Food physical and chemical testing data processing (2)

(3) Selection of suspicious values ​​in the measured data

In the parallel measurement of the same sample, some individual measurement values ​​may be significantly larger or smaller than other measurement values

1.

Inspection steps:

①The measured values ​​are arranged from small to large: x ₁ , x ₂ , x ₃ ,.

②Calculate statistics O _meter

Where |x _suspect— x _neighbor |—neighbor difference (the absolute value of the difference between the suspicious value and its neighboring data)

(x _n --x ₁ )-range (the difference between the maximum and minimum data)

(Note: When the number of measurements n>7, the calculation formula of the statistic Q _meter is different from the above)

③Check the Q value table (see Table 1-11): According to the number of measurements and the required confidence, check the critical value Q _table

Table 1-11 Q value table under different confidence levels

Note: More critical Q values ​​can be found in related books or manuals

④ Judgment

Q meter ≥ Q meter, suspicious value should be discarded

Q meter <Q meter, suspicious value should be kept

[Example 1-1] The moisture content of the hamburger was measured 4 times in parallel, and the data were 64.

Solution: Arrange the measured values ​​from small to large: 55.

Calculate statistics Q _meter :

Check the Q value table: when n=5 and a is 0.

Judging the suspicious value choice:

Since 0.

Note: When the number of measurements n>7, the formula used to calculate the statistic Q _meter is different from the above, please refer to the relevant books or manuals

2.

Inspection steps:

①The measured values ​​are arranged from small to large: x ₁ , X ₂ , x ₃ ,.

②Calculate the average value and standard deviation s (including the suspicious value)
.

③Calculate statistics G _meter
.

④Check table 1-12: According to the number of measurements n, the significance level a, check the critical value G _table
.

Table 1-12 Critical G value

Note: More critical G values ​​can be found in related books or manuals
.

⑤ Judging whether to choose the suspicious value
.

G _meter ≥G _table , the value should be rounded down suspicious

G _meter <G _meter , suspicious value should be kept

Note: If there are two suspicious values, regardless of whether they are on the same side or both sides of the n data sorting, the suspicious value with a large deviation must be found first and discarded temporarily
.
Using the remaining (n-1) pieces of data, calculate the average and standard deviation s, and check for suspicious values ​​with small deviations
.
The method is the same as above
.

If the suspicious value with a small deviation is judged to be an abnormal value, the suspicious value with a large deviation previously discarded is even an abnormal value
.
If the suspicious value with a small deviation is judged to be a normal value, then n data are reused, the average value and standard deviation s are calculated, and the suspicious value with a large deviation is tested
.
The method is the same as above
.