Accuracy, precision, and you Measuring Accuracy, precision, and you

Measuring We use tools to measure - scales, balances, rulers, graduated glassware, and so forth When we read any measuring instrument, we strive to measure with high accuracy and the correct level of precision.

Accuracy vs Precision What’s the difference between accuracy and precision? What do we mean when we say that something is “accurate?” How is that different from “Precise?”

Accuracy and Precision

Accuracy: How close a measurement is to the actual value. Note: when we are conducting a research project, we DO NOT KNOW what the “real” answer is. We never will. All we can do is get as close as possible. Think: how do we know whether or not our results are accurate or not?

How do we measure accurately? Understand the tool! First, determine the scale of the tool. That’s how many units are between the calibration marks. What is the scale of this cylinder? 0.2 mL. You can see that the water is between 6.6 and 6.8 mL

Precision – two meanings It’s an indication of the agreement among a number of measurements made in the same way (i.e., how close the numbers are to each other). Or, precision can mean how many numbers you can/should use to record a measurement – sometimes the correct level of precision would be 1 m, sometimes 1.5 meters, sometimes 1.5000296 m. It depends on the tool you use.

Precision (first meaning) and accuracy

4 darts on a dart board High accuracy, low precision High accuracy and precision Low accuracy, high precision Neither accurate nor precise

Limit of Certainty You can say with complete certainty that there’s more than 6 but less than 8 mL in the cylinder. You cannot be certain whether it’s closer to 6.7 or 6.6 mL. Thus, the limit of certainty is in the 1’s place.

Limit and Precision The precision of your reading is limited by the tool. The limit is the smallest decimal place that is consistently marked with a calibration line. Here, every mL is marked (6, 7, 8), so you can be certain of the one’s place But every 1/10 mL is not ( 0.1, 0.3, 0.5 . . . ), so you are uncertain of the 1/10’s place So, the limit of this cylinder is the one’s place.

Again: Precision is limited Always read the measuring tool to one place past the limit (in this case, the 1’s place) You can say for certain that the actual value is between 6 and 7 mL You cannot say for certain that the value is between 6.6 and 6.7 mL because there’s no calibration mark at 6.7 mL So, this tool’s limit of certainty is the 1’s place. Record numbers to one decimal place past the limit

Practice: Find the scale and limit of each ruler

Scale: ¼ (unit) Limit 1’s place Scale: ½ (unit) Limit: 1’s place Cannot tell for sure! Scale: 1 mm Limit: 1’s place

Again: How precise can your recording be? Rule: Find the limit, record measurements to that decimal place, and then record one more digit. The last digit is an estimate. STOP. Go no further!

How much water? You know the water level is between 6.6 and 6.8 ml. Record to the limit, the 1’s place (6 mL.) Then record one more digit, your estimate 6.7 mL.

ALL MEASUREMENTS ARE ESTIMATES! You will see that there is always some space between the calibration lines in any tool you use. So, no measurement is absolutely correct, no matter how precise (how tiny the limit) it is. Consider a pencil. When you measure it with a ruler (limit = cm), you might estimate that it is 7.6 mm, and I might estimate that it is 7.5 mm. Both estimates are good Joe says it is 7 cm – not precise enough! Jane says it is 7.57 mm – too precise!

Estimate the length of the blue section. 0cm What is the scale of this ruler? What is the limit of this ruler? 1 2 3 4 cm

How long is that blue strip? The scale is ½ cm The limit is the 1’s place; you must record a value to the 1/10th place You can state for certain that the reading is between 3.5 cm and 4.0 cm. Can you record 3.75 cm? NOPE! You can only record to the 1/10 place.

Errors in measuring Alignment errors – always check where the measured item begins. Estimation errors – be sure you understand the scale

Practice

Practice 27 cm 5.7 degrees C 4.5 g 25.0 mL