|Topic 8 Applied Product Testing
(detailed objectives) (available resources)
Goal: Students learn to design and conduct an experiment and draw analytical conclusions from the observations.
[standards: NM-DATA.6-12.1-3, NM-PROB.REP.PK-12.3, NM-PROB.COMM, PK-12.1-4]
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This topic presents a convenient opportunity for student to exercise an entire experimentation project (beyond simply conducting the experiment). It is an opportunity to dispel misconceptions that science doesn't allow creative expression. After completing this topic, students should have the skills necessary to complete the testing phase of their major class project.
Like any other project, an experimentation project should have clearly defined phases. Typically these include planning, design, construction, debugging, execution, data analysis and reporting. An experimentalist may want to re-define these or supplement with other phases. In this class, the student team is responsible for the entirety of the experimentation project in support of the testing phase of the class project. To be successful you will need to be keenly aware of two fundamental principles. First, all measurements are uncertain and have some error associated with them. Measurement errors include both bias and precision errors. When design decisions are based on experimental conclusions, the errors need to be accounted for. Second, there are underlying assumptions to any experiment. It is not necessary that an experimental model (or prototype) exactly replicate the final product. However, the assumptions about similarity and the similarity of testing conditions to real-world operating conditions should be well understood.
A "Descriptive Statistic" is any single numerical or graphical representation that describes a data set. They are simply succinct summaries of the data. For data sets involving a single measured variable (univariate statistics), we generally want to describe a dataset using its distribution, or its central tendency, or its dispersion. Most likely some combination of the three. The most common measure of the frequency of individual values or the range of values is the frequency distribution (histogram). The most common measures of the central tendency include the mean, median, and mode. The most common measures for the spread of values around the central tendency include the range and the standard deviation.
The term "normal distribution" is used quite loosely in the presentation. Simply speaking, if the data follows the normal distribution then there are commonly accepted descriptions of the central tendency and variance that we can easily use. For example, if we say we have a dataset that is normally distributed with a mean of 5.2 and a standard deviation of .8, then all statisticians know exactly what we are talking about. There are many advanced tests that can be performed on the dataset to see if it truly comes from a normally distributed population. The short story is that the data might deviate from normal in "skewness" (favoring one side or the other) or kurtosis (too sharp or flat of a peak). If students are advanced enough to calculate the standard deviation, then they are encouraged to report their findings in terms of "confidence intervals." As an example, if the data analysis yielded a mean of 5.2 and a standard deviation of .8, then the 95% confidence interval would be 5.2 +/- 1.96*.8 You then might conclude "based on the data we are 95% confident that the true mean is between 3.6 and 6.7." The following values indicate the various confidence intervals (assuming that a lot of data points are taken).
Fraction Number of StandardOne foundational truth of experimentation is that we cannot have much confidence in the results if we don't take enough samples. However, performing an excessive number of repetitions can waste time without producing any additional insight. The rule of thumb is that below thirty samples is a "small sample size" ... but you can get away with n = [1.96*St.Dev] 2 samples in the dataset (95% confidence and standard error =1). [Expert statisticians will recognize some cheating here...but it will likely serve most pre-collegiate students well enough]
Begin with class discussion about uncertainty and assumptions in the context of engineering designs. Explain the need for experimentation and apply the project taxonomy to describe an experiment plan. Discuss common statistics using a pre-defined dataset. Then have the students quickly gather some data as a class and calculate simple statistics for their data. Allow the students to work in small groups to apply what they know about planning and executing an experiment. Then have the students individually exercise the plan that their small group created and individually report the results.
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