how many bluebells are there in the wood
there are millions how do you count them
well one way is to take one square meter
count those carefully and then multiply
them by the square meters of the wood it
would work if the sample square meter we
take is an accurate representation of
the meter age of the word choosing a
representative sample is a problem for
anyone collecting data for James
Thompson studying the effects of climate
change on the pollination of glacier
lilies it's very important this plant
basically needs what we call out
crossing it needs them to mate with
another plant and that involves pollen
being moved by insects bees that are
successful at pollinating these rather
large flowers are large animals
specifically there the Queen's of
bumblebees and bumblebees have a
lifestyle where the queen is the only
animal that lives through the winter so
when spring comes a bumble bee queen
burrows up from the soil and it's her
responsibility to start a successful
nest she collects pollen and nectar she
lays eggs on a massive that she produces
offspring and eventually then the
offspring become worker bees who take
over and then the Queen stops foraging
if the flowers are blooming too early
then these aren't darn even emerged so
these guys don't have any reproduction
by seed if pollinators are out of the
system in order to track the rate of
pollination over many years he has to
choose a sample of flowers that reflects
the distribution of flowers in the
tundra the classiest statistical way to
draw a random sample of glacier lilies
would be to go and enumerate each
glacier lily in the in the field here
give each one an individual code and
then use a computer and a random numbers
generator to pick a random set of those
and go do them I can't do that they'd be
out of balloon before I done it so I
need to
take a sample that's going to be
representative I try to spread each of
my selections over a large enough
spatial area that I won't be getting
strange results just because something
weird happened right here or some deer
came and started grazing and took all my
plants so I have to pay attention to
getting representative plants I'd say
that's the most important thing so in
this film we look at sampling and
accuracy how big a sample do we need to
be able to make conclusions within some
known margin of error this is important
whether you're studying wastewater
climate change or politics in an earlier
film we followed Caroline wooldridge as
she campaigned for a seat on the
Basingstoke County Council the labor
party here in Brighton hill in
basingstoke was trying to decide whether
they might be able to win a place on the
council that's tended to be liberal
democrats how can they know if they have
a chance to win should they invest extra
time and energy if they have a chance
brighton hell is interesting because
it's been clearly Liberal Democrats but
Carolyn feels she's got a genuine chance
this time yeah that's realistic that's
good I mean amazing if you change it but
she's worked very hard over very over
this period would think that's
translating into vote it's big swing to
win if you don't see my swing what
everything you said you're talking
you're talking easily plus twenty-five
percent TLC I mean that's that's out
there I mean that's right on the edge of
probability yes but at the same time the
feedback on the doorstep is this
possible encouraged by positive
responses on the doorstep at national
opinion polls that indicated a swing
away from the liberal democrats labor
was mobilized in basingstoke to work
hard to take the seat one reason why I
think we stand a chance this time
because people are just welcoming us
back so and it has been swinging our way
certainly they last especially the last
few nights it's been really swinging our
ways
one important way to influence the
outcome is by using tellers each party
keeps lists of known supporters and
tellers keep track of who's voted in the
who hasn't this is looking up like what
were you have to do now is you have a
list here of these are all people who
where they've been canvassed but on the
telephone they've pledged that they're
going to vote Labour right and we cross
their names off as the laser boats come
in which we can tell them the polling
number right so what we have here is a
list of people who haven't yet voted so
what we're doing late in the afternoon
we're actually going out and knocking on
the door and saying excuse me Griffin
the local labour party we have recorded
here that someone's promised to vote
Labour and you haven't voted yet would
you like to get out and vote right ok
hello there look Labour Party have you
bolted you have you been out there bones
are a very important part of the
democratic process and politicians watch
them very closely even if they deny it
in public number one it depends on who
they're talking to if they're talking to
the television or to a public audience
they don't believe in opinion polls they
believe in that the second is that if
they're talking in private they believe
them beyond all recognition and the
third one if they change their policies
I'm delighted because it says they're
listening to public opinion and if
they're not there to represent the
public what are they doing in Parliament
one widely used scheme including in
political polling is stratified random
sampling where the population is divided
into a number of non overlapping
subpopulations called structure and then
a random sample is taken out of each
stratum the basis of the stratification
might be age income residents this
increases the reliability of the sample
making it more representative of the
population while saving some costs
samples from different strata can be
different in size non-proportional if
they need to reflect the different size
or significance of the strata for
example if the proportion of population
over 60 is larger or if a larger
proportion of this age votes the
pollsters might then want to interview
more of those and less of Sadie 18 to 25
group another form of stratified
sampling is quota sampling where
personal judgment plays a significant
role in the selection process such
samples we call judgment or non
probability samples if we use
non-probability sampling we can't use
quite the same formula that we use if we
have probability sampling
do hereby you notice that the number of
votes recorded for each candidate at the
same election is following Caroline won
the election let's look at what happened
we have two tables of data here the
first is a national opinion poll taken
very close to the local elections the
second is the result in Brighton hill in
basingstoke as you can see the results
are somewhat different what are the main
reasons first Brighton Hill is not
representative of the National picture
second people may have changed their
minds between being polled and voting
third some of those who said they'd
support a particular party may not have
wanted to support a particular local
candidate or vice versa finally people
may not have bothered to vote at all
even though they said they would but are
the opinion polls themselves reliable
the polls conducted by the local
politicians I've got an element of bias
in it because people are inclined to say
whatever the local interviewer wants to
hear do you worry that people will say
anything to please the interviewer oh
yes that does happen yes I mean by the
tall we put person knocks on the door
they'll say they can't devote to even
the Labour person knocks on the door
they get so again etc but yes at the
same time they know at the end of the
day people might be telling the rubbish
so you know there's an element about
reliability obviously yes yes but is
there a problem about the professional
pollsters even there they may be an
interview effect where people listen to
the tone of voice of the interviewer and
respond still to what they think the
interviewer wants to hear so there are
two issues here one is the reliability
of the sample accurately reflecting
opinion to is the value of the polis of
forecasting tool good when voting
intentions can change quickly
thinking about that first issue are they
accurate just how big a sample do you
need to get a useful estimate of the way
people are thinking about voting our
understanding of Statistics will give us
an insight into this now here's the
sampling problem we want to solve
assuming we've got say 1569 electors and
twenty percent are known to be Labour
Party supporters how many people would
we have to sample to be confident we've
got a suitably representative
cross-section of voting opinion
there's a formula that we can use to
find the number of voters we need to ask
the size of the sample will call n and n
must satisfy the equation Z sub naught
times the square root of P Q divided by
n equals e where p is the proportion
favoring a particular party in our case
the labor party q is the rest of our
population it might be just the
Conservatives or the Conservatives
Liberal Democrats and others Z sub
naught is the confidence limit and E is
the maximum error that's acceptable
notice that of course p plus q will
equal one but p times q won't now our
unknown is n so to find then we'll need
to rearrange our equation with n on the
left hand side doing this gives us that
n equals Z sub naught squared times P Q
divided by E squared now here we'll
choose that Z sub naught B 1.96 we need
to be within 1.96 standard deviations of
the mean to give us ninety-five percent
confidence in our answer p is not point2
so q is nor point eight
and we'll choose to be naught point 01
because we want to be within one percent
with a ninety-five percent certainty
so using these values n equals 1.96
squared x naught point 16 / naught point
naught naught naught 1 which gives us
not point 06 14 6 56 / naught point
naught naught naught 1 which equals 614
point 65 now we can't interview point 65
of a person so the minimum we need to
interview is 615 people that's the size
of the sample will need and what
difference would it have made if the
electorate had been say 5,000 people and
the answer perhaps surprisingly is no
difference at all for large numbers the
sample size is independent of the size
of the whole population
what difference would it have made if
say thirty percent rather than twenty
percent had been Labour Party supporters
the answer is quite a bit you might
rework the formula to discover the
necessary number now
wastewater tree climate change research
and elections seem unrelated but they do
have statistical similarities often we
rely on statistics to make inferences
about larger systems we can't know what
each voter is thinking we can't judge
climate change by looking around forever
we can't judge the effectiveness of
wastewater treatment with just one
sample we need to understand the use of
statistical techniques if we are to
arrive at the meaningful answers within
some known lunch in a very
Oh