Variation and sampling error.
Hi. I'm Dr Nic. And in this video I'm going to tell you
about why statistical methods are needed.
I will also explain variation and error,
including sampling error and non-sampling error.
Variation is everywhere.
It has practical implications.
That is why statistical methods are used
to make sense of data.
There are several sources of variation in data.
Today, we're going to talk about:
1. Natural or 'real' variation.
2. Explainable variation,
sometimes called 'confounding'.
3. Sampling error,
or sampling variation,
and 4. Variation due to non-sampling error.
For example,
say we want to know how many texts, on average,
a 19-year old student sends in a day on their mobile phone.
This could be useful when setting up a pricing scheme to attract students.
We could ask one 19-year old student,
but we know that not all 19-year old students
send the same number of texts in a day.
There is natural variation.
If all students sent the same number of texts in a day,
taking a sample of one student
would give us all the information we need.
But, all students don't send the same number of texts in a day;
there is variation.
And this is true of almost all human, natural and manufacturing processes--
there will be variation.
In some cases,
such as weights of medicines,
the variation may be very small,
but it will still be there even if we can't measure it.
There are other reasons why asking one student
wouldn't give us the information we need
about texting habits of 19-year old students.
The men and women could send different numbers of texts,
and students from different countries might have different texting habits.
This can be called
In some statistical tests,
we try to find out things like the differences between groups,
such as males and females,
or maybe the relationship between age of the student
and number of texts.
We try to see what variation we can attribute
to known factors.
Statistical inference
is the process of drawing conclusions about population parameters
based on a sample
taken from the population.
Because of natural and explainable variation,
each sample will only approximate the population.
Say I took a sample of five students,
and you took a sample of five students-- from the same class--
and asked them about the number of texts they sent yesterday.
Do you think you and I would get the same mean or average?
I presume you said no, because that is correct.
Because our samples will include different people,
we're unlikely to get the same mean or average.
That is another kind of variation.
The fact that our samples included different people
is the underlying cause of sampling error or sampling variation.
Because we are looking at a subset of the population,
we are not getting all the information about the population,
and there are almost infinite different samples we could take,
each with its own distribution.
The term 'sampling error' is a bit of a problem
as the word 'error' suggests that a mistake has been made.
But this is not actually the case.
Sampling error arises due to the variability
that occurs by chance because a sample,
rather than an entire population,
is surveyed.
When samples are small,
the potential effect of sampling error is greater,
but even with a big sample
we can never eliminate sampling error completely.
Typically, a larger sample size
leads to an increase in the precision of a statistic
as an estimate of a population parameter.
You might think
that if we are
we might avoid sampling error.
But even perfectly random samples
are subject to sampling error.
Sampling error exists
because a sample is not the complete picture of the population.
You might think that if you take a larger percentage of the population
that will reduce your sampling error.
But, strangely enough, unless the population is really small,
what matters is the size of the sample,
not the percentage of the population it represents.
So, a sample of 100 from a population of one million
is just as useful as a sample of 100 from a population of ten thousand.
The sample size, known as 'n',
is what matters.
The larger the sample is,
the less influence sampling error will have on the information we get.
We cannot generally measure the extent of sampling error.
To do this we would need to know the true population parameters
such as the mean, median and standard deviation,
as well as the equivalent sample statistics.
And if we knew the true population parameters,
we would not need to take a sample.
But, with probability modelling,
and procedures like boot-strapping,
we can get a good idea of the effect of sampling error.
Probability models underpin statistical tests like the t-test,
chi-sq test and F test.
Confidence intervals express estimates of population parameters
based on the information gained from a sample.
Statistical tests generally require that the sample is random and unbiased,
and with as little error as possible.
There are many ways that the distribution of a sample
may not represent the true distribution of the population.
The other errors that may occur
when a sample is used to infer about a population
are categorised as non-sampling error.
Examples of non-sampling error are:
badly worded questions
and self-selection of sample members.
Both of these can cause bias,
which is a non-sampling error.
There are many sources of non-sampling error
which we will talk about
in our companion video,
Bias and non-sampling error
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