Data Science Board Exams |
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A measurement system can be accurate but not precise, precise but not accurate,
neither, or both. For example, if an experiment contains a systematic error, then
increasing the sample size generally increases precision but does not improve
accuracy. The result would be a consistent yet inaccurate string of results from
the flawed experiment. Eliminating the systematic error improves accuracy but
does not change precision.
A measurement system is considered valid if it is both accurate and precise.
Related terms include bias (non-random or directed effects caused by a factor or
factors unrelated to the independent variable) and error (random variability).
The terminology is also applied to indirect measurements—that is, values
obtained by a computational procedure from observed data.
In addition to accuracy and precision, measurements may also have a
measurement resolution, which is the smallest change in the underlying physical
quantity that p
Accuracy vs. Measurement - ✔ ✔ In industrial instrumentation, accuracy is the
measurement tolerance, or transmission of the instrument and defines the limits
,of the errors made when the instrument is used in normal
operating conditions.[4]
Ideally a measurement device is both accurate and precise, with measurements
all close to and tightly clustered around the true value. The accuracy and precision
of a measurement process is usually established by repeatedly measuring some
traceable reference standard. Such standards are defined in the International
System of Units (abbreviated SI from French: Système international d'unités) and
maintained by national standards organizations such as the National Institute of
Standards and Technology in the United States.
This also applies when measurements are repeated and averaged. In that case,
the term standard error is properly applied: the precision of the average is equal
to the known standard deviation of the process divided by the square root of the
number of measurements averaged. Further, the central limit theorem shows
that the probability distribution of the averaged measurements will be closer to
a normal distribution than that of individual measurements.
With regard to accuracy we can distinguish:
the difference between the mean of the measurements and the reference
value, the bias. Establishing and correcting for bias is necessary for calibration.
the combined effect of that and precision.
A common convention in science and engineering is to express accuracy
and/or precision implicitly by means of significant figures. Here, when not
explicitly stated, the margin of error is understood to be one-half the value of
the last significant place.
, Quantification - ✔ ✔ In mathematics and empirical science, quantification
(or quantitation) is the act of counting and measuring that maps human
sense observations and experiences into members of some set of numbers.
Quantification in this sense is fundamental to the scientific method.
Scientific Method - ✔ ✔ The scientific method is a body of techniques for
investigating phenomena, acquiring new knowledge, or correcting and integrating
previous knowledge.[2] To be termed scientific, a method of inquiry is commonly
based on empirical or measurable evidence subject to specific principles of
reasoning.[3] The Oxford Dictionaries Online define the scientific method as "a
method or procedure that has characterized natural science since the 17th
century, consisting in systematic observation, measurement, and experiment, and
the formulation, testing, and modification of hypotheses".[4]
The scientific method is an ongoing process, which usually begins with
observations about the natural world. Human beings are naturally inquisitive, so
they often come up with questions about things they see or hear and often
develop ideas (hypotheses) about why things are the way they are. The best
hypotheses lead to predictions that can be tested in various ways, including
making further observations about nature. In general, the strongest tests of
hypotheses come from carefully controlled and replicated experiments that
gather empirical data. Depending on how well the tests match the predictions,
the original hypothesis may require refinement, alteration, expansion or even
rejection. If a particular hypothesis becomes very well supported a general
theory may be developed.[1]
Although procedures vary from one field of inquiry to another, identifiable features
are frequently shared in common between them. The overall process of the
scientific method involves making conjectures (hypotheses), deriving predictions
from them as logical consequences, and then carrying out experiments based on
those predictions.[5][6] A hypothesis is a conjecture, based
Questions with 100% Verified
Answers
A measurement system can be accurate but not precise, precise but not accurate,
neither, or both. For example, if an experiment contains a systematic error, then
increasing the sample size generally increases precision but does not improve
accuracy. The result would be a consistent yet inaccurate string of results from
the flawed experiment. Eliminating the systematic error improves accuracy but
does not change precision.
A measurement system is considered valid if it is both accurate and precise.
Related terms include bias (non-random or directed effects caused by a factor or
factors unrelated to the independent variable) and error (random variability).
The terminology is also applied to indirect measurements—that is, values
obtained by a computational procedure from observed data.
In addition to accuracy and precision, measurements may also have a
measurement resolution, which is the smallest change in the underlying physical
quantity that p
Accuracy vs. Measurement - ✔ ✔ In industrial instrumentation, accuracy is the
measurement tolerance, or transmission of the instrument and defines the limits
,of the errors made when the instrument is used in normal
operating conditions.[4]
Ideally a measurement device is both accurate and precise, with measurements
all close to and tightly clustered around the true value. The accuracy and precision
of a measurement process is usually established by repeatedly measuring some
traceable reference standard. Such standards are defined in the International
System of Units (abbreviated SI from French: Système international d'unités) and
maintained by national standards organizations such as the National Institute of
Standards and Technology in the United States.
This also applies when measurements are repeated and averaged. In that case,
the term standard error is properly applied: the precision of the average is equal
to the known standard deviation of the process divided by the square root of the
number of measurements averaged. Further, the central limit theorem shows
that the probability distribution of the averaged measurements will be closer to
a normal distribution than that of individual measurements.
With regard to accuracy we can distinguish:
the difference between the mean of the measurements and the reference
value, the bias. Establishing and correcting for bias is necessary for calibration.
the combined effect of that and precision.
A common convention in science and engineering is to express accuracy
and/or precision implicitly by means of significant figures. Here, when not
explicitly stated, the margin of error is understood to be one-half the value of
the last significant place.
, Quantification - ✔ ✔ In mathematics and empirical science, quantification
(or quantitation) is the act of counting and measuring that maps human
sense observations and experiences into members of some set of numbers.
Quantification in this sense is fundamental to the scientific method.
Scientific Method - ✔ ✔ The scientific method is a body of techniques for
investigating phenomena, acquiring new knowledge, or correcting and integrating
previous knowledge.[2] To be termed scientific, a method of inquiry is commonly
based on empirical or measurable evidence subject to specific principles of
reasoning.[3] The Oxford Dictionaries Online define the scientific method as "a
method or procedure that has characterized natural science since the 17th
century, consisting in systematic observation, measurement, and experiment, and
the formulation, testing, and modification of hypotheses".[4]
The scientific method is an ongoing process, which usually begins with
observations about the natural world. Human beings are naturally inquisitive, so
they often come up with questions about things they see or hear and often
develop ideas (hypotheses) about why things are the way they are. The best
hypotheses lead to predictions that can be tested in various ways, including
making further observations about nature. In general, the strongest tests of
hypotheses come from carefully controlled and replicated experiments that
gather empirical data. Depending on how well the tests match the predictions,
the original hypothesis may require refinement, alteration, expansion or even
rejection. If a particular hypothesis becomes very well supported a general
theory may be developed.[1]
Although procedures vary from one field of inquiry to another, identifiable features
are frequently shared in common between them. The overall process of the
scientific method involves making conjectures (hypotheses), deriving predictions
from them as logical consequences, and then carrying out experiments based on
those predictions.[5][6] A hypothesis is a conjecture, based
