Enrichment · Passion Projects · Lab science

How close together
are your replicates?

Paste your repeated measurements. The calculator gives the mean, the spread and the spread as a percent of the mean, puts a confidence interval on the result, and points out any replicate that sits far from the rest.

Check the precisionWhat you get

The replicate variability calculator

The worked example is six made-up titration endpoints. Nothing you type leaves this browser.

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What you get

Enrichment · Passion ProjectsFree

What you finish with
Mean, SD, RSD, SE, a 95% confidence interval, the range and each replicate’s deviation, with the precision goal checked. It prints for a lab notebook and downloads as a spreadsheet.
Who it is for
Chemistry, biology and physics students writing lab reports, science teachers, and science fair students.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
Free. No account, no sign-in and nothing to install. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The Passion Projects space in Caveat Enrichment.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Paste the replicate values, one per line.
  2. Type the units and the precision goal.
  3. Choose how many decimals your instrument reads.
  4. Read the RSD and the interval.
  5. Look into any flagged replicate in your notebook.

Check the precision

How the spread is measured

Standard deviation, scaled and turned into an interval.

The worked example: six titration endpointsMean24.325six endpoints, mLSD0.0485n − 1 in the divisorRSD0.20%SD ÷ mean95% CI± 0.051t = 2.571, SE = 0.0198The worked example: six titration endpointsMean24.325six endpoints, mLSD0.0485n − 1 in the divisorRSD0.20%SD ÷ mean95% CI± 0.051t = 2.571, SE = 0.0198
The spread, scaled to the size of the measurement, is what makes replicates comparable across experiments.

Why relative

A standard deviation of 0.05 mL is excellent for a 25 mL titration and poor for a 0.5 mL pipette. Dividing by the mean gives the relative standard deviation, a percent you can compare across experiments and against a lab’s precision goal.

The interval

The standard error, SD ÷ √n, is how much the mean itself would wobble if you repeated the whole set. Student’s t widens the interval for small samples: with six replicates it is about 2.57 standard errors either side for 95 percent confidence, against 1.96 for a very large sample.

Sources

  1. National Institute of Standards and Technology. NIST/SEMATECH e-Handbook of Statistical Methods, sections on standard deviation and confidence limits (itl.nist.gov).
  2. Harris, D. C. (2020). Quantitative Chemical Analysis (10th ed.). W. H. Freeman. Chapter on experimental error and statistics.
  3. Joint Committee for Guides in Metrology. JCGM 100:2008, Guide to the Expression of Uncertainty in Measurement (bipm.org).
  4. American Chemical Society. Guidelines for chemistry laboratory reports and data analysis (acs.org).

The worked example is made up. Your measurements stay in this browser. Support: team@caveatacademic.com.