Statistics Learning Centre presents
Understanding Statistical Inference.
Hi, I'm Dr Nic,
and in this video,
I'm going to explain what statistical inference is.
Statistical analysis has two main focuses:
1. Descriptive statistics, and
2. Inferential statistics.
Descriptive statistics summarise data
using graphs and summary values
such as the mean and interquartile range.
Descriptive statistics can help us identify
relationships and patterns.
Descriptive statistics do not draw conclusions
beyond the data we already have.
Inferential statistical analysis
does
beyond the data we have
to the population
from which it was drawn.
A definition of inference is:
The process of drawing conclusions
about population parameters
based on a sample taken from the population.
The sample
is the data we collect from the population.
Here are some examples
of populations and samples.
The population is
A sample is 100 apples we pick from the orchard.
The population is
A sample is the 30 bars we choose to melt down
and weigh the nuts from.
The population is all the voters in New Zealand.
A sample is 1000 people who are asked their opinion
in an online survey.
In each of these examples,
we can use the data from our sample
to draw some conclusions about the objects or people
in the population.
For example,
we want to know about the weights of the apples in the orchard.
So we take a sample of apples and weigh them
and use that information
to draw conclusions
about the weights of apples
in the whole orchard.
There are 3 main ideas underlying inference:
1. A sample is likely to be a good representation of the population.
2. There is an element of uncertainty
as to how well the sample represents the population.
And,
3. The way the sample is taken matters.
First, it is reasonable to expect that a sample of objects
from a population
will represent the population.
If our orchard has only red apples
of a fairly consistent size,
then we would expect the sample to contain red apples
of a fairly consistent size.
If our machine is producing chocolate bars
with a percentage of nuts within a certain range,
then we would expect the sample to also have nuts within that range.
If 40% of the people in New Zealand believe that the economy is getting worse,
then about 40% of the sample will also believe that.
Second, there is an element of uncertainty
as to how well the sample represents the population.
A sample will never be a perfect representation
of the population from which it is drawn.
This is the reason for sampling error.
We have a video about sampling error.
Nor will all the samples drawn from the same population
be the same.
But through simulation and probability theory,
we can get an idea of what the population is likely to be like
from the information the sample gives us.
For example,
let us assume that 40% of the population of New Zealand
think the economy is getting worse.
If we took a sample of 1000 people
how likely is it that 50% or more of them
will say that they think the economy is getting worse?
We can work this out
using probability theory,
or we can run a simulation on the computer
to see what we would expect
from a whole lot of samples of size 1000
taken from a population with 40% thinking the economy is getting worse.
This graph is the result of a simulation
with 1000 samples of 1000 people each
drawn from a population with a proportion of success
of 0.4 or 40%.
We define "success" as being
that the person thinks the economy is getting worse.
It turns out
that if the true proportion in the population is 40%,
the probability of getting a sample with 50% or more people
saying that they think the economy is getting worse
is zero.
It won't happen.
Just about always,
the sample proportion
will be within about 3% of the population proportion
when we use a sample size of 1000.
That 3% is called the
It can be used to create confidence intervals.
Confidence intervals give a range within which we think
the population parameter is likely to be.
You can see more about confidence intervals
in our video,
"Understanding confidence intervals".
In inferential statistics we can also test hypotheses.
Our videos, "Understanding the p-value" and "Hypothesis testing" explain these.
The third principle is,
the way the sample is taken matters.
This principle relates to non-sampling error,
which we also have a video about.
The sample must be representative of the population.
And this happens best when each person or thing in the population
has an equal chance
of being selected in the sample.
In natural or manufacturing processes we may be able to take random samples
reasonably easily.
However, when our population consists of people,
this can be more difficult and costly.
So we do the best we can.
We explain this further in our video on sampling methods.
This video has been about sample-to-population inference.
We are interested in what the sample tells us about the population.
It is not about causation
which is covered in other videos.
This video was brought to you
by Statistics Learning Centre.
Visit our website for more resources to help you learn.