In this lecture, we are going to learn about Errors in Measurement, the Definition of Error, and different types of Errors like Gross Errors, Systematic Errors, and Random Errors. So let’s start with the definition of Error.

The aim of every experiment is to determine a physical quantity as accurately as possible. Every measurement, however, consists of some error that may occur due to the observer, the instrument used, or both. Errors may also creep in due to small changes in the condition of the experiment or due to various factors inherent in the experiment. The measured value of a quantity differs somewhat from its true value due to the presence of such errors.

**Definition of Error**

The difference of magnitude between the measured value and true value is called Error.

- In general, error means (absolute error) i.e.

- No plus, no minus
- Only magnitude.

Error is represented by,

E=A_m-A_t

where E is the error, A_{m }is the measured quantity, and A_{t }is the true value.

NOTE:Why do we do error analysis- The objective of error analysis is to find a suitable compensation methodology so that accuracy can be improved.

**Types of Errors in Measurement**

- The errors are broadly classified into two types:

**Static error**: an error that is independent of time is called a static error.**Dynamic Error**: error that depends on time is called a dynamic error.

**Relative Static Error**

- Static error taken over the true value is called relative static error.

Absolute\; error = |V_A-V_E|

Percentage\; error = \frac{|V_A-V_E|}{V_E} \times 100

Relative\; Error = \frac{Absolute \;error}{actual\; value}

**Guaranteed accuracy Error (GAE**)

- when accuracy is measured in terms of error, it is called guaranteed accuracy error. If this error is expressed with respect to full scale deflection, it is called “%GAE”.

- It is expressed by the manufacturer and it is constant for the meter.

- Error is represented by +-

- Deflection is represented without +-

- So, while choosing a meter error should be as minimum as possible and deflection should be as high as possible.

**Limiting error or Guaranteed error**

- It is the deviation of the measured value from the true value specified by the manufacturer himself. As the absolute value of error does not signify any valuable information and also it is constant irrespective of deflection, the relative limiting error decreases with an increase in deflection.

Relative\; Limiting \; Error \; \varepsilon _r = \frac{\delta A }{A_s }

- Relative Limiting Error is expressed in percentage and hence,

\%\; Relative\; Limiting \; Error \; \varepsilon _r = \frac{\delta A }{A_s } \times 100

**Types of Static Error**

**Gross Error**

- They are completely due to human mistakes i.e. loose connections, reading the values, taking the values, memorizing, and doing calculations.

- These errors are not common for all observers, hence called variable errors.

**Note:**the reading can be taken correctly from the meter when the meter is in a vertical position and eye contact should be over the pointer (i.e. 90 degrees to the meter).

**Systematic Error**

- Systematic errors are constant errors as these are common for all observers.

#### I**nstrumenta**l **Error**

- due to inherent shortcomings of the instrument, aging effect, frictional error, hysteresis error, also due to misuse of instruments such as choosing a wrong range of instruments, and due to loading effects also.

**Environmental** **Error**

- due to temperature, pressure, humidity, etc.

**Observational Error**

- due to improper observation methodology.

**Note:**to eliminate the shadow of a pointer a mirror strip is placed in between the scale and the pointer.

**Random Error or accidental Error**

- error due to unidentified sources. These errors come suddenly and eliminate suddenly but the reason is not known.

- To eliminate the random error statistical analysis is carried out i.e. multi-sample data in which the same input value is measured no. of times which are instrumented by one observer or many observers.

**Hysteresis Error**

- if a meter gives less than the actual value for ascending value and shows more than the actual value for descending values i.e. if a meter gives two different readings for the same input value is called a hysteresis error.

**Drift Error**

- It is an error that occurs due to the instability of components and it is constant throughout the range of the scale.
- Drift errors are
**caused by deviations in the performance of the measuring instrument**(measurement system) that occur after calibration. - These errors may be reduced by carrying out frequent calibrations as the ambient temperature changes or by maintaining a stable ambient temperature during the course of a measurement.

**Difference between Systematic Error vs Random Error**

- The main difference between systematic error and random error is that systematic errors are consistent and predictable, while random errors are unpredictable and vary in magnitude and direction.

- Systematic errors are caused by factors that consistently affect the measurement process in the same direction and magnitude. These factors can include the calibration of equipment, the measurement technique used, or the observer’s bias. These errors can be corrected by properly calibrating the equipment or by using a more accurate measurement technique.

- Random errors, on the other hand, are caused by unpredictable factors such as environmental conditions or variations in the measurement process. These errors cannot be corrected and can only be reduced by increasing the number of measurements taken and averaging the results.

- In general, it is important to minimize both systematic and random errors in order to obtain accurate and reliable results.