Gross Error, Systematic Error, and Random Error

Introduction

Gross error, systematic error and random error are different types of errors. The error may be defined as the difference between the true value and the measured value. The actual value is the average value of multiple times the measured value. The measurement taken by the observer as accurately as possible is called a measured value. The quantities which we generally measure may be mass, length, time, volume, temperature, current, degree, etc. in all these cases observation finally reduces to the reading of a scale or noting the coincidence between two marks. As the personal judgment of the observer is employed in estimating the coincidence between two marks or in recording the position of a pointer which is between two marks of a scale, an error is inevitable.

Measurement

Measurement is the most valuable part of science. Also, it is most important for living too. We measure weight, height, time, etc. We measure how many calories are burnt when we walk, we measure the size of clothing, and a lot more. So not only in science measurement plays a crucial role in our lives. It is the foundation for all technological development. The accuracy of measurement is more important in science. But sometimes we fail to calculate the exact value in the measurement. It's quite hard to find the exact value of any measurement. In such cases, it will cause an error. So, there is no possibility to find accurate measurements.

For example, when we buy any fruits or vegetables, vendors measure the unknown weight of the fruits or vegetables with the known weight with the help of a weight scale. The uncertainty in the measurement is called an error.

Types of Errors

There are many types of errors while measuring.

• Gross Errors

• Systematic Errors

• Random Errors

Gross Errors

Gross Errors are called human errors. Carelessness of an observer leads to gross error.

For Example, when an observer takes the reading, he may write 76 as 70. It is noted as an error. To avoid those gross errors, observers should be very careful while taking the reading because in some scientific experiments 0.1 value mistake also makes a huge difference. So, the observer must follow proper care in recording the data. In case of any error in the reading observer also calculate the accurate value of the error. So, these errors can be minimised only when an observer is careful and mentally alert.

Systematic Errors

If during an experiment a factor operates in such a way as to make the observed value always higher or lower than the true value, this type of error is said to be a systematic error.

Examples − Instrumental errors (zero error, bench error, etc.,) radiation loss or gain in calorimetry.

It is divided into many types. Equipment errors, Personal errors, Environmental errors, and Observational errors

• Equipment Errors − Equipment errors were caused because of the bad condition of the equipment or instrument. With the improper condition of the instrument, these errors may arise. So, instruments should be in proper condition to avoid these errors.

• Personal Errors − These errors may arise when the initial adjustment is not set up properly by the individuals who are performing the experiment.

• Environmental Errors − Slight changes in experimental conditions for example small changes in temperature, pressure, voltage, etc may occur during the experiment and lead to small uncertain errors.

• Observational Errors − The observational errors are given underneath.

  • Sometimes due to an accidental error of observation, a particular result comes out to be exceptionally too high or too low.

  • This should be rejected or its observations, if possible, should be checked again, for it will otherwise mar the whole result.

Random Errors

The errors arising out of small changes in the experimental conditions and the personal judgment of the observer are known as random errors. When random errors are due entirely to chance, and not due to any personal bias on the part of the observer, they are likely to be positive as well as negatives.

• When an observation gives a higher value than the true one, the error in the observation is said to be positive. Large random errors due to chance are less likely to occur than small ones.

• If a large number of observations of the same quantity is made it is likely that most of them will have small errors, each one of which has a greater chance of being positive as negative.

Error Calculation

Let us consider an example for Error calculation.

Q1. To find the radius of curvature of a concave mirror by a spherometer. Given that l=4.4 cm and h=0.085 cm

Ans. We know that

$$\mathrm{ R=\frac{l^2}{6h}-\frac{h}{2}}$$

Taking log of both sides

$$\mathrm{\log {R}=2 \log {l}-\log {6}-\log {h}+\log {h}-\log {2}}$$

Differentiating both sides, we get

$$\mathrm{\frac {\delta R}{R}=\frac{2 \delta l}{l}+\frac{2 \delta h}{h}}$$

$$\mathrm{\frac {\delta R}{R}=\frac{2 \times 0.1}{4.4}+\frac{2 \times 0.001}{0.085}}$$

δl=0.1cm is the least count of the metre scale.δh=0.001cm is least count of spherometer

$$\mathrm{\frac {\delta R}{R}=0.045+0.023=0.068}$$

$$\mathrm{Maximum\: possible\: error\:=0.068 \times 100=6.8 \%}$$

It is important to note that the maximum contribution to a total error in the result is due to the individual error i.e. 4.5% in the measurement of distance (l) between the fixed legs of the spherometer. Hence ‘l’ should be measured most carefully.

Reason for Errors

• There are many reasons for Errors. equip mental error, conditional error, and person Error are the general causes of Error.

• Results are the deciding factor of errors which can be a random errors or systematic error

• Check the accuracy of the instrument to avoid instrumental errors.

• The environmental error arises because of exterior conditions like temperature, humidity, and magnetic field.

• The irresponsibility or sloppiness of the spectator causes the human error. So, the observation of the data may be affected.

Statistical Methods of Assessing Measurement Error

Systematic error and random error are the primary components of measurement. Both error elements should be evaluated for the clinician to describe the error with the conclusion regarding systematic achievements as an alternative to the statistical significance of any reliability indicators. Researchers should be careful in

• The result of a test-retrieval correlation should be collected for the new sample of persons involved in an experiment.

• Comparisons of test-retest compounds between different reliability studies.

How to reduce Errors in Measurement

• Check the formula which is used for measurement is correct.

• If the relative difference when calculated in percentage (%), is very large, it should be certainly rejected.

• Use the good condition instrument to reduce the error. So that an exact value will be calculated.

• Use various measurements for one instrument to avoid errors.

• Make sure observers and measurement takers are well educated.

Conclusion

In every measurement, there is uncertainty called an error. Measurement is the most important thing in scientific technologies. Without measurement, there is no science at all. So, in the measurement, the errors arise due to many reasons like systematic and random errors. These errors are divided into subdivisions. So, the explanation for error may be the ratio of the true value and measured value. True value means the average value of infinite measurement.

FAQs

1. How measurement is used in our daily life?

We can’t buy anything without measurement. For example, we buy slippers by the size of our feet. From slippers to gold, we use measurements to buy or sell things.

2.What does gross error signify?

It signifies that there is something wrong in the measurement system or using the wrong instrument to measure or measure the wrong thing.

3.How do solve the systematic errors?

Systematic errors are solved by following techniques

• Using multiple techniques to record the observations.

• Calibrating an instrument or comparing instruments so that, we can calculate the actual value with a known reading.

4. Give examples of random errors and systematic errors.

Random Error: An observer misreading a screw gauge measurement. So even a 0.1 mm value may result in an error.

Systematic Error: Weights are calculated higher than the actual value because of a mis calibrated instrument.

5.What is absolute reliability?

Repeated measurements will vary for every person. Absolute reliability is the degree to calculate this variation. Reliability is higher when the variation is less.