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Is this number actually going up, or is it just noise?

Plot time-ordered data with a median centre line and apply the run chart rules, so you can tell a real change from ordinary variation.

Run Chart · measure · Foundation · free, no account needed

Use this when

  • A metric moved and someone wants to know whether it means anything
  • You changed something and need to show whether it worked
  • A weekly report compares this week with last week and you suspect that is meaningless

Run Chart

sandbox
Run chart of 24 median wait values in time order. Median 39.5. 3 signals: shift, shift, too few runs. Longest run on one side of the median: 12 points.median58.2424.76Week 1Week 2Week 3Week 4Week 5Week 6Week 7Week 8Week 9Week 10Week 11Week 12Week 13Week 14Week 15Week 16Week 17Week 18Week 19Week 20Week 21Week 22Week 23Week 24
Points in time order — never sorted. The centre line is the median, not a target. Squares mark points inside a rule signal.
Show the data behind this chart
Run chart of 24 median wait values in time order. Median 39.5. 3 signals: shift, shift, too few runs. Longest run on one side of the median: 12 points.
#Labelmedian waitVs median
1Week 146above
2Week 252above
3Week 341above
4Week 449above
5Week 544above
6Week 655above
7Week 743above
8Week 848above
9Week 951above
10Week 1045above
11Week 1147above
12Week 1250above
13Week 1338below
14Week 1433below
15Week 1536below
16Week 1631below
17Week 1735below
18Week 1829below
19Week 1934below
20Week 2032below
21Week 2137below
22Week 2230below
23Week 2333below
24Week 2428below

Points

24

Median

39.5

Longest run

12 points

Above median
12
Below median
12
Runs observed
2
Expected range
8–18

shift12 consecutive points above the median (points 1–12). A run of 6 or more is unlikely by chance alone, so something about the process changed here — the chart says when, not what.

shift12 consecutive points below the median (points 13–24). A run of 6 or more is unlikely by chance alone, so something about the process changed here — the chart says when, not what.

too few runs2 runs where 8 or more would be expected (p < 0.001). Too few runs means the points cluster on one side and then the other — the process is not varying around a single stable level.

One observation per line, oldest first: Week 1, 34 — or just the number. Do not sort it. The order IS the data.

How this is calculated

The centre line is the median, not the mean — a single extreme value moves the mean and would drag the centre line towards the very point you are trying to notice.

  • Shift — 6 or more consecutive points on one side of the median. Points sitting exactly on it are skipped, neither extending nor breaking a run.
  • Trend — 5 or more consecutive points all rising or all falling. Shown, but the weakest of the three: it fires on random data more often than people expect.
  • Too few / too many runs — the number of times the series crosses the median, compared against the exact distribution of the number of runs. The critical values here are computed from that distribution rather than looked up in a table.

A fourth classic rule — an “astronomical” point obviously unlike the rest — is deliberately not automated. It is a judgement about the process, and any threshold would get it wrong in both directions.

Source: Provost & Murray (2011), The Health Care Data Guide, Ch. 3 for the rules; Swed & Eisenhart (1943), Annals of Mathematical Statistics 14(1) and Gibbons & Chakraborti, Nonparametric Statistical Inference 5e §3.2 for the runs distribution.

Saved runs can be attached to a project deliverable as evidence. Both what you entered and what the tool computed are stored, so the result can be checked again later.

How this is calculated

Median centre line. Shift = 6+ consecutive points on one side of the median, with points on the median skipped. Trend = 5+ consecutive rises or falls, ties collapsed. Runs test critical values are computed from the exact distribution of the number of runs, P(R=2k) = 2*C(n1-1,k-1)*C(n2-1,k-1)/C(n1+n2,n1), rather than transcribed from a table.

Source: Provost, L.P. & Murray, S.K. (2011), The Health Care Data Guide, Ch. 3, for the shift and trend rules; Swed & Eisenhart (1943), Annals of Mathematical Statistics 14(1), and Gibbons & Chakraborti, Nonparametric Statistical Inference 5e Sec. 3.2, for the runs distribution.

Learn the method