as students of economics geography
sociology or politics
you're clearly interested in those
bigger ideas that are central to an
understanding of society perhaps you're
interested in solving the problems of
poverty or minimizing inequality maybe
you're concerned about climate change
mass migration globalization or perhaps
the politics of change now these issues
presenting norms challenges and
opportunities for a new generation of
leaders but there's simply no way to
handle these challenges without some
understanding of statistical methods the
best ideas often come from some insight
into the way the world works
and the insights into the way the world
works quite often come from
understanding numbers I mean to have a
feeling about data how to analyze data I
think everybody has to do that and
therefore statistics that caution
statistics is the best foundation for
getting some appreciation of how to go
about doing that
boring boring good heavens no I think
it's one of the most interesting things
somebody can do you can't really
understand people in any depth on any
aggregate basis without a reasonable
understanding of statistics you don't
have to be a statistician but you have
to understand the basics this series of
films will reveal insights that can only
be discerned using statistics learning
statistics may take some effort but the
rewards are enormous when I started
doing statistics at university yes it
was hard but I think anything that's
worth doing tends to be hard first you
have to go through the challenge of
working something out and understanding
how it works
our first film focuses on descriptive
statistics in particular we look at a
few interesting issues in the social
sciences which cover the main techniques
used to present data focusing on what
these techniques tell you and what they
don't tell you the politicians seek to
maximize the welfare of the electorate
or their own welfare
as a strong case for saying that at
least part of their attention is devoted
to their own welfare people in marginal
constituencies one the government needs
to win if they're to retain power at the
next election might be favored more than
people in Don marginals in order to
influence voting behavior of those
people whether votes are thought to
matter more for example researchers look
to see if the number of acute hospital
beds per head of population is higher in
the marginal constituencies let's have a
look at the evidence using a very common
form of presentation of data that we
call the bar chart the bar chart
indeed shows that there are more acute
hospitals per head of population in
marginal constituencies the figure plots
the mean number of hospitals per 1
million people within a 30 kilometre
radius of the centroid of a political
constituency against the winning margin
in 1997 of the governing party that was
then Labour
when labor is not the winning party the
margin is the negative of the difference
between the winning party usually
conservative and the next closest party
the margin is denoted as X
so for example the fourth bar can be
read as X is between 0 & 5 percent the
tallest bars tend to cluster around the
more marginal constituencies
notice that the vertical axis doesn't
begin at zero but at three hospitals per
million of population the effect of
starting the bar there is to emphasize
the differences in acute hospital
provision now we're not looking at this
evidence to make some political point
the purpose of looking at the data is to
illustrate the power of the bar chart to
illuminate statistical information
sometimes bar charts illuminate
sometimes they're downright misleading a
Lib Dem conservative government raised
value-added tax and produced a bar chart
claiming that it showed the tax to be
progressive that is to say the higher
income groups
pay more than the lower income groups as
a proportion of their income the
opposite is in fact true it's a
regressive tax it affects the lowering
comes proportionately more than the
higher income groups let's first of all
make sure that we're clear what we mean
by regressive 'no sand then we'll turn
to the bar chart and show you how it's
designed to mislead the table is
illustrative data but data like this is
valuable to illustrate a principle
imagine a society where as annual income
rises more taxes paid you can see this
illustrated in the first two columns of
the table when income doubles from ten
to twenty thousand tax paid rises from
two thousand to three thousand pounds
the higher income person pays more tax
but now look at column three tax paid by
the lower income person is a higher
proportion of income 20 percent as
against 15 percent for the higher earner
that's because as income Rises the extra
tax paid on the additional pound the
marginal tax rate is falling
such a system is called a regressive tax
system because as income Rises the
proportion of income paid in tax Falls
alternatively expressed as income Rises
the marginal tax rate declines
Chrissa tax system might look like the
second table not only does a rise in
income lead to more tax being paid but a
higher proportion of income is paid in
tax that is the marginal tax rate is
rising not all the price of the petrol
goes to the petrol companies much of it
is tax some a specific duty on petrol
some of it value-added tanks now whether
I'm rich or poor if I put seventy pounds
worth of petrol into the tank it's gonna
cost me 70 pounds but that seventy
pounds is a larger part of a smaller
income then of a larger income so the
effect of the tax is actually regressive
now look at the bar chart which purports
to show how as income Rises more value
added taxes paid by higher income groups
because they have a higher expenditure
this is the effect of a VAT rise from
seventeen point five to twenty percent
on households at different income levels
is this true that higher income groups
will pay more of that absolutely the bar
chart shows this very clearly is the tax
progressive absolutely not
the higher-income groups pay more of
that but as a proportion of their income
they pay less that is by nature
regressive
a bar chart can present information in a
very powerful way there was a study done
recently in the States looking at the
distribution of wealth a Harvard
Business professor and a behavioral
economist asked more than 5,000
Americans how they thought wealth is
distributed in the United States most of
that it's more balanced than it actually
is asked to choose their ideal
distribution of wealth 92% of these
people picked one that was even more
equitable let's look at the stacked bar
chart to see how this information is
conveyed the bars are the same link this
time because we're looking at
proportions so in each case we look at
the distribution of all 100% of wealth
we've lost the precision that we would
have in a table it's difficult to see
exactly what percentage is owned by say
the top 20% of wealth holders but this
form of presentation gives a very
powerful impression of the difference
between what the distribution is what
people think it is and what people think
it should be
the distribution of wealth is a very
important topic in the social sciences
so we'll be returning to this issue in
several later films all societies have a
mix of different kinds of output to
satisfy needs any society will produce
some agricultural goods some
manufactured products some services but
the proportions of services to
manufacturing to agriculture will vary
considerably between countries a part of
the explanation for that is in the
nature of their resources some countries
are particularly suited to agriculture
they produce a lot of it and then export
some of it to pay for manufactured
imports but there's something else that
goes on as well that is that over time
demand tends to change so you find that
countries will often when they're less
developed produce lots of agricultural
products less manufactured products and
very few services as they develop they
begin to shrink their agricultural
sector and people move more into the
towns and the manufacturing sector grows
but when we reach a high level of income
its the demand for services which grows
so manufacturing output begins to fall a
useful way to present this information
is via a pie chart we look at three
search chance to show the proportions of
output represented by agriculture
manufacturing and services in three
different economies the first is the UK
each slice of the pie represents a
sector notice how powerfully the diagram
represents the relative proportions of
output
the UK is an advanced economy notice how
relatively tiny the agricultural sector
is
now look at China notice the pie chart
covers the same area as that for the UK
whatever the size of the economy each
one has an output level of 100 percent
the Chinese economy has grown very
rapidly in recent years so although
agricultural output is huge it has
shrunk relative to its manufacturing
sector
finally consider Sierra Leone a
relatively less developed economy the
pie chart is the same size as for the UK
and China despite the fact that it's a
small economy
the pie chart emphasizes the different
proportions of output agriculture is
easily the biggest sector here
if you're nervous about percentages we
devote a whole film to the topic later
in the series
we live in a world of rising prices
sometimes more slowly sometimes more
quickly a few might even fall the
general level of prices is tending to
rise
this we call inflation to define it
another way over time we have a fall in
the value of money in our leisure
program we'll look at how we can use our
knowledge of statistics to calculate
inflation rates but for now let's look
at how to present inflation data by the
use of a graph rates of inflation vary
over time sometimes it's just a few
percentage points each year and at other
times so much more a graph is a very
common device for the presentation of
data here we have UK data from 1990 to
2010 showing the annual percentage
change in prices
the first graph has up the vertical axis
and your percentage change of prices the
horizontal axis shows the years from
1990 to 2010 note that all the changes
are positive there was inflation every
year but the rate of increase vary
greatly and let's look at the second
graph this country also has a
continually rising price level but the
variations appear much smaller the graph
is much flatter
do you have any idea which country this
second country might be
when it's the UK again and over exactly
the same time period the vertical scale
is different changing the scale gives a
quite different impression of UK
inflation variability always read the
axes very carefully when interpreting a
graph
do you see a close link between the
level of income that people enjoy and
their happiness as people's incomes rise
does their happiness rise alongside of
it well you know it's the controversial
areas you indicated I think the newest
research in that area generally showed
two things one that richer countries are
happier on the average in poorer
countries and that richer people in the
same country are on the average happier
than poor people in that country and
these results are kind of consistent
with each other so I think the most
latest research I think is questioned
the questioning of whether there's a
link between happiness and incomes you
know it's not a perfect link by any
means we all know quite wealthy people
really miserable and so on and people
are not wealthy or poor and quite
content so it's a lot of deviations I
think on as an average as a statistical
relation yes I am confident that the
data show a positive relationship
between happiness and income I do
see no reason why that should change as
averaging comes around the world rise
well it gets weaker I mean if you're
going from a level of income where you
can hardly survive to a level of income
where you survival as a short key that
has a significant effect unhappiness
everybody has always agreed to that so
that effect isn't going to be as large
when you go from an income of let's say
50,000 a year to sixty thousand or a
hundred thousand hundred 10,000 most
effects are going to get smaller but I
think it's going to be positive
nevertheless let's sketch the
relationship between income and reported
happiness based on data from many
countries
here we use sketches not graphs
the first sketch shows the relationship
between income and what people report
should be their level of happiness as
income Rises happiness tends to increase
but not by as much at higher income
levels
but now look at the second sketch where
we have the same information but this
time the horizontal axis has a log scale
if they're not familiar with logs the
basic idea is quite simple the log scale
plots
proportionate changes so on the first
graph an increase in income from say 20
to $40,000 is the same distance as from
40 to 60,000 dollars both being a 20,000
dollar rise in income but on the second
graph arise from 20 to $40,000 is
plotted as the same as an increase from
40 to 80 thousand dollars because in
each case this would represent a
doubling of income
the relationship appears more linear as
incomes rise reported happiness goes on
rising by as much when we focus on
proportionate changes rather than
absolute changes
neither sketch shows the right way to
present the data but seeing information
presented in a different way helps us to
reach of view provided that we're clear
how to interpret it even when we've
examined the data we won't always be
able to agree about everything even
leading academics disagree about some
issues but our differences are likely to
be less and will certainly be better
informed and able to make better
judgments but we can do much more than
we've done so far we'll be able to make
inferences draw conclusions that take us
beyond the data and this is the kind of
thing we'll be doing many times over in
the coming films a knowledge of
statistics is pretty fundamental to
being a good citizen in the world we
live in today we're bombarded by numbers
from all directions trying to persuade
us to buy something or believe something
that a politician is saying or to take
some action but unless you've got some
facility to understand that you've got
no way of judging whether this bombard
of numbers has actually got any meaning
or not or it's someone just trying to
change your mind
so you're at sea so every little bit of
statistics you know is going to help you
make better choices in your life
you