Accuracy & Precision

Distinguish exact and uncertain numbers

Quantities derived from counting or by definition are examples of exact numbers.

There are exactly _____ gumballs in this jar due to ability to obtain an exact count.
There are exactly 100 cm in one meter due to the definition of a centimeter.

Quantities derived from measurements other than counting are uncertain to varying extents due to limitations of the measurement process (devices) used.

each gumball is approximately 2.25 grams but they are not all the same. The size and shape vary as well.

Define accuracy and precision

When we measure things, most people are only worried about how accurate, or how close to the actual value, they are. Looking at the process of measurement more carefully, you will see that there is another important consideration: precision.

Define accuracy and describe how accuracy can be improved. Give an example.

Accuracy refers to the closeness of a measurement or result to the true or accepted value. It is a measure of how well an experimental or calculated value reflects the actual value.

Calibration: Regularly calibrating instruments and equipment helps ensure they provide accurate readings.
Training: Properly training personnel involved in measurements can minimize human errors.

Example:

If you have a laboratory balance used to measure the mass of substances, regular calibration with known masses can improve accuracy. Additionally, using the balance in a controlled environment, following the correct weighing procedures, and ensuring the balance is free from any interferences can contribute to higher accuracy in mass measurements.

Define precision and describe how precision can be improved. Give an example.

Precision refers to the degree of reproducibility or consistency in a set of measurements. It indicates how close multiple measurements are to each other, regardless of their accuracy.

Use of Precision Instruments: Utilizing instruments with more finely incremented scales can improve the precision of measurements.
Standardization: Ensuring that all measurements are taken under the same conditions and using the same equipment helps enhance precision.

Example:

In a laboratory setting, if you are measuring the length of a metal rod with a ruler, using a ruler with smaller increments (e.g., millimeters instead of centimeters) can improve precision. Taking multiple measurements of the same length and calculating the average helps reduce the impact of any individual measurement error, contributing to higher precision.

Accuracy in Measurements

Accuracy refers to the closeness of a measured value to a standard or known value.

For example, if in lab you obtain a weight measurement of 3.2 kg for a given substance, but the actual or known weight is 10 kg, then your measurement is not accurate. In this case, your measurement is not close to the known value.
Accuracy improves with properly calibrated measurement tools.

Precision in Measurements

How consistently you can get a particular result. Precision improves with more finely incremented tools that require less estimation.

Precision refers to the closeness of two or more measurements to each other.

Using the example above, if you weigh a given substance five times, and get 3.2 kg each time, then your measurement is very precise.
Precision is independent of accuracy. You can be very precise but inaccurate, as described above. You can also be accurate but imprecise.

A good analogy for understanding accuracy and precision is to imagine a basketball player shooting baskets.

If the player shoots with accuracy, her aim will always take the ball close to or into the basket.
If the player shoots with precision, her aim will always take the ball to the same location which may or may not be close to the basket.
A good player will be both accurate and precise by shooting the ball the same way each time and each time making it in the basket.

Precision & Accuracy

In class example

Lab Group #1

Lab Group #2

Lab Group #3

Lab Group #4

Application

Suppose a quality control chemist at a pharmaceutical company is tasked with checking the accuracy and precision of three different machines that are meant to dispense 10 ounces (296 mL) of cough syrup into storage bottles. She proceeds to use each machine to fill five bottles and then carefully determines the actual volume dispensed, obtaining the results tabulated in the table below.

Volume (mL) of Cough Medicine Delivered by 10-oz (296 mL) Dispensers

Considering these results, what should she report about each dispenser in terms of accuracy and precision?

Statistically significant

Statistical significance is a measure of the probability that the measured observation being true compared to the acceptable level of uncertainty regarding the true answer.

A statistically significant finding means that the differences observed in a study are likely real and not simply due to chance.

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