# Osmometer Results Precision Notes

In addition to the information in the User Manuals the following notes have been extracted from Advanced Instruments documentation regarding accuracy and precision of results.

### Factors Contributing To the Acceptable Range Of Results

#### Error Contribution of the Calibrator/Control

There is a tolerance associated with formulating a calibrator/control due to normal variations in the production and quality control processes. This tolerance can affect the mean value obtained from testing multiple samples of the calibrator/control, and is independent of any specifications associated with the instrument.

#### Error Contribution of the Osmometer

The linearity and repeatability specifications for the Osmometer also affect the test results. These specifications are independent of the formulation tolerance of the calibrator/control.

The linearity (accuracy) specification defines the maximum deviation of the mean of an actual set of test data from the nominal value of the calibrator/control being tested. It is frequently expressed as a percentage of the nominal value of the calibrator/control.

The repeatability (precision) specification defines the limits of variation for any individual test result with respect to the calculated mean of a series of results. Repeatability is frequently expressed as a standard deviation (S.D.), with 1 standard deviation (1 S.D. ) incorporating approximately 67% of a normally distributed population relative to the calculated mean of the results. For any given series of tests it is possible to have individual test results that lie beyond this 1 standard deviation limit. When establishing allowable limits for test results that encompass population percentages higher than 67%, multiples of the repeatability specification should be used in the calculation (i.e. for results that encompass 95% of the population, a repeatability value equivalent to 2 standard deviations should be used).

#### Total Probable Variations

In situations where several independent factors combine to comprise the total variation possible for a system, the calculation that numerically adds the limits of each contributor (assuming that all exist at their maximum possible allowance), can produce limits, which exceed the amount of variation experienced during actual testing. In this case, a more realistic calculation of the total expected variation in system performance can be obtained from a root-mean-square (RMS) calculation. Although this method is most appropriate when the number of contributors is large, the calculation for the combination of the calibrator/control and the Osmometer would be:

Using this result, the acceptable range of results for any individual test result within the data set are:

Lower range limit: 290 - 4.05 = 285.95 mOsm/kg H_{2}O

Upper range limit: 290 + 4.05 = 294.05 mOsm/kg H_{2}O.

**Notes:**

- The above example does not include any effects from:
- Improper instrument calibration
- Improper pipeting technique (sample-to-sample volume variation, trapped air bubbles, etc.)
- Instrument operation at a temperature significantly different from the calibration temperature
- Long-term instrument drift since last calibration.

These factors can add additional variation to the overall system performance and further broaden the range of expected results.

- Although osmolality is determined by monitoring the temperature of a sample being frozen through a highly controlled and repeatable process, this freezing process is nevertheless a natural process with its own level of randomness. This can occasionally produce test results with unexpectedly high or low values that exceed the acceptable range as determined above. On these rare occasions, the sample should be retested or the test repeated by testing a fresh sample to confirm or reject the prior result.

#### Using Specifications

Combining the allowable accuracies of the calibrator/control and the Osmometer provide the expected range of the mean for a series of tests. The Osmometer repeatability specification is not considered when determining this combined accuracy.

For example, assume that the specifications are:

Formulation tolerance of 290 mOsm/kg H_{2}O (nominal) control solution:

±2 mOsm/kg H_{2}O

Osmometer linearity specification: ±1%

Converting the linearity percentage to a mOsm/kg H_{2}O value at the

nominal value of 290 mOsm/kg H_{2}O gives:

±2.9 mOsm/kg H_{2}O

Thus the combined accuracy of the control solution and the

osmometer is

±2 mOsm/kg H_{2}O + ±2.9 mOsm/kg H_{2}O = ±4.9 mOsm/kg H_{2}O

Therefore the acceptable range of values for the mean of a set of results is:

290 mOsm/kg H_{2}O ±4.9 mOsm/kg H_{2}O, or 285.1 to 294.9 mOsm/kg H_{2}O.

Now consider the osmometer repeatability. If the osmometer repeatability

specification is stated in terms of a standard deviation and has a

value of:

1 S.D. = 2 mOsm/kg H_{2}O

and the actual standard deviation calculated from a set of data is ± 2 mOsm/kg H_{2}O, then the osmometer is performing acceptably from a repeatability standpoint.

Using the acceptable range of values for the mean from above and a 1 standard deviation value for the repeatability, the acceptable range of results for any individual sample tested within the data set is:

Lower range limit: 285.1 - 2 = 283.1 mOsm/kg H_{2}O

Upper range limit: 294.9 + 2 = 296.9 mOsm/kg H_{2}O.

Using a repeatability value equal to 2 standard deviations, the acceptable range of results for any individual sample tested within the data set is:

Lower range limit: 285.1 - (2 X 2) = 281.1 mOsm/kg H_{2}O

Upper range limit: 294.9 + (2 X 2) = 298.9 mOsm/kg H_{2}O.

Therefore, with this osmometer and testing this calibrator/control, if the mean of a series of test results lies between 285.1 and 294.9 mOsm/kg H_{2}O and the standard deviation of that group of test results is ± 2 mOsm/kg H_{2}O, then the complete system (i.e. calibrator/control and the osmometer) is performing acceptably with an acceptable range of results as determined above.

Please see the table below for specific instrument information.