Accuracy and Precision

1. Accuracy and Precision • Much of science has to do with the collection and manipulation of quantitative or numerical data. • The value of computations using numerical data is greatly dependent on the accuracy and precision of that data.

2. Accuracy and Precision • Accuracy and precision can not be considered independently • A number can be accurate and not precise • A number can be precise and not accurate • The use of the number determines the relative need for accuracy and precision

3. ACCURACY • Accuracy can be defined as how close a number is to what it should be. • Accuracy is determined by comparing a number to a known or accepted value.

4. PRECISION • The number of decimal places assigned to the measured number • It is sometimes defined as reproducibility

5. Example 1: • How old are you? • I am 16 years old • I am 15 years and 8 months old • I am 15years, 8 months, and 5 days old • I am 15 years, 8 months, 5 days, and 10 hours old

6. Accuracy vs. Precision for Example 1 • Each of these statements is more accurate and more precise than the one before it. • Statement two is more accurate and more precise that statement one. • Statement three is more accurate and more precise than statement two.

7. Example 2: • How long is a piece of string? • Johnny measures the string at 2.63 cm. • Using the same ruler, Fred measures the string at 1.98 cm. • Who is most precise? • Who is most accurate? • The actual measurement is 2.65 cm.

8. Accuracy vs. Precision for Example 2 • Johnny is fairly accurate and also very precise. • Fred is very precise, however, he is not very accurate. His lack of accuracy is due to using the ruler incorrectly.

9. Example 3 • Using a centigram balance, • Mary measured a sample at 3 g. • Ashley measured the same sample at 3.00 g. • Who is most precise? • Who is most accurate? • The actual measurement is 3.01 g.

10. Accuracy vs. Precision for Example 3 • Mary is reasonably accurate. She was not very precise because the balance was capable of measuring to two decimal places. • Ashley is much more accurate because of the precision of her measurement and closeness of her value to the actual value.

11. ACCURACY/PRECISION • You can tell the precision of a number simply by looking at it. The number of decimal places gives the precision. • Accuracy on the other hand, depends on comparing a number to a known value. Therefore, you cannot simply look at a number and tell if it is accurate

12. In Conclusion • In science we depend upon both the accuracy and precision of the numbers we use. • The need for accuracy and precision varies with the circumstance and other measurements being used.

13. Measurements • Length: meters • Volume (space occupied by an object): meter3 – OR - liter • Mass (measured by comparing mass of object to standard mass of 1kg): gram • Density (ratio of mass of an object to its volume d=m/v): g/m3 –or- g/l • Temperature: °C or K

14. More on Temperature *The zero point on the Kelvin scale, 0 K, or absolute zero, is -273°C *A change of 1°C is the same as 1 K K= °C + 273 -or- °C= K - 273

15. Evaluating Measurements • Accepted Value: true or correct value based on reliable references • Experimental value: the measured value determined in the experiment or lab • Error: difference between the accepted and experimental values • Percent error: |error| x 100% accepted value