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Sampling error and variation in statistics and data science - YouTube
Channel: Dr Nic's Maths and Stats
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variation and sampling error hi I'm
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doctor Nick and in this video I'm going
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to tell you about why statistical
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methods are needed I will also explain
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variation in error including sampling
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error and non sampling error variation
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is everywhere it has practical
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implications that is why statistical
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methods are used to make sense of data
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there are several sources of variation
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and data today we are going to talk
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about one natural or real variation to
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explainable variation sometimes called
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confounding three sampling error or
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sampling variation and four variation
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due to non sampling error for example
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say we want to know how many texts on
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average a 19 year old student sins in a
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day on their mobile phone this could be
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useful when setting up a pricing scheme
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to attract students we could ask one
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nineteen year old student but we know
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that not all nineteen year old students
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send the same number of texts in a day
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there is natural variation if all
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students sent the same number of texts
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in a day taking a sample of one student
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would give us all the information we
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need but or students don't send the same
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number of texts in a day
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there is variation and this is true of
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almost all human natural and
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manufacturing processes there will be
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variation in some cases such as weights
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of medicines the variation may be very
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small but it will still be there even if
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we can't measure it there are other
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reasons why asking one student wouldn't
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give us the information we need about
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texting habits of 19 year old students
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the men and women could send different
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numbers of texts and students from
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different countries might have different
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texting habits this can be called
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explainable variation in some
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statistical tests we try to find out
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things like the differences between
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groups such as males and females or
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maybe the relationship between age of
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the student and number of
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texts we're trying to see what variation
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we can attribute to known factors
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statistical inference is the process of
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drawing conclusions about population
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parameters based on a sample taken from
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the population because of natural and
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explainable variation each sample will
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only approximate the population say I
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took a sample of five students and you
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took a sample of five students from the
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same class and asked them about the
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number of texts they send yesterday do
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you think you and I would get the same
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mean or average I presume you've said no
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because that is correct because our
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samples will include different people we
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are unlikely to get the same mean or
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average that is another kind of
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variation the fact that our samples
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included different people is the
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underlying cause of sampling error or
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sampling variation because we are
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looking at a subset of the population we
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are not giving all the information about
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the population and there are almost
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infinite different samples we could take
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each was its own distribution the term
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sampling error is a bit of a problem as
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the word error suggests that a mistake
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has been made but this is not actually
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the case
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sampling error arises due to the
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variability that occurs by chance
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because a sample rather than an entire
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population is surveyed when samples are
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small the potential effect of sampling
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error is greater but even with a big
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sample we can never eliminate sampling
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error completely typically a larger
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sample size leads to an increase in the
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precision of a statistic is an estimate
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of a population parameter you might
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think that if we are really careful to
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take a random sample we might avoid
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sampling error but even perfectly random
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samples are subject to sampling error
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sampling error exists because a sample
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is not the complete picture of the
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population you might think that if you
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take a larger percentage of the
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population that will reduce your
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sampling error but strangely enough and
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this the population is really small what
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matters is
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size of the sample not the percentage of
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the population that represents so a
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sample of 100 from our population of 1
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million is just as useful as a sample of
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100 from a population of 10,000 the
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sample size known as in is what meters
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the larger the sample is the less and
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fluent sampling error will have on the
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information we get
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we cannot generally measure the extent
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of sampling error to do this we would
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need to know the true population
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parameters such as the mean median and
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standard deviation as well as the
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equivalent sample statistics and if we
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knew the true population parameters we
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would not need to take a sample but with
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probability modelling and procedures
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like bootstrapping
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we can get a good idea of the effect of
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sampling error probability models
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underpins statistical tests like the
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t-test chi-square test and if test
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confidence intervals Express estimates
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of population parameters based on the
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information gained from a sample
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statistical tests generally require that
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the sample is random
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and unbiased and with as little error as
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possible there are many ways that the
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distribution of a sample may not
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represent the true distribution of the
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population the other errors that may
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occur when a sample is used to infer
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about a population are categorized is
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non sampling error examples of non
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sampling error are badly worded
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questions and self selection of sample
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members both of these can cause bias
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which is a non sampling error there are
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many sources of non sampling error which
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we will talk about in a companion video
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bias and non sampling error this video
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was brought to you by statistics
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Learning Center within our website for
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