Measuring change over time: statistics terms explained

Terms for comparing one period with another: real and cash terms, percentage points, index numbers, seasonal adjustment and growth rates.

Real terms

A figure adjusted to remove the effect of inflation, so amounts from different years can be compared by what they would buy rather than their face value.

Real terms means a money figure has been adjusted for inflation so that it reflects purchasing power at the prices of one chosen year. A comparison in real terms answers the question: has the amount gone up by more or less than prices?

Worked example

Suppose a budget is £100 million in year one and £110 million in year five. In cash terms it has risen by 10%. If prices rose by 15% over the same period, the £110 million buys what about £95.7 million bought in year one (110 divided by 1.15). In real terms the budget has fallen by roughly 4%.

How it trips up claims

Which inflation measure? Public spending is usually adjusted with HM Treasury's GDP deflator, while household incomes and pay are usually adjusted with CPIH or CPI. Different deflators give different real-terms answers.
Which base year? A statement such as "in 2025-26 prices" tells you the base year. Without it, a real-terms figure cannot be checked.
Per head or total? A budget can rise in real terms in total but fall per person if the population grows faster.

For a step-by-step method, see how to compare cash and real terms.

Also searched as: inflation-adjusted, constant prices, real terms meaning, what does real terms mean

Official definitions: HM Treasury: GDP deflators at market prices, and money GDP · ONS: Consumer price inflation, latest bulletin

Cash terms

A money figure stated at the prices of the time it refers to, with no adjustment for inflation. Also called nominal terms.

Cash terms (also called nominal terms or current prices) are money amounts exactly as they were recorded at the time, with no adjustment for changes in prices. Most budgets, salaries and price tags are stated in cash terms.

Worked example

A hypothetical pension rises from £150 a week to £180 a week over a decade. In cash terms that is a 20% increase. If prices rose by 30% over the same decade, the £180 buys less than the £150 did at the start, so the pension has fallen in real terms even though the cash figure is higher.

How it trips up claims

Over long periods, almost any spending line rises in cash terms simply because prices rise. A "record" cash figure therefore says little on its own.
Comparing a cash figure from one year with a real-terms figure from another mixes two different measures.
Official tables usually label the basis: ONS series say "current prices" or "CP" for cash and "chained volume measures" for inflation-adjusted output (see chained volume measure). HM Treasury spending tables and OBR forecasts state whether figures are nominal or real.

Both views are legitimate; the useful step is to say which one is being used. See how to compare cash and real terms.

Also searched as: nominal terms, current prices, money terms, cash terms vs real terms

Official definitions: HM Treasury: Public Expenditure Statistical Analyses (PESA) · HM Treasury: GDP deflators at market prices, and money GDP

Percentage point

The arithmetic difference between two percentages. A rise from 4% to 5% is one percentage point, but a 25% increase in the rate.

A percentage point is the plain difference between two percentages. It is different from a percentage change, which describes how much one number has grown relative to its starting size.

Worked example

A hypothetical unemployment rate rises from 4% to 5%.

The change is 1 percentage point (5 minus 4).
The change is also a 25% increase in the rate (1 divided by 4).

Both statements describe the same movement, but they sound very different. If an interest rate falls from 5.25% to 5%, that is a cut of 0.25 percentage points, often written as 25 basis points (one basis point is one hundredth of a percentage point).

How it trips up claims

Saying a rate "rose by 1%" when it moved from 4% to 5% is ambiguous: it could mean to 4.04% or to 5%.
Small rates make percentage changes look large. A rise from 0.1% to 0.2% is only 0.1 percentage points but a 100% increase.
Official bulletins such as the ONS unemployment rate and Bank of England Bank Rate decisions describe changes in percentage points.

Also searched as: percentage point vs percent, basis point, pp, percent vs percentage point difference

Official definitions: ONS: Labour market overview, latest bulletin · Bank of England: Interest rates and Bank Rate

Year-on-year change

The change between a figure for one period and the same period twelve months earlier, such as March this year compared with March last year.

A year-on-year change compares a value with the same period a year before: this March with last March, or this quarter with the same quarter a year ago. The annual inflation rate is a year-on-year measure: it compares prices in one month with prices twelve months earlier.

Worked example

A hypothetical price index stands at 120 this June and 114 last June. The year-on-year change is (120 minus 114) divided by 114, which is about 5.3%. The index might have fallen between May and June, yet the annual rate can still be positive because it reflects the whole twelve months.

How it trips up claims

"Inflation is falling" usually means the year-on-year rate is lower than last month. Prices themselves are still rising if the rate is above zero.
Year-on-year comparisons avoid most seasonal effects, which is why they are often used for figures that are not seasonally adjusted.
A single unusual month a year ago (a "base effect") can make this year's annual rate jump or drop without much happening now.
Do not compare a year-on-year rate with a quarter-on-quarter rate; they measure different spans.

Also searched as: annual rate, 12-month rate, yoy, year over year, annual change

Official definitions: ONS: Consumer price inflation, latest bulletin · ONS: GDP monthly estimate, latest bulletin

Quarter-on-quarter change

The change from one three-month period to the next, such as April to June compared with January to March. Used for GDP growth.

A quarter-on-quarter change compares one calendar quarter (three months) with the quarter immediately before it. ONS headline GDP growth is reported this way, using seasonally adjusted figures so that, for example, the Christmas period does not distort the comparison.

Worked example

If hypothetical quarterly output is £500 billion in the first quarter and £502 billion in the second, quarter-on-quarter growth is 0.4%. If the same pace continued for four quarters, the annual growth rate would be about 1.6%, so a quarterly figure should not be read as an annual one.

How it trips up claims

A "technical recession" is commonly described as two consecutive quarters of negative quarter-on-quarter GDP growth. Small revisions can move a quarter from slightly negative to slightly positive.
Monthly GDP is also published, but the ONS notes that monthly figures are volatile and points users to three-month comparisons.
Check whether a figure compares a quarter with the previous quarter or with the same quarter a year earlier (year-on-year); both appear in the same bulletins.

See the GDP growth key figure page.

Also searched as: q/q, quarterly growth, qoq, quarter on quarter growth

Official definitions: ONS: Quarterly national accounts, latest bulletin · ONS: GDP monthly estimate, latest bulletin

Rolling average

An average recalculated each period over a fixed window, such as the latest three months or twelve months, to smooth out short-term ups and downs.

A rolling average (or moving average) takes the average over a fixed number of recent periods and moves forward one period at a time. Rolling totals work the same way, adding up a fixed window such as the last twelve months.

Worked example

Monthly figures of 90, 120 and 105 give a three-month rolling average of 105. Next month, if the new figure is 135, the oldest month drops out and the average becomes (120 + 105 + 135) divided by 3, which is 120.

Where you will see it

The ONS headline labour market figures from the Labour Force Survey cover three-month periods, such as June to August, compared with the previous non-overlapping three months.
Migration and crime statistics are often given for the "year ending" a particular month, which is a rolling twelve-month total.

How it trips up claims

Overlapping periods share most of their data, so comparing June to August with May to July shows little change by design.
A rolling figure lags behind sudden changes: a sharp rise in one month is spread over the window.
"Year ending June" is not the same as the calendar year or the financial year.

Also searched as: moving average, rolling total, three-month average, year ending

Official definitions: ONS: A guide to labour market statistics · ONS: Long-term international migration, provisional, latest bulletin

Index number

A number that shows how a value compares with a chosen reference period set to 100. An index of 110 means 10% higher than the reference period.

An index number expresses a series relative to a reference period, usually set equal to 100. Price indices such as CPI are published as index numbers, and inflation rates are calculated from them.

Worked example

Suppose a hypothetical index is 100 in the reference year, 125 in year five and 130 in year six.

Between the reference year and year six, the value rose by 30%.
Between years five and six it rose by 5 index points, but by 4% (5 divided by 125). Points and percentages are not the same once the index has moved away from 100.

How it trips up claims

A fall in an index "by 2 points" is not a 2% fall unless the index stands at 100.
Index levels from series with different reference periods cannot be compared directly; compare their percentage changes instead.
When producers rebase an index to a new base year, every level changes but the growth rates should not.

The ONS publishes the CPI index (2015=100) as series D7BT and the RPI index (January 1987=100) as series CHAW.

Also searched as: index, 2015=100, index points, what is an index number

Official definitions: ONS: CPI index, all items, 2015=100 (D7BT) · ONS: RPI all items index, January 1987=100 (CHAW)

Base year

The reference period against which an index is set to 100, or whose prices are used to express real-terms figures.

The base year (or reference period) is the point that other values are compared with. It has two common uses in official statistics:

For an index number, it is the period set to 100, such as "2015=100".
For a real-terms figure, it is the year whose prices are used, such as "in 2024-25 prices".

Worked example

A hypothetical spending line is £200 million in year one and £240 million in year four, with prices up 20% between those years. Expressed in year-four prices, year one becomes £240 million, so real spending is flat. Expressed in year-one prices, year four becomes £200 million, again flat. The base year changes the level shown but not the real change.

How it trips up claims

Two real-terms tables using different base years show different pound amounts for the same year. Before comparing, convert both to one base.
Choosing a base year at an unusual high or low point can make later changes look larger or smaller when shown as index levels.
HM Treasury's GDP deflator tables let you re-express spending in the prices of any year they cover.

Also searched as: reference year, reference period, prices of year, constant prices base

Official definitions: HM Treasury: GDP deflators at market prices, and money GDP · ONS: CPI index, all items, 2015=100 (D7BT)

Seasonally adjusted

Figures that have had regular calendar patterns removed, such as Christmas shopping or summer jobs, so that underlying movements between months or quarters can be seen.

A seasonally adjusted series has had its regular, predictable calendar effects estimated and removed. Retail sales jump every December and some jobs rise every summer; adjustment strips out these repeated patterns so that a month can be compared fairly with the month before.

Worked example

Imagine hypothetical sales of 100 in November and 130 in December. If December is normally 30% above November, the seasonally adjusted figures would show no change. If December came in at 120, the raw data show a rise but the adjusted data show a fall, because sales were weaker than the usual December boost.

How it trips up claims

Comparing one raw (non-seasonally adjusted, often marked NSA) month with the previous month can show "rises" or "falls" that are just the season.
Seasonal factors are re-estimated as new data arrive, so adjusted figures for past months can be revised.
For data that are not adjusted, compare with the same month a year earlier (year-on-year).

The ONS explains its methods and labels each time series as SA or NSA in the series title.

Also searched as: SA, NSA, seasonal adjustment, what does seasonally adjusted mean, not seasonally adjusted

Official definitions: ONS: Seasonal adjustment · ONS: A guide to labour market statistics

Base effect

When a rate of change is pushed up or down by what happened in the comparison period, rather than by what is happening now.

A base effect occurs when a year-on-year rate changes because of an unusual movement in the base (comparison) period a year earlier. Annual inflation, for example, compares prices with the same month a year before. If prices jumped sharply in that earlier month, the annual rate will fall once that month drops out of the comparison, even if prices are still rising.

Why it matters when checking a claim

Inflation "falling" is not prices falling. A lower inflation rate usually means prices are rising more slowly, not that they are lower.
Recoveries look dramatic. Growth measured from a very weak period (such as 2020) can produce unusually large percentage rises.
Look at the level as well as the rate. The ONS consumer price bulletin explains which items drove each month's change, including base effects from energy price changes.

See is UK inflation going down.

Also searched as: base effects, base effect inflation, base effect meaning, base period effect

Official definitions: ONS: Consumer price inflation, latest bulletin · Bank of England: Inflation and the 2% target

Compound annual growth rate

The constant yearly growth rate that would take a figure from its starting value to its end value over a period. Different from simply dividing total growth by the number of years.

The compound annual growth rate (sometimes called CAGR or the average annual growth rate) is the steady yearly rate that would turn a starting value into an end value over a given number of years. It is calculated as (end value divided by start value) raised to the power of one divided by the number of years, minus one.

Worked example

A hypothetical budget rises from £100 million to £150 million over five years. Total growth is 50%, but the compound annual rate is about 8.4% a year, not 10%, because each year's growth builds on the last.

Why it matters when checking a claim

Dividing total growth by the number of years overstates the yearly rate.
Over long periods, small differences in annual rates add up to large differences in levels.
The OBR and ONS often quote average annual growth rates; check whether they are compound and whether they are in real terms.

Also searched as: CAGR, average annual growth rate, annualised growth rate, compound growth

Official definitions: Office for Budget Responsibility: Economic and fiscal outlook · ONS: GDP quarterly national accounts

Discontinuity (break in series)

A point where the way a statistic is collected or defined changes, so figures before and after it cannot be compared directly.

A discontinuity, or break in series, happens when a change in definitions, data sources, recording practice or methods means that figures before and after a date are not measuring quite the same thing. Producers flag these in tables and charts, often with a vertical line or a footnote.

Examples in UK statistics

Police recorded crime rose in some categories after recording practices were tightened from 2014, so part of the increase reflected better recording.
Survey changes, such as the move to a transformed Labour Force Survey or a new mode of interview, can shift levels.
New definitions, such as a change in what counts as a homeless household or a school absence, alter counts.

Why it matters when checking a claim

A "record" or "biggest rise" claim that spans a break may be comparing different measures. Read the notes beside the table and the methodology page before comparing across the break. See how to read an ONS bulletin.

Also searched as: break in series, series break, discontinuity in data, not comparable over time

Official definitions: Office for Statistics Regulation: Code of Practice for Statistics · ONS: Crime in England and Wales, latest