Metric Definitions

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Precision, Accuracy

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and Error Notes

Metric Basic Definitions

Length: Length is the distance between two points. Measured in meters etc.

Volume: Volume is defined as the amount of space an object takes up. It is usually measured in liters or meters3

Mass: Mass is a measurement of the amount of "stuff" an object possesses. "Stuff" equates to atoms and molecules. It is measured in grams.

Weight: Weight is defined as the pull of gravity upon an object's mass. Weight itself is not a metric measurement, however a similar unit of force in metrics is the Newton (measured in m/sec2).

Temperature: Temperature is a measure of how much thermal (heat energy) a substance possesses. Stated from the atomic perspective, temperature is a measure of the speed of the molecules/atoms a substances possesses. Measured in degrees C, or degrees K.

Density: The amount of atoms and molecules in a certain sized container ( 1cm3 or 1ml). Density is a derived quantity. That means that it is derived from a relationship between other quantities. Thus:

Density = Mass/Volume (measured in g/cm3 or g/ml)

 

True & Measured Value, Error, Precision, & Accuracy

What you measure isn't alway a true measure of what something really is. That's because there many ways for errors to creep into measurements. The old adage, "Measure twice, cut once" (and record both!) is a good guide when working with scientific instruments.

True Value:

The actual value of an object, it can rarely be measured accurately due to limitations of eyesight and instruments

Measured Value:

The value you measure an object to be. For example, the true value maybe 1.234562985746354085746353434675689 mm. However the meter stick you are using can only measure the object to be 1.2 mm.

Error:

What is error - The difference between the True Value and the Measured Value .

Error is defined to be a mistake in perception, measurement or process. Statistically speaking, Error is the difference between the True value and the Measured Value in an experiment.

If there is one thing that haunts a researcher or and engineer, its error. There are so many forms of error that students need to learn to recognize and avoid sources of error early on in school. Error is usually caused by uncontrolled variables and can cause havoc in experiments. So lets get serious and learn what error is, where error can creep into experiments, and how to avoid error.

Practically speaking, there are other types of error besides those with numbers... in science, most errors end up ruining a scientist's data, or numbers, which are essential for their work.

Precision:

A close agreement between repeated measurements

(Show using overhead by plotting values of one set of measurements) For example, a Triple Beam Balance is a precision instrument. The Triple Beam Balance will give close to the same measurement of a sample over and over. (However, if it is not calibrated it can give the same INCORRECT readings over and over!)

Accuracy: The absence of error. Close agreement between the true value and measured value

Types of Error

Six factors that commonly cause error in investigations.

a. Experimental Design error:

Error written into the actual design of the experiment. For example: The procedure overlooks a key element, fails to control variables, skips steps, doesn't list necessary materials, or isn't

b. Operator Error.

Errors made by the people actually performing the experiment, which are numerous!

c. Observation Error:

Mistakes by the observer. Observers are human and people make mistakes by reading scales incorrectly, seeing things that don't actually happen the way one thinks is so, etc !

d. Recording Error:

Recording incorrect data. Human recorders and recording devices can make mistakes when recording data.

Some of these mistakes are hard to find, especially when a researcher is using tools to record data. At first, the last thing a new researcher will look for when hunting down the source of an error is their equipment. Later, its one of the first!

e. Calculation Error

An error in performing calculations for an experiment. Most everyone who has used a calculator, or added a long string of data is familiar with this source of error! (ex 2.4 + 2.4 = 5.3!) Gosh, I've seen people saying some mighty mean things to their computer with the Excel spreadsheet isn't coming up with reasonable calculations.

f. Measuring tool limitation.

Using a tool that is not equal to the measurements you are taking. This occurs when the scale, size or design of a tool is lacking. This means the researcher is not using the correct tool for the job.

As a result, a tool may not measure to the degree of accuracy needed, the measurements may not be as precise as needed, or perhaps the tool has a faulty design and doesn't stay in calibration

Examples of Errors

1. Design Error (Experimental / Procedure).... some examples....

no controls

not enough trials to ensure reliability (Repeat 3x)

more than one manipulated variable

improper procedure

failure to control or account for uncontrolled variables

2. Operator Error

not following procedure,

measuring incorrectly,

incorrect materials,

improper selection of measuring devices.... etc

3. Observer

misreading scale

not understanding scale

not accounting for error in device

parallax (explain),

4. Measuring Tool Limitations

design (hard to read etc)

scale (only to a couple places. ie 2.3cm vis 2.35cm

type of device

size of device

5. Recording

not writing to proper place

reversing numbers

incorrect units

6. Calculation

Bad Math...incorrect calculations

Improper formula or programming spreadsheet

 

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