Navigating numbers: How data are used to create statistics

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Hello, we’re the Office for National
Statistics, or the ONS.
We’re an independent producer of official statistics and
the recognised national statistical institute of the UK.
At the ONS, we collect, analyse and disseminate
statistics about the UK's economy, society and
population.
The government, charities, community groups,
businesses and individuals use these statistics to make
informed decisions on important issues that affect us
all - everything from healthcare and school places to
environmental issues.
We have created five toolkits
based on real world themes.
Each toolkit introduces a
different tool or dataset to
help you explore some of the
data we use in our statistics.
You will also find three
activity or project ideas in
each toolkit to get you
started.

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Main principles in data and
statistics
The following slides will help you get familiar with
some common terms and statistical concepts,
including:
1. collecting data and making statistics
2. sample design and estimation
3. time series
4. index numbers
5. measuring uncertainty
6. communicating data and statistics

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To create statistics, we collect
data from a variety of sources,
including:
• our own surveys
• the census that happens every
10 years
• data that other organisations
collect, which is known as
admin data
Collecting data and making statistics

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Sample design refers to how the samples
in surveys are specified and selected.
For some statistics, we collect the data using
surveys based on a sample of people, households,
businesses, or whatever we want to find out about.
The samples we use can be complicated, so we
need to design them carefully for high quality
statistics about the economy and society.
Larger samples produce statistics that are more
precise, or more likely to be close to the true value.

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Stratified sampling
Stratification is dividing the list we are
sampling from into groups, or strata, and
drawing independent samples from each of
these strata.
This is more efficient than using a simple
random sampling approach, which could by
chance result in a sample that does not look
like the population. For example, a health
survey sampling more people in older age
groups would show more ill health than the
true health of the population. Or it could work
the other way with more younger people.
If we know information about the people on
the list, or sampling frame, we can divide it
into strata, such as age group. Then we can
decide how much of the sample to take from
each stratum.
For many surveys, we would sample in
proportion to the size of the stratum. For
example, if 10% of addresses were in a
region, we would draw 10% of the sample
from that region.

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Cluster or multi-stage sampling
If we need to visit people to collect data, it’s
more efficient if the addresses we need to
visit are close together.
We can achieve this by dividing the
sampling frame into groups, or clusters, of
addresses. We can then draw a random
sample of those clusters. We can take all
the addresses within those sampled
clusters, or a random sample within the
cluster.
Estimates from a clustered sample are less
precise than from a non-clustered sample of
the same size, but the cost of collecting the
data is less. So, this comes down to a
balance of cost and precision.

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Estimation is the process of creating
estimates from data.
At the ONS, we use estimates when calculating the
characteristics of the population as a whole from the
responses given by those people and businesses
responding to a sample survey.
Estimation is usually achieved through ‘weighting’.
Responses from a sample are weighted to ensure
they represent the entire population without bias,
producing good quality outputs.

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A time series is a series of data points
indexed in time order.
A time series is typically plotted on a line
chart and is often used to show the history
of a subject. For example, looking at
changes in spending on a certain item over
time.

14
What are index numbers?
Index numbers are
used to measure
changes and simplify
comparisons.

15
Sometimes, we’re most interested in
how things have changed, rather than
the actual values over time. For
example, instead of saying that the
average cost of a pint of milk has gone
from 80p to 84p, we’d say the price has
risen by 5%. An index is a statistical
measure designed to help understand
change and is a statistical measure of
average change.
The Consumer Price Index (CPI)
Tracks the variation in prices for
different consumer goods and
services over time for the country.
It’s used to help calculate inflation,
which is the change in prices.

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Index numbers typically measure average change
over time, such as inflation, cost of living, house prices
and employment. They can also be used to make other
comparisons, such as between regions of the UK.
Mathematically, an index number is a figure reflecting
price or quantity compared with a standard or base
value. Usually, the base equals 100, with the index
number expressed as 100 times the ratio to the base
value. Here’s an example.
The original average price for a pint of milk was 80p and
we can set this as 100. If it rises to 84p, the index
becomes (84/80 x 100) = 105. This clearly shows the
5% increase.
INTERESTING FACT!
Index numbers are most
often used in economics
as they allow economists
to turn complex data into
easily understood terms.

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Using a sample means that statistics are uncertain,
an estimate might differ from the ‘true value’.
At the ONS, the methods we use to report
uncertainty in our statistics include:
• standard error
• confidence interval
• coefficient of variation
• statistical significance
Further explanations of the individual
methodologies are available.
Understanding sampling and the effect it
has on statistics is also important for
interpreting these measures of uncertainty.
As well as random sampling, we also report
on other factors that impact the quality of
our estimates. This helps to make sure that
people use our statistics correctly.

20
Communicating data and statistics is
more than just presenting the numbers.
At the ONS, we deal with a lot of complex
data and concepts. Good communication
can help ensure data is interpreted
accurately and used appropriately. It also
allows us to be completely open about the
methods we use to collect data and
calculate statistics.
Some common challenges include:
• working out which statistical terms and
classifications can be simplified, and
which cannot
• finding out which facts are most
important and deciding whether to
make those more prominent
• making it clear what conclusions the
statistics do, and do not, support

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Data visualisation is the graphical
representation of information and data.
Tables of estimates presented as rows and columns of
numbers can be difficult to read. Using visual elements,
such as charts, graphs and maps, we can provide an
accessible way to see and understand trends, outliers
and patterns in data.
A graph should look good, but it should also present
information in a way that can be easily understood and
analysed.

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Charts for change over time
These charts usually have time on the
horizontal axis, moving from left to right,
with the variable of interest’s values on the
vertical axis.
Bar charts
Show value through the heights of
bars from a baseline.
Line charts
Allows more flexibility with the y-axis or
when there would be too many bars to plot.
Box plot
When there’s a distribution of values for each
time period, a box plot is helpful to visualise
the most common data values.

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Charts for composition
Used to show the different components of
a total.
Pie chart
Represent the whole with a circle,
divided into parts.
Stacked bar chart
Each bar is divided into multiple sub-
bars, for demonstrating composition of
multiple values.
Stacked area chart
Show composition of cumulated totals
over time.

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Charts for data distribution
Used to show the different components of
a total.
Bar charts
Ideal for when a variable is qualitative
and has discrete values.
Histogram
Ideal for analysing data of an ordered
categorical variable.
If ordered, focus on the shape of the
distribution by bringing the bars together.
If you move the bars apart, it becomes a
bar chart.

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Charts for relationships
between variables
For analysing two or more variables
against one another, and to observe
trends and patterns between them.
Scatter plot
Shows the relationship between
two variables.
Bubble chart
Like the scatter plot but can be used to include
more than two variables by adding colour, shape
or size to each point as indicators.
Combination chart
Dual axis charts combine two different types
of charts that share an X axis but have
separate Y axes. Used to illustrate
relationships or correlations between
variables with different scales.

Navigating numbers: How data are used to create statistics

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