QC Mean, SD and CV Calculator

The tool covers the two times a bench works these numbers out by hand.

1. A new control lot. Run the new lot alongside the old one and paste its results, one per line, a column per level. Westgard's rule of thumb is at least 20 measurements over at least 10 working days, and preferably 20 working days, before you set limits. With fewer than 20 the tool says so and the limits are provisional.
2. A monthly summary. Paste the month's results for each level. To carry the lot forward, enter last month's lot-to-date n, mean and SD: the tool adds this month to them and gives the lot-to-date statistics, which Westgard calls “a better representation of long term test performance” than one month alone.
3. Print the summary for the QC binder (it carries a reviewed-by line), or copy it as tab-separated text into a spreadsheet. Then draw the limits on a Levey-Jennings chart.

Everything runs in this browser tab. Nothing you paste is sent to AssayDeck or stored.

For each control level, from its n results x₁ … xₙ:

mean = Σx ÷ nSD = √( Σ(x − mean)² ÷ (n − 1) )CV = SD ÷ mean × 100limits = mean ± 1 SD, ± 2 SD, ± 3 SD

The SD divides by n − 1. That is the sample standard deviation, the one Westgard's QC calculations lesson and Bio-Rad's statistics workbook both use, and the one QC software reports: twenty control results are a sample of everything the method will ever produce, not the whole population. In Excel that is STDEV.S, which “assumes that its arguments are a sample of the population”; STDEV.P treats the results as the entire population, divides by n, and comes out slightly smaller, more so when n is small.

Means and limits show one more decimal place than your results, and the SD two more. Westgard advises carrying extra figures and rounding at the end, after the limits are worked out.

For the lot to date, the previous summary and this period are pooled as if every result had been kept: Westgard totals the n, Σx and Σx² of each month, and the tool does the same algebra from the n, mean and SD you enter.

The coefficient of variation (CV) is the standard deviation written as a percentage of the mean. An SD on its own is in the test's units, and it tends to grow as the concentration grows, so SDs at different levels or on different methods cannot be compared directly. The CV can.

Bio-Rad's workbook gives the classic case. One glucose method has an SD of 4.8, another 4.0, so the second looks more precise. But their means are 120 and 100, and 4.8 ÷ 120 and 4.0 ÷ 100 are both 4 %: they are equally precise.

Outside the lab the idea is the same. A CV of 2 % says the results scatter by about 2 % of their average; a CV of 20 % says they scatter ten times as widely.

There is no single number. Bio-Rad's workbook lists where to look for the precision to expect: the assay reagent insert or instrument manual, interlaboratory comparison programs, proficiency surveys, published method evaluations, and regulatory proficiency limits such as CLIA's.

The CLIA limit gives a sense of scale. Proficiency testing accepts a potassium result within ±0.3 mmol/L of the target (§ 493.931). The default level 1 control here has an SD under 0.03 mmol/L, so its random error uses a small part of that allowance. If the SD were a third of the limit, the ordinary ±3 SD scatter alone would fill it, with nothing left for bias. The sigma metric calculator puts that margin into one number.

Peer programs put a number on it. Your CV divided by the peer group's CV is the CV ratio; in Bio-Rad's guidance “Ratios greater than 1.5 indicate a need to investigate the cause of imprecision and any ratio greater than 2.0 indicates need for troubleshooting and corrective action”. The QC peer programs compared page sets out who offers that data.

CLIA does not name a formula or a CV target. It requires the numbers this tool produces and leaves the acceptability criteria to the lab:

• Statistical parameters “(for example, mean and standard deviation) for each batch and lot number of control materials must be defined and available” (§ 493.1256(d)(10)(i)).
• An assayed control's stated value may be used if it is for your method and instrument “and is verified by the laboratory” ((d)(10)(ii)); an unassayed control's parameters “must be established over time by the laboratory” ((d)(10)(iii)).
• Each quantitative procedure needs two control materials of different concentrations at least once each day patient specimens are assayed (§ 493.1256(d)(3)), unless the lab follows an approved individualized quality control plan; see how often to run QC.
• QC records are kept “for at least 2 years” (§ 493.1105(a)(3)), so keep each monthly summary with its charts.