Hello, dear.
Now, we have discussed about descriptive statistics.
And descriptive statistics, we have learned about the measures of central tendency like mean median
mode, we have talked about the different type of distributions that we have and how the distributions
vary, the respect of the dosis which is present in those.
Lord, or with respect to the Skewness.
Apart from that, we have discussed about the measures of offspring, which is ratings on standard deviation.
Now, all of these are part of descriptive statistics, which basically provide a summary of the data.
But usually what we will be working with is not the descriptive statistics, but with the inferential
statistics.
So let us look at what inferential statistics it's.
So influential statistics consists of making inferences from samples to populations, hypothesis testing,
data mining, relationship among variables and making predictions, which is based on the probability
theory.
In case of descriptive statistics, we organize the data and we summarize the data.
In case of inferential statistics, we will be taking up a sample and based on the sample, we will
make different inferences regarding the population data because usually we will not be able to find
out everything about the population.
Finding out the measures regarding the population is a very tedious task.
For example, we are talking about salaries of all the people in the world.
Now, calculating the salaries for all the people in the world will take a lot of pain.
So instead of calculating and summing up the salaries of all people of the world, what we do is we
take small samples of people from all over the world.
And then based on these samples, the light of day, we try to find out these salaries, which would
be belonging to the all the people of the world.
So this is what inferential statistics is.
We will have some sample data and based on the sample that we will try to find out about the population.
Again, we will try to compare different samples and find out if they belong to the population or not
or if there is some relationship between these two samples or not.
So these kind of things, which when we do those are called inferential statistics.
So why do we need this so descriptive statistics describes the data, why the influential statistics
allows us to make predictions, that is inferences from this data which we have now with inferential
statistics.
You can dig the data from samples and generalize about the population, which is we can the mean of
the sample and then try to find out what would be the mean of the population itself.
For example, I have a bit of a sample of people who are diabetic.
So from their diabetes level, I can find out about the diabetes level of people all around the population.
So why do we need this?
Inferential statistics provides a view of going from a sample to a population, inflating the barometer's
of a population from the data on the statistics of the sample.
So based on the statistics which are belonging to sample, we are trying to find out the bottom of the
entire population.
Now, it is usually necessary for a researcher to work with samples rather than the whole population,
but one difficulty is that a sample is generally not identical to the population which it comes from.
So it is difficult to find out that the population sample has to be a part of the population completely.
We need to make sure that the sample is identical to the population and.
The sample actually represents the population.
Now, another difficulty is that no samples are the same.
When we are taking some random values from a population, the values tend to differ.
We cannot always get the same sample from the population.
So how can we know which is the best described sample?
Which sample will actually describe the population?
So this is why we need rules which will actually be able to relate the samples to the population.
Now, what a different estimation techniques, how do we actually estimate these values, so there are
two different approaches for estimating, one being the point destination and another being the interval
estimation.
The point dimension, we give one value for a characteristic which is hopefully to lose to the unknown
value.
So in case of point destination, what happens is it will try to provide a value for me or it will try
to provide a value of a standard deviation.
And based on the standard deviation, we are not really sure if the standard deviation of the sample
will actually be the standard deviation of the population or the mean which we have calculated for the
sample will actually be the mean of the population because the samples are generated randomly and because
these samples are generated randomly, the values in the samples would differ.
So the mean will each and every day.
So we need to find out a value which would be exactly similar to the population or which is as close
as possible to the population.
So we cannot actually expect to find the precise value describing the population then only using date
of the sample.
So when we are finding out some point estimations from the sample, we can not be completely sure that
the sample mean, which we have calculated will always be equal to the population.
This is something which we can very easily see because we are not sure how the sample has been generated
and if this sample actually represent the population.
So we need to calculate and find out several samples.
And from those several samples, we will have to find out the mean which will actually justify the population.
We.
So we cannot see about a population from just one single sample.
So what do we do now?
The other method which we have is interval estimation now, what does interval estimation, though,
do?
It gives an interval of likely values.
So instead of seeing that the mean is 20, it will see that the mean value for the population lies between
18 and 22.
And I am 90 percent sure that it will be correct on I am 95 percent sure that this value is always good.
So what will happen is what I'm trying to say here is that when I say 95 percent confident that I'm
95 percent confident that the population mean is 20 or or the meanness between 18 and 22.
So this means that if we do these sampling hundred times, then out of those hundred samples, 95 percent
of the times, the mean value will lie between 18 and 22.
This is what this in Doel estimation will actually allow us to.
So it will give you an interval of likely values where the width of the interval, which is from 18
to 20.
So here the word this four.
So the width of the interval will depend on the confidence to be required to have in this in the.
So this will be basically dependent on how much confidence.
So what will happen if I am very, very, very confident?
So if I am saying that I'm 99 percent confident, so I will have to have a larger window to be 99 percent
confident.
I will have to have something like I'm 99 percent sure of the values line between fifteen to twenty
five.
So in that case, I can be 99 percent sure now for being 95 percent sure the window will be because
I am decreasing the window now.
So by decreasing the window of the estimation, I will be a little less sure because I have to be very
precise here.
So if I have something like 18 to 22, so now I can be only 95 percent sure.
And then when I'm seeing my mean value is between 19 and 21, so in that case, I am only 90 percent
sure about this.
So this is what in the world estimation will provide us.
The smaller the window we are trying to get, the less of the confidence we.
So that is what usually happens, but we will actually see how we will derive this confidence, how
we will be driving the values and the intervals, so all these things are what we will be learning in
these estimation techniques and information statistics.
So one thing to remember is that statistics never proves anything.
So with statistics, I can see that of all the people who are drinking coffee will actually have insomnia,
so I cannot say something like that.
So it will not give me a causal relationship relationship.
It will not prove anything.
It will just indicate a relationship that increases.
The intake of coffee is high.
Then the chances of insomnia is also high.
But it will not to I cannot see that likely that insomnia is caused by Heigl's.
High amount of coffee.
So you see the difference between this, when I see it will never prove prove anything.
So here I am saying that it will not give a causal relationship.
So an association does not necessarily negate US shortfalls, effect relationship.
So this means that I'm trying to say I cannot see that golf will cause insomnia, but I can only say
using statistics that coffee and insomnia go hand in hand.
So that is something which I consider.
Now, statistics can always be wrong, however, there are things that researchers can do to improve
the likelihood that the statistical analysis is correctly identifying a relationship between the lead.
So here, what we will be doing is we will be trying to find out and trying to make as correct predictions
as possible.
But we are not really sure about that.
We cannot be 100 percent sure about what we will try to be as precise as possible.
So we will learn about video tapes in the next session.