Plotting experimental data and reading a standard curve

Plot the measurement, not just the average

A chart should show what was measured. Individual points, or means with an error bar, are more honest than a bare line drawn through one value per condition, because the reader can see the spread and judge how far the summary can be pushed. Label both axes with the quantity and its unit, and label the error bars with what they represent; an unlabelled error bar is decoration rather than information.

Match the chart type to the data. Scatter is right for independent measurements of one quantity against another, and a connecting line is right when the order of the points carries meaning, such as a time course or a wavelength scan. Connecting arbitrary categories, or drawing a trend through points that should not be ordered, suggests a relationship that the experiment did not test.

Error bars say more than they look

Error bars can show the standard deviation of repeated measurements, the standard error of the mean, a confidence interval or an instrument tolerance, and those are different claims. The standard deviation describes how spread out the observations are; the standard error describes how precisely the mean is known and shrinks as the number of replicates grows. Decide which one answers the question and state it in the caption.

An error bar is not a significance test. Means whose bars overlap can still differ after a proper analysis, and bars that do not overlap do not prove a difference on their own. The bar also says nothing about sample size, so a narrow bar from one careful replicate can look more convincing than a wide bar from many measurements. Report n alongside the chart.

Reading a standard curve

Standards are measured in the same conditions as the samples, at known concentrations, and a straight line is fitted to their signals. The slope gives the signal change per unit concentration and the intercept gives the predicted signal when concentration is zero, which is useful for judging background even when a blank is not part of the fit. Samples are then read from the same line: signal = slope × concentration + intercept, so concentration = (signal − intercept) ÷ slope.

The trustworthy part of the curve is the range covered by the standards. A sample below the lowest or above the highest standard is an extrapolation: the line is being extended where no data exists, so the number is an estimate until standards bracket it. Re-run standards with each batch when the detector can drift, and check the fit's residuals rather than trusting the R² alone.

R² is correlation, not accuracy

R² measures how much of the variation in the signal the straight line explains within the calibrated standards. A value near 1 means the points sit close to the line; it does not mean the line sits in the right place. A wrong standard concentration, a mis-set blank, a drifting lamp or systematic pipetting error can all produce a tidy set of points around a line that gives wrong sample concentrations.

Accuracy is a separate question, checked against reference materials, recovery experiments or an independent method. Precision is what the fit's scatter describes, and a precise line through biased standards is still biased. When the calibration matters, report the equation, the range, the number of standards and the acceptance criteria your method uses, not just R².

Reporting percent error and the final result

Percent error compares a measured value with an accepted one: |experimental − accepted| ÷ |accepted| × 100. The absolute value makes the percentage non-negative, so state separately whether the experimental result was above or below the accepted value. Percent difference compares two measurements when neither is a reference: |a − b| ÷ |(a + b) ÷ 2| × 100, which is symmetric but undefined when the two values average to zero.

Whichever statistic is chosen, give the measured value with its unit and uncertainty, quote the number of observations, and round only at the end to the significant figures the measurement supports. If the number came from a calibration curve, say which standards defined the line and whether the sample sat inside or outside that range. A percentage on its own, with no reference, unit or range, is impossible to check.

• Label each axis with the quantity and its unit, and say what the error bars show.
• Report n and the calibration range next to any fitted line or percentage.
• Keep the measured value, its uncertainty and the percentage error together.
• Confirm that samples sit inside the standard range before quoting a concentration.
• Round at the end to the significant figures the measurement supports.