# (Statistics) Alternative phrases for growth rate?

The figures represent the number of tourists who visited a country in thousands. The red annotations do not mean anything.

In the fifth row of this chart, we can see that the data for Europe had the highest growth (change/past) rate rather than increase over the years compared to the figures for other countries. However, since the word "growth rate" seems inappropriate here, what are the other ways to express this idea?

Thank you.

• Why does growth rate seem inappropriate? What does the table show? How about rate of change?
– Jim
Commented Nov 27, 2020 at 0:43
• Rate of growth? Commented Nov 27, 2020 at 1:59
• Please clarify your question. First, what are the black numbers? Are they a population count? What does change/past refer to? Which change? Which past? Should we ignore the red material? What do you mean by world? Should it have been word, or phrase? Commented Nov 27, 2020 at 8:20
• @Anton Sorry just edited it Commented Nov 27, 2020 at 20:31
• That makes it possible to answer. Thank you. Commented Nov 27, 2020 at 22:37

In this context, a rate is a change relative to a time period.

rate = a measurement of the speed at which something happens or changes, or the number of times it happens or changes, within a particular period

Cambridge dictionary

A rate would therefore be expressed as change per time. In this case, "number per year".

Turning now to your statement: there are at least three ways of interpreting "data for Europe had the highest growth (change/past) rate rather than increase over the years"

(1) change relative to 1991: the maximum value (2.3) is for Europe in 1999 (2) change in numbers from the previous year: maximum (121) is for United Kingdom in 1999 (3) change relative to the previous year: maximum (1.31) is for United Kingdom in 1999

It is thus clear that your statement can only refer to (1) as "change relative to 1991". This is a ratio of numbers visiting; it is not a rate (which would be expressed as number per year). This means that Europe had the highest relative growth over the period 1991-1999.

The phrase you seek is "relative growth".

• @PhilSweet Art & intuition are false friends; you err. Relative growth from time T0 to T1 is the ratio of numbers (N1) at the end to those at start (N0); i.e. N1 relative to N0 => N1/N0. It is not a rate. N1/N0 divided by time (T1-T0) gives an average rate of relative growth (per year, not necessarily % per year). This says nothing whatsoever about exponential growth or decay. Exponential growth and decay are special cases that only occur if the rate of relative growth (R) is constant over any time period you consider, small or large. Exp. growth occurs when R>1; exp. decay when R<1. Commented Nov 28, 2020 at 17:59
• @PhilSweet There is no "of course" about it. You seem to assume that numbers relating to some other metric (which you do not define and do not quantify) would be different (in some way that you do not specify) but also (from your "just compute to ...") irrelevant (for reasons that you do not give). Why mention them if they are irrelevant? Such baselessly assertive comment shows a disregard for definition and quantification that may confuse and certainly does not help the PO, who asked a reasonable question and deserves a reasoned answer.. Commented Nov 28, 2020 at 18:14
• @PhilSweet You clearly have a confused notion of exponential growth, which neither the PO nor I mentioned, and which you have unproductively introduced for no good reason into the discussion. This exchange is now closed before the moderators decide quite rightly to move it all to chat. Commented Nov 28, 2020 at 18:19

The presence or absence of the word rate cannot be relied on to make the distinction between, say, the annual rate of change over a multi-year period and the total change over a multi-year period. There are many terms not using rate that are nevertheless defined as rates and understood to be rates in both normal conversation and in technical usage. Growth is one of these. Furthermore, rate frequently appears in cases where there is just one unit of time, so the rate of change is equal to the total change. It also frequently intrudes on cases where multi-period timespans are in play, but the context is the total change.

In the case of growth, you really need to explicitly opt out of the rate notion by stating so. Or you can take the direct approach and show the calculation you want to use in the comparison.

The use of the term growth rate to mean total growth over a period is so common that you just can't say it is wrong, but it is ambiguous. It can also mean any of the following and more -

• Relative Growth Rate - RGR = (ln(x2) - ln(x1))/(t2 - t1), the answer depends on the units of time.

• Compound [daily, weekly, monthy, annual, or other time step] Growth Rate - CGR = (x2/x1)^(1/n) -1 ,n is number of days, weeks, months, years, etc. between x2 and x1.

• Simple Average Growth Rate - SAGR = (x2/x1)/(number of years, months, etc).

• Arithmatic Mean Growth Rate. AMGR = sum of all annual (or biannual, in your case) YTY changes divided by the number of periods.

Comparisons using any of the first three will yield the same result. However, that is not necessarily true of the fourth one.

So you either need to define your term with a formula on the first instance, or define it in an introductory list of variables, and then use it consistently thereafter; or just show the computation if it's a one-off.