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ProfessionalEngineering# Direct observation error analisys

##### Calculates error of direct measurements for given measured value series and confidence interval.

- linear dimensions measurement by measurement instruments like ruler, calipers or micrometer,
- time intervals measurement by the stopwatch
- voltage or amperage measurement by the special electrical measuring instruments

Any measurement can be performed with a certain accuracy. Wherein measured value differs from true value, because measurement instruments, human senses and methodologies are imprefect. Therefore,

Measurement errors can be divided in two major categories: systematic error and random error.

Random factors, which affect measurement accuracy, affect the

The calculator below evaluates random error of direct measurement set for a given confidence interval. Some amount of theory follows the calculator.

In most cases measurement result distribution is subject to normal distribution law. Therefore true value equals to the limit:

In case of limited number of measurements, mean value is the nearest to true:

According to the Gauss error theory,

, standard deviation square is called the

To estimate

According to error addition law, mean error is less than error of particular measurement. Standard deviation of mean equals to:

Absolute random error Δх equals to:

, where - Student t-value for the given confidence probability and degrees of freedom k = n-1.

Student t-value can be obtained by a table or by using our Student t-distribution quantile function calculator. You should be aware, that quantile function calculator gives one sided Student t-value. Two-sided t-value for a given confidence probability equals to one-sided t-value for the same degrees of freedom and confidence probability equals to:

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