Measurement in science Notes

Why Measurement Matters In Science

1. Science is based on evidence, and much of this evidence comes from measurements.
2. Measurements allow scientists to describe natural phenomena using numbers rather than opinions.
3. Accurate and reliable measurements make it possible to:
   1. Compare results from different experiments
   2. Identify patterns and relationships
   3. Test hypotheses and scientific models
4. If measurements are poor or inconsistent, conclusions drawn from them may be unreliable.

Physical Quantity

1. A physical quantity is something that can be measured and expressed using a number and a unit.
2. Physical quantities describe measurable properties of objects or events.
3. Common physical quantities used in Physics include:
   1. Length
   2. Mass
   3. Time
   4. Temperature
   5. Force

Units and the SI System

1. To ensure consistency and clear communication, scientists use a standard system of units.
2. This system is called the International System of Units (SI).
3. Using SI units allows scientists around the world to compare measurements reliably.

SI Prefixes and Scale

1. In physics, quantities can be very large or very small.
2. Writing long numbers can be confusing, so SI prefixes are used.
3. SI prefixes represent powers of ten and make numbers easier to read and compare.

Measuring Instruments and Resolution

1. All measuring instruments have a limited resolution.
2. Resolution is the smallest change in a quantity that an instrument can detect.
3. Choosing an instrument with suitable resolution is essential for reliable data.

Experiments Connect Ideas To Reality Through Variables

1. Scientific investigations aim to find relationships between variables.
2. To ensure a fair test, scientists carefully identify and manage variables.

1. Independent Variable

1. The independent variable is the variable that the experimenter deliberately changes.
2. Only one independent variable should be changed at a time.
3. Changing the independent variable allows scientists to observe its effect.

2. Dependent Variable

1. The dependent variable is the variable that is measured or observed.
2. It changes in response to the independent variable.
3. The dependent variable provides the data used for analysis.

3. Controlled Variables

1. Controlled variables are factors that must be kept constant during an investigation.
2. Keeping these variables constant ensures that any change in the dependent variable is due only to the independent variable.
3. Failure to control variables reduces the validity of results.

Precision, Accuracy, And Uncertainty Decide How Strong the Evidence Is

1. Measurements are never perfect.
2. To decide whether data supports a hypothesis, you must judge the quality of the measurements.

Accuracy

1. Accuracy describes how close a measured value is to the true or accepted value.
2. A measurement can be inaccurate even if it is carefully taken.
3. Accuracy is affected by:
   1. Calibration of instruments
   2. Systematic errors

Precision

1. Precision describes how close repeated measurements are to each other.
2. Highly precise measurements show little variation.
3. Precision depends on:
   1. Instrument resolution
   2. Consistent measurement technique
4. A set of measurements can be precise but inaccurate.

Reliability

1. Reliability describes whether measurements can be repeated and give similar results.
2. Reliable data increases confidence in conclusions.
3. Reliability is improved by:
   1. Repeating measurements
   2. Using consistent methods
   3. Controlling variables

Uncertainty

1. No measurement is perfectly exact.
2. Uncertainty describes the range within which the true value is expected to lie.
3. Uncertainty arises because:
   1. Measuring instruments have limited resolution
   2. Human judgment is involved in reading scales
4. The uncertainty of a measurement is often related to the resolution of the instrument.

Random Errors

1. Random errors cause measurements to vary unpredictably.
2. They occur due to small, uncontrollable factors.
3. Random errors affect precision but not accuracy.
4. They can be reduced by repeating measurements and calculating an average.

Systematic Errors

1. Systematic errors cause measurements to be consistently too high or too low.
2. They are often caused by faulty calibration or zero error.
3. Systematic errors affect accuracy and cannot be removed by repetition alone.

Graphs Turn Tables Into Relationships You Can See

A table of numbers is important, but a graph is often the fastest way to spot a trend, pattern, or relationship.

Choosing Scales And The Origin Changes What You Notice

1. A graph does not have to start at zero, but the choice of scale affects the visual message.
2. In the ball-bearing ramp example, plotting time on a $y$-axis that starts close to $1\ \text{s}$ makes small differences easy to see.
3. Plotting from $0\ \text{s}$ makes the graph mostly empty, which can hide subtle trends.
4. However, communicators can also choose scales to exaggerate or downplay differences.

Scatter Plots And Lines Of Best Fit

1. When data points show a pattern, you may draw a line of best fit (or curve) to represent the overall relationship.
   1. A straight-line trend suggests a linear relationship.
   2. A curved trend may indicate an inverse, quadratic, or exponential relationship.
2. At this level, the main idea is that the line represents the "signal" (the relationship), while the scatter around it reflects uncertainty and uncontrolled variables.

Unexpected Measurements Can Challenge Theories

1. Measurements can also reveal something current theories cannot explain, and this is where science can change direction.
2. A famous example is the precession (gradual rotation) of Mercury's orbit.
3. Very precise measurements showed Mercury's orbit rotated slightly faster than Newtonian physics predicted.
4. The difference was small, but too large to be explained by experimental uncertainty.
5. Later, Einstein's general relativity accounted for the extra rotation, and Mercury's orbit became an early test of the new theory.

Publishing And Peer Review Make Measurement Trustworthy

1. Scientific knowledge grows when researchers share methods and results so others can check them.
2. Peer review helps to catch errors, judge whether conclusions follow from evidence, and identify work that is not original.
3. After publication, results still need replication (independent repetition) to become widely trusted.

Scientific Evidence And Other Ways Of Knowing

1. Science is not the only way humans build knowledge.
2. For example, religion may involve faith, which does not usually produce testable hypotheses. Science requires claims to be testable against measurement.
3. This difference helps explain why different communities can be persuaded by different forms of evidence.