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+ | ===== Uncertainty in Measurement ===== | ||
+ | |||
+ | There is little that can be scientifically investigated without taking | ||
+ | measurements. By taking and analyzing data, we can develop models that | ||
+ | inform us of how the world works. However, to be able to analyze data | ||
+ | effectively, critical decisions need to be made regarding how the data | ||
+ | are being taken in order to determine its validity. | ||
+ | |||
+ | This uncertainty is not a fault of experimental science, and does not | ||
+ | give credence to "theory being more perfect than experiment." The idea | ||
+ | of uncertainty is found in every aspect of science -- in experiment we | ||
+ | call it *error* or *uncertainty*, in theory we are limited by the | ||
+ | *assumptions* made, and in engineering we define our products to be | ||
+ | within a *tolerance.* In all instances, these forms of uncertainty | ||
+ | describe how *confident* the scientist is in their measurement -- it | ||
+ | defines the range of values within which they are *sure* the reported | ||
+ | value falls. | ||
+ | |||
+ | Defining uncertainty is a skill that is developed over time and, like | ||
+ | any other skill, takes practice. As it is a major tool used in nearly | ||
+ | every aspect of science, it has become a major learning goal of DATA | ||
+ | Lab, both this semester and next (should you take PHY 252). | ||
+ | |||
+ | In this workshop, you are tasked with taking a series of measurements. | ||
+ | Your data will be pooled with the rest of the class -- affording us a | ||
+ | backdrop against which to discuss measurements and uncertainty. The | ||
+ | discussions with the larger group will help inform your decisions in | ||
+ | experiments as well as help you develop a deeper understanding of what | ||
+ | uncertainty means and how it is used in science. Afterwards, you and | ||
+ | your group will be presented with a final measurement that you will | ||
+ | record and assign uncertainty to. By using the information in class, you | ||
+ | will justify your experimental decisions and value reported. | ||
+ | |||
+ | ==== Research Concepts ==== | ||
+ | |||
+ | In order to be productive in class, it would be helpful to research | ||
+ | before class: | ||
+ | * What reported data means | ||
+ | * Why uncertainty is assigned to measured data | ||
+ | * How the assigned uncertainty reflects the confidence of the reported value | ||
+ | * The difference between random and systematic uncertainty | ||
+ | * How to calculate the mean of data set | ||
+ | |||
+ | ==== Measurements and Uncertainty ==== | ||
+ | |||
+ | **Part 1 -- Measurements** | ||
+ | |||
+ | There are five measurements you are tasked with taking: the length of a | ||
+ | metal block, the diameter of a bouncy ball, the length of a string, the | ||
+ | mass of a weight, and the angle of a board. After you take these | ||
+ | measurements, record the values you obtained on the white boards | ||
+ | provided. It may be helpful to consider and document in your notebook | ||
+ | * How was each measurement taken? | ||
+ | * Were there any complications that arose while taking your measurements? | ||
+ | * Did the way you took your measurement affect the value you obtained? | ||
+ | |||
+ | **Part 2 -- Discussion of Uncertainty** | ||
+ | |||
+ | Scientists will include values of uncertainty when they report data. | ||
+ | Your group will be assigned one of the sets of measurement data to | ||
+ | discuss. In this discussion, consider: | ||
+ | * What do the reported values mean? | ||
+ | * How difficult was the measurement to make? Why? | ||
+ | * What does the amount of variability tell you about the uncertainty in the measurement? | ||
+ | * Are there other things the variations tell you? | ||
+ | * Can you assign a quantitative value for the uncertainty of this set of data? | ||
+ | |||
+ | You will then report your group's discussion to the class. | ||
+ | |||
+ | **Part 3 -- Obtaining and Reporting Data** | ||
+ | |||
+ | Your group will be tasked with taking one additional measurement. The | ||
+ | experimental decisions your group makes will affect the value and | ||
+ | uncertainty of your measurement. Document these decisions and determine | ||
+ | a value for the measurement and its uncertainty. Justify your values | ||
+ | based on the decisions you made and the discussions held in class. | ||
+ | |||
+ | At the end of the day, you will each turn in your notebook. While your | ||
+ | entire entry will be evaluated, in order to narrow our scope feedback | ||
+ | and assessment will primarily focus on what you submit for **Part 3**, | ||
+ | especially | ||
+ | * The value reported and the uncertainty assigned. | ||
+ | * How you documented your measurement and the experimental decisions you made. | ||
+ | * Justification for your assigned value and uncertainty and how it related to the discussions held in class. | ||