Name: how measurement errors affect results
Uploaded: 2023-04-30T12:12:04.000Z
Duration: 1 min 20 s
Channel: JoVE

K12 Standards

Florida Department of Education

High School

Nature of Science

SC.912.N.1

SC.912.N.1.4

Random and Systematic Errors

測定プロセスにおけるエラーは一般的な問題です。このようなエラーは、ランダムとシステマティックの2つのカテゴリに分類されます。
ランダムエラーは、測定プロセスの不一致または測定される量の変動の結果です。これらにより、真の値付近で変動が高すぎたり低すぎたりします。
科学者がノギスを使ってミミズの長さを測定することを考えてみましょう。科学者がスケールを正しく読み取るための一貫性がない場合、または測定中にミミズが連続的に体を動かしていると、長さの測定値が正しくなくなる可能性があります。
ランダムエラーは避けられませんが、試行を繰り返すことで平均化できます。
系統誤差は、持続的な問題の結果であり、測定に一貫した不一致をもたらします。これらの誤差は、真の値と比較して、すべて高すぎるか、または低すぎる傾向があります。たとえば、不適切に校正された天びんを使用して重量が測定されている。
これらは予測可能で、ほとんどが楽器に関連しています。ただし、ランダム誤差とは異なり、繰り返し測定して平均化することはできません。

ランダムエラーと系統的エラー

科学者は常に、最高の精度と精度で測定値を記録するために最善を尽くしています。 ただし、エラーが発生する場合もあります。 これらのエラーはランダムまたは系統的に発生する可能性があります。 測定プロセスの不一致や変動、または測定される量自体の変動により、ランダムな誤差が観察されます。 このような誤差は、測定を繰り返すと真の値より大きくなったり小さくなったりして変動します。 科学者が定規を使ってミミズの長さを測定しているとします。 この測定プロセスにおけるランダムな誤差は、科学者がスケールを読み取る方法が一貫していなかったり、ミミズが動いていたりした結果である可能性があります。 ランダムエラーは避けられません。 ただし、試行を繰り返すことで平均化できます。

系統的誤差は継続的な問題から発生し、測定値に一貫した不一致が生じます。 これらの誤差は、常に真の値より大きいか小さい傾向があります。 これらは予測可能であり、本質的に役立つことがほとんどです。 たとえば、不適切に校正された秤量天びんは、常に真の値よりも重い物体の重量を計量する可能性があります。 ランダム誤差とは異なり、系統誤差は繰り返しの測定で平均化することはできません。

このテキストは <a href="https://openstax.org/books/chemistry-2e/pages/1-5-measurement-uncertainty-accuracy-and-precision"> から編集されたものです。 Openstax, Chemistry 2e, Section 1.5: Measurement Uncertainty, Accuracy, and Precision.</a>

科学者は常に、最高の精度と精度で測定値を記録するために最善を尽くしています。ただし、エラーが発生する場合があります。これらのエラーは...

Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

Units, Dimensions, and Measurements

単位、次元、および測定

KEY TERMS AND CONCEPTS

主要用語と概念

how measurement errors affect results

Measurement errors can change how accurate and precise a result appears. Scientists try to record measurements as carefully as possible, but errors can still happen. These errors are usually random or systematic.

Random errors come from inconsistency or fluctuation in the measuring process. They can also come from changes in the quantity being measured. In repeated measurements, random error may make a value appear greater than the true value one time and less than it the next.

A simple example is measuring the length of an earthworm with a ruler. The error could come from reading the scale differently each time. It could also happen if the earthworm moves during the measurement. Random error cannot be avoided, but repeated trials can help average it out.

Systematic errors come from a persistent problem that causes a steady measurement shift. They usually make results consistently greater than the true value or consistently less than it. These errors are predictable and are often instrumental in nature.

An improperly calibrated weighing balance is one example of systematic error. It may keep weighing objects heavier than they really are. Unlike random error, systematic error cannot be averaged out by repeating the measurement.

How Measurement Errors Affect Results

the scope of physics

How Physics Shapes Science and Technology

Physics studies the interactions of energy, matter, space, and time. It looks for the basic mechanisms that explain natural phenomena. The word physics comes from the Greek word physis, which means nature. Physics helps us understand the natural world at its most fundamental level. It relies on quantitative laws, or rules written in numbers and measurements, to describe how things behave. That approach can also help other fields improve the limits of current technology. Physics matters in...

orders of magnitude

Estimating Scale with Powers of 10

Orders of magnitude help estimate the scale of a number using powers of 10. It is a simple way to round values to the nearest power of 10. This makes it easier to compare very large and very small numbers. To find the order of magnitude of a number, take its base-10 logarithm and round to the nearest integer. The result gives the power of 10 that most closely matches the original value. This method gives a consistent estimate of size without using exact digits. Orders of magnitude are useful...

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models, theories, and laws

Scientific Models, Theories, and Laws

Scientific models, theories, and laws help physicists describe natural phenomena. A model is a simplified version of a physical system that is too complex to study in full. It acts as a rough mental or visual picture of what may be happening. Good models keep the important parts and simplify the rest so the problem becomes workable. The light wave model is one example. Light waves are usually invisible, so they cannot be seen in the same way as water waves. Even so, it is useful to think of...

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units and standards of measurement

SI Units for Physical Quantities

SI units give a standard way to measure physical quantities. A physical quantity can be defined by how it is measured or by how it is calculated from other measurements. For example, the mass and dimensions of a metallic cube can be found with a weighing machine and a meter scale. Some quantities are built from others. The volume of a cube is the cube of its side length. The density of the cube is then found by dividing mass by volume. Measurements are written in units, which are standardized...

estimation of the physical quantities

Fermi Estimation for Physical Quantities

Fermi estimation helps physicists, scientists, and engineers make rough calculations for physical quantities. These estimates are also called guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. Enrico Fermi was known for making these kinds of estimates with surprising precision. Estimation is not random guessing. It uses prior experience and sound physical reasoning to get a rough value for a quantity. This kind of reasoning helps build...

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base quantities and derived quantities

SI Base Units Behind Measured Quantities

SI base units are the starting point for measuring physical quantities. In any system of units, some quantities must be defined through direct measurement. These are called base quantities, and their units are base units. Other physical quantities are built from these base values by algebraic combinations. These are called derived quantities, and their units are derived units. For example, area comes from two lengths multiplied together. It is a derived quantity and is written in SI base units...

conversion of units

Unit Conversion Steps and Real-World Errors

Unit conversion lets you change a measurement from one unit to another. It is useful in everyday life, such as when a cookbook gives amounts in liters or ounces and you need cups instead. It also helps when directions use feet or meters, but you want to know the distance in miles. The first step is to list the given unit and the unit you need. The second step is to choose a conversion factor, which is a ratio that shows how many of one unit equal another unit. For example, 1,000 meters equal 1...

accuracy and precision

Repeated Measurements in Science

Repeated measurements help scientists check the quality of their results. They are used to judge both precision and accuracy. These two ideas are related, but they do not mean the same thing. Measurements are precise when repeated trials give very similar results. Precision shows how closely the values agree with one another. Measurements are accurate when the result is very close to the true value or the accepted value. Accuracy shows how closely the values agree with the real target. High...

random and systematic errors

Measurement errors can change how accurate and precise a result appears. Scientists try to record measurements as carefully as possible, but errors can still happen. These errors are usually random or systematic. Random errors come from inconsistency or fluctuation in the measuring process. They can also come from changes in the quantity being measured. In repeated measurements, random error may make a value appear greater than the true value one time and less than it the next. A simple...

rules for significant figures

Measurement Precision and Significant Figures

Measurement precision depends on the tool used, and significant figures show that precision. A ruler can measure length to the closest millimeter. A caliper can measure length to the nearest 0.01 mm, so it gives a more precise measurement because it can detect very small changes in length. When a value is written from a measurement, the last digit is not exact. The person making the measurement must estimate that digit. For example, a stick that seems to fall between 13.2 cm and 13.3 cm must...

significant figures in calculations

Rounding Rules for Significant Figures

Rounding rules for significant figures help show the right level of certainty in measured results. When a calculation is reported with the correct number of significant figures, it better matches the uncertainty in the measurements. The rounding rule depends on the type of math being done. For addition and subtraction, the result should have the same number of decimal places as the number with the fewest decimal places. For multiplication and division, the result should have the same number of...

dimensional analysis

Dimensional Checks in Physics Equations

Dimensional consistency is a key check in physics equations. It means the dimensions on both sides of an equation must match. The idea helps show whether an equation can represent a real physical law. The first rule is simple: expressions on each side of the equal sign must have the same dimensions. That makes sense because you can only add or subtract quantities of the same type. The second rule says that the input to a standard mathematical function, such as a trigonometric function, a...

problem solving: dimensional analysis

Dimensional Checks for Physics Equations

Dimensional analysis helps check whether physics equations make sense. It compares the dimensions on each side of an equation and shows whether the units are consistent. This method is useful for spotting algebra errors, typos, and for remembering physical laws. A valid equation must follow two rules. First, both sides of an equality must have the same dimension, so only quantities with matching dimensions can be added or subtracted. Second, common math functions such as exponential,...

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solving problems in physics

Physics Problem Solving: Strategy to Check

Physics problem solving uses general physical principles to work out specific situations. It is a key skill in physics, and it can also help with everyday life. The same analytical skills can be used in new situations, while a list of facts can never cover every possible case. Solving physics problems also takes creativity and insight. These skills grow with experience and practice. There is no simple step-by-step method that works for every problem, but a three-stage process can guide the...

key terms and concepts

Learn how random and systematic errors affect scientific measurements, with clear examples like a moving earthworm and an uncalibrated balance.

How Measurement Errors Affect Results | JoVE K12

physics

JoVE Core 物理学は、運動学、力学、流体力学、静力学、波動、音響などの基礎的な物理学の理論と応用を、簡潔でわかりやすいアニメーション ビデオで紹介します。さらに、科学者の実際のビデオでは、世界中の今日の研究所で行われている古典的および独自の研究実験における関連概念の適用を示しています。

The Scientific Method

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Psychology as a Science

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Define a problem based on a specific  body of knowledge, for example: biology, chemistry, physics, and earth/space science, and do the following:  
Pose questions about the natural world, (Articulate the purpose of the investigation and identify the relevant scientific concepts). 
Conduct systematic observations, (Write procedures that are clear and replicable. Identify observables and examine relationships between test (independent) variable and outcome (dependent) variable. Employ appropriate methods for accurate and consistent observations; conduct and record measurements at appropriate levels of precision. Follow safety guidelines). 
Examine books and other sources of information to see what is already known, 
Review what is known in light of empirical evidence, (Examine whether available empirical evidence can be interpreted in terms of existing knowledge and models, and if not, modify or develop new models). 
Plan investigations, (Design and evaluate a scientific investigation). 
Use tools to gather, analyze, and interpret data (this includes the use of measurement in metric and other systems, and also the generation and interpretation of graphical representations of data, including data tables and graphs), (Collect data or evidence in an organized way. Properly use instruments, equipment, and materials (e.g., scales, probeware, meter sticks, microscopes, computers) including set-up, calibration, technique, maintenance, and storage). 
Pose answers, explanations, or descriptions of events, 
Generate explanations that explicate or describe natural phenomena (inferences), 
Use appropriate evidence and reasoning to justify these explanations to others, 
Communicate results of scientific investigations, and 
Evaluate the merits of the explanations produced by others.

SC.912.N.1.1

Describe and explain what characterizes science and its methods.

SC.912.N.1.2

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Correlation and Causation

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Recognize that the strength or usefulness of a scientific claim is evaluated through scientific argumentation, which depends on  critical and logical thinking, and the active consideration of alternative scientific explanations to explain the data presented.

SC.912.N.1.3

Scientific Laws and Theories

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Identify sources of information and assess their reliability according to the strict standards of scientific investigation.

Describe and provide examples of how similar investigations conducted in many parts of the world result in the same outcome.

SC.912.N.1.5.

Describe how scientific inferences are drawn from scientific observations and provide examples from the content being studied.

SC.912.N.1.6

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SC.912.N.1.7

How Measurement Errors Affect Results

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