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

Accuracy and Precision There is always some degree of ERROR in a measurement. This is due to: There is always some degree of ERROR in a measurement. This is due to:  Precision of the Equipment  Accuracy of the Measurement

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

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

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

Example 1: How old are you? 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

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

Example 2: How long is a piece of string? 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. The actual measurement is 2.65 cm.

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

Example 3 Using a centigram balance, 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. The actual measurement is 3.01 g.

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. 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. Ashley is much more accurate because of the precision of her measurement and closeness of her value to the actual value.

ACCURACY/PRECISION You can tell the precision of a number simply by looking at it. The number of decimal places gives the 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 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

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

Measurements Length: meters Length: meters Volume (space occupied by an object): meter 3 – OR - liter Volume (space occupied by an object): meter 3 – OR - liter Mass (measured by comparing mass of object to standard mass of 1kg): gram 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/m 3 –or- g/l Density (ratio of mass of an object to its volume d=m/v): g/m 3 –or- g/l Temperature: °C or K Temperature: °C or K

More on Temperature Freezing Point OfWater 0°C 273 K (Kelvin) Boiling Point ofWater 100°C 373 K (Kelvin) °C *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 or- °C= K - 273

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