Measurement Errors

JEE Crash Course 2022

Measurement Errors Introduction

Measurement errors also called observational errors are defined as the difference between the actual response acquired and the measured response value. The actual response value is the average of the infinite number of measurements in this case while the measured response value is the accurate value.

Classification of Measurement Errors

The Measurement errors can be classified into three different kinds -

  1. Random errors

  2. Systematic errors

  1. Environmental

  2. Instrumental

  3. Observational

  1. Gross errors

Random Errors: When repeated measurements of value are taken, the inconsistencies in the values account for the so-called Random Errors. They are always present within the instrument. They occur with the fluctuations in the values after each measurement. 

Systematic Errors: These are not determined by chances but occur due to inaccuracies that are inherent in the system. They are sometimes referred to as Statistical bias. In general, they are constant and are predictable w.r.t. to the true value.

Due to the inappropriate calibration of the instruments or imperfect methods of observation, or due to the interference of the environment with the measurement process the systematic error occurred. Imperfect zeroing of the instrument under study is an example of these errors.

Systematic measurement errors are also classified as  sampling errors and non-sampling errors,  

Sampling Errors: Non-representative samples fall under this category.

Non-Sampling Errors: It includes:

  1. Paradigm Error: A scientific method to study the measurable phenomenon.

  2. Researcher Bias: A researcher is keen to confirm the particular theory which has been devised by him that can influence the decisions.

  3. Participant Bias: By Social desirability, supporting or opposing a particular opinion, etc participants are influenced.

  4. Reliability and validity of measurement tools.

Gross Error: The gross error arises mainly due to human mistakes or it can also be said to be physical errors. This results in gross error and incorrect data is recorded. By being careful and making sure that the reading that is taken is correct it can be avoided.

Type A and Type B Evaluation of Uncertainty

The knowledge of an input quantity is taken into the Type A measurement only after considering repeated measured values. For measurement in input or other words of repeated values, we consider the Gaussian distribution.

On the other hand, the scientific judgment or other information concerning the possible values of the quantity has been taken into account by the type B measurement. It can be termed as a Type B evaluation of Uncertainty. Here, we use the concept of a rectangular probability distribution with limits.

Statistical Methods of Assessing Measurement Error

To assess the measurement error, which includes there are certain methods that are adopted:

  • Standard Error of Measurement (SEM): About the deviations or true values of how an instrument when used for multiple times produces the desired output is being known with this.

  • Coefficient of Variation (CV): How the values vary on repeated measurements is being defined by it. The results are closer to the true value if the CV is low in value.

  • Limits of Agreement (LOA): Where a proportion of the differences lie between the measurements, it gives the estimate of the interval.

Ways To Minimize Errors

  1. Use instruments of higher precision.

  2. Improve the experimental techniques.

  3. Adjust the zero of the instruments properly.

  4. The value of the reading by standing straight to the instrument has been taken and not from the sides to avoid Parallax errors.

  5. Take its algebraic mean for a closer result by repeating the experiment several times.

  6. Take care of the environment if possible.

  7. In order to avoid gross errors carefully take the measurements.

Other Types of Errors

There are various types of errors that can happen in our common day to day life. Some of these are:

  1. Absolute Error: The amount of error in the measurement has been definite by absolute error.

  2. Greatest Possible Error: This error has been definite as the error which is to be one half of a measuring unit.

  3. Instrument Error: The error associated with the instrument is known as instrument error. The inaccuracy of the instrument is being told with this.

  4. Operator Error: An operating error is being caused by the operator. E.g. in an experiment to be conducted in the lab, a man notes the voltmeter to read 5 volts, where it was 4 V. Thus, such types of errors are commonly referred to as operator error. They are also called personal errors.

Measurement Location Error: Measurement location errors have been caused by the instrument that is kept at a location in which it was not bound to be kept. For example, take the case of a thermometer, which is told to be kept away from the sun. Such cumulative errors are broadly classified under this category.

Parallax Error: Due to taking the wrong sides of measurement, parallax error occurred. By standing straight in front of the instrument and not from its sides, always take readings.

External Error: External Errors are caused due to external factors like wind, environment, etc. contribute to External errors. 

Percentage Error: The error that is defined as the ratio of the difference of the actual value and the measured value to the actual value is called a Percentage error.

Fun Facts

  1. Two components of measurement which are number and unit can be reduced. 

  2. The unit depends on what is being measured is the mass, length or some other property. 

  3. The process of measuring something involves, giving a number to some property of the object.

FAQs (Frequently Asked Questions)

1. How can measurement errors be reduced, random or systematic?

Firstly, the pilot tests your instruments, getting feedback from your respondents regarding how easy or hard the measure was, and information about how the testing environment affected their performance. Secondly, if you are gathering measures using people to collect the data (as interviewers or observers) you should make sure you train them thoroughly so that they aren’t inadvertently introducing errors. Thirdly, when you collect the data for your study you should double-check the data thoroughly. If you enter the data twice, the second time having your data entry machine check that you are typing the same data that you did the first time. Fourth, you can use statistical procedures in order to adjust the measurement error. You can just apply directly to your data to very complex modelling procedures for modelling the error and its effects. Finally, the best thing to deal with measurement errors, especially systematic errors, is to use multiple measures of the same construct.

2. How can the accuracy of measurement be improved?

The main way to improve the accuracy of a measurement is to control the other variables as much as possible. Accuracy refers to the measure of the closeness of the values to the true value. Precision refers to the measure of how closely the successive measurements agree with each other. It would not be sensible to use a measuring device capable of four decimal places if the successive measurements do not agree to one decimal point.