“Precision & Accuracy”
GOAL: To understand the distinction between precision and accuracy as they are used in scientific measurement.
MATERIALS: Candle
12-Inch Ruler
Match
Someone’s Watch
INTRODUCTION: A principle objective of science is to describe the physical world through measurement. While we often begin with a hypothesis in science, it is important to make precise measurements and to determine the accuracy of these measurements.
Definition of Precision & Accuracy
If repetitive measurements always yield the approximately same number, the measurements are said to be precise whether or not they are correct. Precision is a measure of conformity among several individual measurements. If the measurements produce the correct number, the measurements are said to be accurate. Accuracy is a measure of conformity between a single measurement or an average of several measurements and a standard value. A standard value is one that is correct by definition.
v If the measurements are all very close to the same number, they are precise.
v If the measurements are very close to the correct number, they are accurate.
Uncertainty
As you will discover, it is not possible to make infinitely precise measurements. It is important that all numbers be interpreted in light of the uncertainty or error. Think of uncertainty as the amount that a number may be off. For example, a person’s age may be given as 30 years old plus or minus 365 days.
Systematic & Random Errors
There is a good reason for making measurements several times and taking an average value. When we use tools to assign a number to a physical quantity, some error may be introduced into the measurement. If the error introduced has a pattern, it is called a systematic error. If it has no pattern, it is called a random error.
PROCEDURE:
You will be making several measurements and determining possible errors for these measurements and which measurements were most precise.
1. Reaction Time
The time it takes to respond to a stimulus is called reaction time. A simple method to determine human reaction time uses the principle of uniformly accelerated motion of a falling object. A ruler will fall at the same rate every time it is dropped, but the ruler will be caught at a different spot each time depending on the reaction time of the person.
Have one person hold the top of a ruler so that the ruler hangs down vertically. At the bottom edge of the ruler, place your index finger and thumb as if you are about to pinch the ruler. As soon as your partner releases the ruler, pinch it as fast as you can. Measure the distance the ruler has fallen and record you results. Repeat 5 times. Calculate the average distance the ruler fell. Have another person in your group try this. Create a data table and calculate the average reaction time. .
From the average distance the ruler fell, determine your reaction time. Typical reaction times are between 0.2 and 0.3 seconds.
2. Candle & Flame
Light the candle and measure the length of the entire candle plus its flame. Be careful that you do not burn yourself or the ruler. Leave the candle burning and measure the candle and flame length once per minute for 10 minutes.
3. Watch
Assume that the clock in your classroom gives the true time. Use this clock to check your watch.
Clock Time
Watch Time
GENERAL QUESTIONS:
1) List 2 possible sources of errors in your measurements for each procedure.
2) Which set of measurements was the most precise? Why?
3) Does a systematic error affect precision, accuracy, or both precision and accuracy?
4) Suppose that a scale used in measuring length is divided with increasing fineness (for example, a ruler that measures to the eight of an inch is changed so that it measures to the sixteenth of an inch). This will definitely increase the
a. Precision of every measurement made with the new scale
b. Accuracy of every measurement made with the new scale c. Both precision and accuracy of every measurement made with the new scale
d. Neither the precision nor accuracy of measurements made with the new scale
5) Teresa, Alexes, Krystina, and Bacall having received degrees in paleontology, each measure the length, in meters, of a dinosaur bone unearthed by Bacall. Bacall, having more experience with bones, measured the correct value. The measurements made by each are:
Teresa
2.0
2.1
1.9
2.0
Alexes
7.3
9.4
4.2
7.0
Krystina
7.0
7.3
7.2
7.1
Bacall
7.3
Whose measurements are…
a) accurate and precise?
b) precise but not accurate?
c) accurate but not precise?
d) accurate only?
e) probably a result of a systematic error?
GOAL: To understand the distinction between precision and accuracy as they are used in scientific measurement.
MATERIALS: Candle
12-Inch Ruler
Match
Someone’s Watch
INTRODUCTION: A principle objective of science is to describe the physical world through measurement. While we often begin with a hypothesis in science, it is important to make precise measurements and to determine the accuracy of these measurements.
Definition of Precision & Accuracy
If repetitive measurements always yield the approximately same number, the measurements are said to be precise whether or not they are correct. Precision is a measure of conformity among several individual measurements. If the measurements produce the correct number, the measurements are said to be accurate. Accuracy is a measure of conformity between a single measurement or an average of several measurements and a standard value. A standard value is one that is correct by definition.
v If the measurements are all very close to the same number, they are precise.
v If the measurements are very close to the correct number, they are accurate.
Uncertainty
As you will discover, it is not possible to make infinitely precise measurements. It is important that all numbers be interpreted in light of the uncertainty or error. Think of uncertainty as the amount that a number may be off. For example, a person’s age may be given as 30 years old plus or minus 365 days.
Systematic & Random Errors
There is a good reason for making measurements several times and taking an average value. When we use tools to assign a number to a physical quantity, some error may be introduced into the measurement. If the error introduced has a pattern, it is called a systematic error. If it has no pattern, it is called a random error.
PROCEDURE:
You will be making several measurements and determining possible errors for these measurements and which measurements were most precise.
1. Reaction Time
The time it takes to respond to a stimulus is called reaction time. A simple method to determine human reaction time uses the principle of uniformly accelerated motion of a falling object. A ruler will fall at the same rate every time it is dropped, but the ruler will be caught at a different spot each time depending on the reaction time of the person.
Have one person hold the top of a ruler so that the ruler hangs down vertically. At the bottom edge of the ruler, place your index finger and thumb as if you are about to pinch the ruler. As soon as your partner releases the ruler, pinch it as fast as you can. Measure the distance the ruler has fallen and record you results. Repeat 5 times. Calculate the average distance the ruler fell. Have another person in your group try this. Create a data table and calculate the average reaction time. .
From the average distance the ruler fell, determine your reaction time. Typical reaction times are between 0.2 and 0.3 seconds.
- For distance measured in inches: (time) = 2 x Distance
- For distance measured in centimeters: (time) = 2 x Distance
2. Candle & Flame
Light the candle and measure the length of the entire candle plus its flame. Be careful that you do not burn yourself or the ruler. Leave the candle burning and measure the candle and flame length once per minute for 10 minutes.
3. Watch
Assume that the clock in your classroom gives the true time. Use this clock to check your watch.
Clock Time
Watch Time
GENERAL QUESTIONS:
1) List 2 possible sources of errors in your measurements for each procedure.
2) Which set of measurements was the most precise? Why?
3) Does a systematic error affect precision, accuracy, or both precision and accuracy?
4) Suppose that a scale used in measuring length is divided with increasing fineness (for example, a ruler that measures to the eight of an inch is changed so that it measures to the sixteenth of an inch). This will definitely increase the
a. Precision of every measurement made with the new scale
b. Accuracy of every measurement made with the new scale c. Both precision and accuracy of every measurement made with the new scale
d. Neither the precision nor accuracy of measurements made with the new scale
5) Teresa, Alexes, Krystina, and Bacall having received degrees in paleontology, each measure the length, in meters, of a dinosaur bone unearthed by Bacall. Bacall, having more experience with bones, measured the correct value. The measurements made by each are:
Teresa
2.0
2.1
1.9
2.0
Alexes
7.3
9.4
4.2
7.0
Krystina
7.0
7.3
7.2
7.1
Bacall
7.3
Whose measurements are…
a) accurate and precise?
b) precise but not accurate?
c) accurate but not precise?
d) accurate only?
e) probably a result of a systematic error?