The standard curve (standard curve in English) refers to a numerical curve of properties obtained by measuring a certain physical and chemical property of a series of standard materials with known components. The standard curve is the functional relationship between the physical/chemical properties of the standard material and the instrument response. The purpose of establishing a standard curve is to derive the physical and chemical properties of the substance to be tested. In analytical chemistry experiments, the standard curve method is commonly used for quantitative analysis. The standard working curve is usually a straight line. Different from the calibration curve, it is a curve plotted from a standard series composed of standard solutions and media. The associated components of the standard series of the calibration curve must match the sample in order for the measurement results to be accurate. Only when the standard curve coincides with the calibration curve, the standard curve can be used to replace the calibration curve.
The abscissa (X) of the standard curve represents the variable that can be accurately measured (such as the concentration of the standard solution), which is called an ordinary variable. The ordinate (Y) represents the response value of the instrument (also called the measured value, Such as absorbance, electrode potential, etc.) are called random variables. When the values ??of X are X1, X2,... Xn, the Y values ??measured by the instrument are Y1, Y2,... Yn respectively. Describe these measurement points Xi and Yi in the coordinate system, and use a ruler to draw a straight line representing the linear relationship between X and Y. This is the commonly used standard curve method. When used as a standard material to draw a standard curve, its content range should include the content of the substance being measured in the test, and the standard curve cannot be extended arbitrarily. The scale of the abscissa and ordinate of the drawing paper used to draw the standard curve and the size of the experimental points should not be too large or too small, and should approximately reflect the accuracy of the measurement.
Practicality of the standard curve
This is an important prerequisite for making a standard curve. This question is actually very simple. It is just this question: Can the instrument response of my sample be used by our method? Establish a standard curve to derive its physical and chemical properties? The answer is based on the specificity of the instrument's response and the matching of the standard series to the sample. On the one hand, we always strive for the response of the instrument to be equal to the standard and the sample; at the same time, we also require that my sample matches the standard matrix. Therefore, the best standard is the matrix matching standard, and the best standard curve is the working curve. In this way, we can also easily understand why most analyzes require the standard curve and samples to be measured in the same batch (unless after experiments, the standard curve does not change much). The same reason can also be understood why we need to insert QC when doing large-scale testing. Test samples to check the stability of the instrument. Even when any information is unknown, we still have to do our analysis and testing (otherwise, we would all be unemployed), because everyone uses the same method to do it, and everyone makes mistakes together; at the same time, because we believe that with the As science advances, the accuracy of our test results gets closer to the truth.
Distribution of points of the standard curve
When calculating the uncertainty of the sample from the uncertainty theory, there are two important conclusions: 1. The center of gravity point of the standard curve, so The sample found has the smallest uncertainty. 2. The more points there are in the standard, the smaller the uncertainty of the sample. The standard curve based on these two conclusions should be as follows: spread as many standard points as possible near the sample concentration. More or less points, and how the points are distributed, will affect the uncertainty of the physical and chemical properties of the sample detected by the standard curve. A good measurement should have a small uncertainty, which is crucial when judging whether the sample result exceeds the standard or meets the limit.
Edit this simple standard curve - single-point calibration
For tests with high analysis costs, single-point calibration is not an option. The most widely used method now is chromatographic analysis. Many national standards or international standards adopt single-point calibration. This is actually based on the high selectivity of chromatographic analysis: our blanks are generally very small and our linearity is generally very good. With the support of so many prior probabilities, a large number of single-point corrections in chromatographic analysis are a reasonable choice. However, single-point correction will lose a lot of information, and this information is uncertainty.
Actual standard curve
Existing methods tend to have standard curves that are applicable to a wider range of sample concentrations.
In the case of a wide concentration span and limited standard points, a uniform distribution of concentration points is the best choice, so that the amount of information provided is the same for all concentrations within the concentration range covered by the standard curve. The setting of odd points comes from our information. We always know the concentration range first, determine the middle point within the concentration range, and then distribute symmetrical standard curve points around the middle point, so there are always odd points. As emphasized before, more points and fewer points will ultimately affect the uncertainty of the physical and chemical properties of the sample detected by the standard curve. How much uncertainty does it meet the requirements? This is how you judge whether the sample results exceed the standard or not. It becomes important when the limits are met.
Evaluation of the standard curve
It is generally believed that the correlation coefficient is used to evaluate the quality of the standard curve. In fact, the most scientific method is to test the randomness of the remaining residuals of the straight line equation. Statistically, it is F test. The AMC committee under the British RSC has a dedicated TN for this.