want to reject the null hypothesis, which is why we want to create this null hypothesis as something
which we want to prove wrong, an alternate hypothesis will always be opposite to the null hypothesis.
So now check for so let us see notice clearly the null hypothesis, so we have a question that is only
certain things that if knee surgery patients go to a physical therapy twice a week instead of three
times, their recovery period will be longer.
Average recovery time for a knee surgery patient is eight point two weeks.
So this is what a researcher thinks.
A researcher thinks that if someone will go for the therapy for twice a week instead of three times,
then the recovery period will be longer.
So they want to prove this wrong.
So if the researcher is wrong, then the recovery time is less than or equal to eight point two weeks.
So the researcher wants to say that the surgery period and the physical therapy should be reduced to
two weeks, if the therapy period is two weeks, then that if the repeated would be longer.
So what we want to say here is we will create a null hypothesis and we will try to prove the research
done wrong here to actually evaluate in the world the researcher thinks is correct or not solve the
evil that I do oppose this statement by the researchers.
So the researchers say that if knee surgery patients go for physical therapy twice a week, then the
recovery period will be longer.
So the opposite of this will be that the recovery period will be less than or equal to eight one two
weeks.
So this is what the null hypothesis will be.
A null hypothesis will state the opposite of what that is such a thing so that we can actually reject
the hypothesis.
So we are seeing that the recovery time is less than or equal to the eight point two weeks.
And the alternative would be completely opposite to the state doing so opposite of this statement would
be here.
The statement is new is less than equal to eight point two weeks.
So the opposite of this will be new, will be greater than eight point two weeks.
So the average recovery time is more than eight point two weeks.
So this is what the null hypothesis and alternate hypothesis looks like.
So what we want to do here is we want to check if the researcher is right or wrong.
So using hypothesis testing, we can only prove if the researcher is wrong or not, we cannot see that
the decision is correct, but we can only say that the decision is wrong.
So for that, we evaluate this null hypothesis.
We see that the researcher is actually wrong.
So we created this statement that research is wrong.
So we can either reject this or accept this.
So this is what null hypothesis will allow us to.
Now let us look further and create more statements so we have another study of the status of critically
ill children in a pediatric intensive care unit and then examine 16 children.
So the number of children examined are 16 here.
And these children are with a woman and B and they were found that the number of missing 132 was one
point and the standard deviation was of one point nine.
Now, the extensive analysis has established that the number of such teeth is wider population of children
is one point four, so.
For example, we have the mean Value 1.0 and the standard deviation of one point nine and the.
Actual value is one point four, so we want to check if the mean value for the critically ill children
is different from the actual population or not.
So this is the actual population and we want to check if this mean value, which we have found out is
different from this one or not.
So we want to prove here that this these both of these belong to two different population instead of
same population.
So for that, we will actually have to prove that this one point two is significantly different from
this one point for so let us see the null hypothesis which we will be creating.
So the statement about the population barometer, we would have to prove this wrong if possible.
So something which we want to prove wrong.
OK, and we want to check here is that.
The meaning of critical children is different from the.
Actual mean of the number of feet.
So our hypothesis will be that the meme is one point for.
And the alternate hypotheses will be.
That this is not equal to one point for.
OK, so the null hypothesis will be that both of these are actually steam and the children are not different,
the mean for both the population is seen and we want to put all this wrong.
So we will see that both of these have same mean.
It is one point for only, and the alternate hypothesis will be that all the populations are different.
And the mean of these 16 students is not equal to one point for.
Now, what is probability theory now, probability theory allows us to calculate the exact probability
that chance was the real reason for the relationship.
That is this what the data which has happened, that is the number of children had missing the as one
point two had the standard deviation of one point five.
So here the mean which came out will be one point two, is actually dealable johns.
And actually the mean is one point for me.
But this is just the Biogen's.
It came to be one point.
So probability theory allows us to produce death statistics and the death statistics is a number that
is used to decide whether to accept or reject the null hypothesis.
So probability theory allows us to accept or reject the null hypothesis.
So we will be able to either accept this or we will be able to reject this hypothesis.
So this is the only thing which we can prove, correct or wrong.
We cannot say anything about this one, so we will be either accepting the null hypothesis or rejecting
the null hypothesis.
So we will learn about the test and the test and how these are conducted in the next session.