Error analysis and data processing of water quality analysis results (2)

4.

(1) Absolute error and relative error

Absolute error (E)=u-τ

Where μ——measured value;

τ-the true value

When the measurement result is greater than the true value, the error is positive, otherwise it is negative

Relative error refers to the ratio of absolute error to true value (usually expressed as a percentage)

(2) Absolute deviation and relative deviation

di=xi-

The relative deviation is the ratio of the absolute deviation to the mean (usually expressed as a percentage), expressed in d:

(3) Average deviation and relative average deviation

The relative average deviation is the ratio of the average deviation to the measured mean value (usually expressed as a percentage):

(4) Very poor

The range is the difference between the maximum value and the minimum value in a set of measured values, which represents the range of error, expressed by R:

R=x _max -x _min

Where x _{max ——measured} value x ₁ , x ₂ ,.

x _min ——the smallest value among the measured values ​​x ₁ , x ₂ ,.

(5) Example of error calculation

[Example 1.

Solution 1: Average value:

Absolute error: 112-110=2(mg/L)

Relative error:

Absolute deviation: di=xi-=112-113.

Relative deviation:

Solution 2: Average deviation:

Relative average deviation:

Extremely poor: x _max -x _min =115-112=3(mg/L)

5.

(1) Significant figures
.

1) The rounding rules of significant figures
.
When recording and sorting out the analysis results, in order to avoid confusion in the report results, it is necessary to determine the use of several "significant figures"
.
Every digit in the report, except for the last digit, is accurately measured, and only the last digit is suspicious
.
Suspicious numbers are meaningless numbers in the future
.
When reporting the results, only the suspicious digits can be reported, not the meaningless numbers
.
The number of reported digits can only be within the sensitivity limit of the method, and the number of digits should not be arbitrarily increased
.
For example, 75.
6mg/L, which means that the laboratory staff is affirmative of 75, 0.
6 is uncertain, it may be 0.
5 or 0.
7
.

When the number after the suspicious number is 1, 2, 3, or 4, the ones that are rounded down, the ones that are 6, 7, 8, and 9 are entered.
If it is 5, the numbers on the right side of 5
.
If the digits to the right of 5 are all zeros, rounding or rounding depends on whether the digits to the left of 5 are odd or even
.
If the left of 5 is an odd number, enter 1, and if the left of 5 is an even number, it will be discarded; if the digits on the right of 5 are not all zeros, regardless of whether the digits on the left of 5 are odd or even, they will be entered
.
For example, if a certain number is 14.
65, it should be reported as 14.
6
.
For example, 0.
35 can be modified to be about 0.
4, and 1.
0501 can be modified to be about 1.
1
.

"0" can be a valid digit or not a valid digit, it just means the number of digits
.
For example, 104, 40.
08, and 1.
2010, all 0s are valid digits; while for 0.
6050g, the 0 before the decimal point is not a valid digit and only serves as a positioning function
.

When 0 is a significant number, it cannot be omitted.
For example, when the burette reads 23.
60mL, it should be recorded as 23.
60mL, but not 23.
6mL
.
If you take a 25mL water sample with a graduated cylinder, you can only write it as 25mL, not 25.
0mL
.
When describing the concentration of a standard solution, it is often written as 1.
00mL containing 0.
500mg of a certain ion.
This number indicates that the volume is accurate to 0.
1mL and the weight is accurate to 0.
01mg; however, 1mL contains 0.
500mg of a certain ion, which is only a rough indication of the content
.

2) Approximate calculation rules
.
When adding or subtracting several numbers, the number of reserved digits after the decimal point shall be the one with the least number of digits after the decimal point
.
For example, the answer of 2.
03+1.
1+1.
034 should not be more than 1.
1, which has the least number of decimal places, so the answer is 4.
2 instead of 4.
164
.
When multiplying and dividing several values, the value with the smallest number of significant digits, that is, the data with the largest relative error, shall prevail, discard the excessive digits in the remaining values, and then perform the multiplication and division
.
Sometimes one more digit can be reserved temporarily, and the extra digits can be discarded after the final result is obtained
.
For example, if you multiply the three values ​​of 0.
0121, 25.
64, 1.
05782, because the first value 0.
0121 has only three significant digits, you should determine the number of digits of the remaining two values, and then multiply them, that is, 0.
0121×25.
6 ×1.
06=0.
328, should not be written as 0.
328182308
.
When exponentiation or extraction, the original approximate value has several significant digits, and the calculation result can retain several significant digits
.
For example, 6.
54 2=42.
7716, the result is 42.
8 with three significant digits; for another example, the result with three significant digits is 2.
72
.

(2) The choice between outlier data and suspicious data
.

1) The concept of outlier data and suspicious data
.
The measurement data that obviously distorts the test results, that is, the data that is not from the same distribution population as the normal data, is called outlier data
.
The experimental results may be distorted, but the measurement data that has not been tested to determine that it is outlier data is called suspicious data
.

2) Generation of outlier data
.
A set of normal data should come from a population with a certain distribution
.
Once the experimental conditions have changed, or there is a gross error in the experiment, the resulting measurement data will deviate from the normal data distribution group, that is, outlier data with greater dispersion will appear
.

3) Elimination of outlier data
.
Eliminating outlier data can make the measurement results more in line with objective reality
.
However, normal data also has a certain degree of dispersion.
If in order to obtain a high precision result, some measurement data with large errors but not outliers are artificially removed, and the resulting high precision measurement results will not Not in line with objective reality
.
Therefore, the selection of suspicious data must follow certain principles
.
Once an obvious systematic error and negligent error are found in the experiment, the resulting data should be eliminated at any time
.
But sometimes even after the experiment is done, it is still not sure which data is outlier
.
At this time, the choice of these suspicious data should be judged by statistical methods, that is, statistical testing of outlier data
.

4) Discriminant criteria for statistical testing of outlier data
.

a.
If the calculated statistic is not greater than the critical value when the significance level a=0.
05, the suspicious data is normal data
.

b.
If the statistic is greater than the critical value when a=0.
05 and at the same time is not greater than the critical value when a=0.
01, the suspicious data is deviating data
.

c.
If the statistic is greater than the critical value when a=0.
01, the suspicious data is outlier and should be eliminated
.

d.
Be cautious when dealing with deviated data.
Only the deviated data for which the cause can be found can be processed as special high-level group data, otherwise it should be processed as normal data
.

e.
After the outliers are eliminated from a set of data, the remaining data after the elimination should continue to be tested until there are no more outliers
.