AP Statistics Curriculum 2007 IntroUses
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- | + | [[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Uses and Abuses of Statistics | |
- | + | ==Uses and Abuses of Statistics== | |
Statistics is the science of variation, randomness and chance. As such, statistics is different from the [http://en.wikipedia.org/wiki/Isaac_Newton Newtonian sciences], where the processes being studied obey exact deterministic mathematical laws and typically can be described as [http://en.wikipedia.org/wiki/Category:Equations systems]. Because statistics provides tools for data understanding where no other science can, one should be prepared to trade this new power of knowledge with uncertainty. In general, statistical analysis, inference and simulation will not provide deterministic answers and strict (e.g., yes/no, presence/absence) responses to questions involving stochastic processes. Rather, statistics will provide quantitative inference represented as long-time probability values, confidence or prediction intervals, odds, chances, etc., which may ultimately be subjected to varying interpretations. | Statistics is the science of variation, randomness and chance. As such, statistics is different from the [http://en.wikipedia.org/wiki/Isaac_Newton Newtonian sciences], where the processes being studied obey exact deterministic mathematical laws and typically can be described as [http://en.wikipedia.org/wiki/Category:Equations systems]. Because statistics provides tools for data understanding where no other science can, one should be prepared to trade this new power of knowledge with uncertainty. In general, statistical analysis, inference and simulation will not provide deterministic answers and strict (e.g., yes/no, presence/absence) responses to questions involving stochastic processes. Rather, statistics will provide quantitative inference represented as long-time probability values, confidence or prediction intervals, odds, chances, etc., which may ultimately be subjected to varying interpretations. | ||
This possibility of multiple interpretations may be viewed by some as detriment or inconsistency. But others consider these outcomes as beautiful, scientific and elegant responses to challenging problems that are inherently stochastic. The phrase ''Uses and Abuses of Statistics'' refers to this notion that in some cases statistical results may be used as evidence to seemingly opposite theses. However, most of the time, common [http://en.wikipedia.org/wiki/Logic principles of logic] allow us to disambiguate the obtained statistical inference. | This possibility of multiple interpretations may be viewed by some as detriment or inconsistency. But others consider these outcomes as beautiful, scientific and elegant responses to challenging problems that are inherently stochastic. The phrase ''Uses and Abuses of Statistics'' refers to this notion that in some cases statistical results may be used as evidence to seemingly opposite theses. However, most of the time, common [http://en.wikipedia.org/wiki/Logic principles of logic] allow us to disambiguate the obtained statistical inference. | ||
- | + | ==Approach== | |
When presented with a problem, data and statistical inference about a phenomenon, one needs to assess critically the validity of the assumptions, accuracy of the models and correctness of the interpretation of the thesis. There are many so called paradoxes, where one can easily be convinced of an erroneous conclusion, because the underlying principles are violated (e.g., [http://en.wikipedia.org/wiki/Simpson_paradox Simpson's paradox], the [http://en.wikipedia.org/wiki/Birthday_paradox Birthday paradox], etc.) Critical evaluation of the design of the experiment, the data collection and measurements and the validity of the analysis strategy should lead to correct inference and interpretation in most cases. | When presented with a problem, data and statistical inference about a phenomenon, one needs to assess critically the validity of the assumptions, accuracy of the models and correctness of the interpretation of the thesis. There are many so called paradoxes, where one can easily be convinced of an erroneous conclusion, because the underlying principles are violated (e.g., [http://en.wikipedia.org/wiki/Simpson_paradox Simpson's paradox], the [http://en.wikipedia.org/wiki/Birthday_paradox Birthday paradox], etc.) Critical evaluation of the design of the experiment, the data collection and measurements and the validity of the analysis strategy should lead to correct inference and interpretation in most cases. | ||
- | + | ==Examples of Common Causes for Data Misinterpretation== | |
- | + | ===Unrepresentative Samples=== | |
- | * | + | These are collections of data measurement or observations that do not adequately describe the natural process or phenomenon being studied. The phrase ''garbage-in, garbage-out'' refers to this situation and implies that none of the conclusions or the inference based on such unrepresentative samples should be trusted. In general, collecting a population representative sample is a hard experimental design problem. |
- | + | * '''Self-selection''' - voluntary response samples, where the respondents, units or participants decide themselves whether to be included in the sample, survey or experiment. | |
- | + | * ''Non-sampling errors'' (e.g., non-response bias) are errors in the data collection that are not due to the process of sampling or the study design. | |
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- | ===Computational Resources: Internet-based SOCR Tools | + | ===Sampling errors=== |
+ | Sampling errors arise from a decision to use a sample rather than measure the entire population. | ||
+ | |||
+ | ===Samples of small sizes=== | ||
+ | |||
+ | ===Loaded questions in surveys or polls=== | ||
+ | |||
+ | ===Misleading Graphs=== | ||
+ | Look at the quantitative information represented in a chart or plot, not at the shape, orientation, relation or pattern represented by the graph. | ||
+ | * Partial Pictures | ||
+ | * Deliberate Distortions | ||
+ | * Scale breaks and axes scaling | ||
+ | |||
+ | ===Inappropriate estimates or statistics=== | ||
+ | Erroneous population parameter estimates (intentionally or most likely unintentionally). The source of the data and the method for parameter estimation should be carefully reviewed to avoid bias and misinterpretation of data, results and to guarantee robust inference. | ||
+ | |||
+ | ==Computational Resources: Internet-based SOCR Tools== | ||
* [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] | * [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] | ||
* [http://www.socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts] | * [http://www.socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts] | ||
- | + | ==Examples & Hands-on Activities== | |
* [[SOCR_EduMaterials_Activities_BirthdayExperiment | Birthday Paradox I]] | * [[SOCR_EduMaterials_Activities_BirthdayExperiment | Birthday Paradox I]] | ||
* [[SOCR_EduMaterials_Activities_Birthday | Birthday Paradox II]] | * [[SOCR_EduMaterials_Activities_Birthday | Birthday Paradox II]] | ||
<hr> | <hr> | ||
- | + | ==References== | |
* TBD | * TBD | ||
Revision as of 18:11, 20 June 2007
General Advance-Placement (AP) Statistics Curriculum - Uses and Abuses of Statistics
Contents |
Uses and Abuses of Statistics
Statistics is the science of variation, randomness and chance. As such, statistics is different from the Newtonian sciences, where the processes being studied obey exact deterministic mathematical laws and typically can be described as systems. Because statistics provides tools for data understanding where no other science can, one should be prepared to trade this new power of knowledge with uncertainty. In general, statistical analysis, inference and simulation will not provide deterministic answers and strict (e.g., yes/no, presence/absence) responses to questions involving stochastic processes. Rather, statistics will provide quantitative inference represented as long-time probability values, confidence or prediction intervals, odds, chances, etc., which may ultimately be subjected to varying interpretations.
This possibility of multiple interpretations may be viewed by some as detriment or inconsistency. But others consider these outcomes as beautiful, scientific and elegant responses to challenging problems that are inherently stochastic. The phrase Uses and Abuses of Statistics refers to this notion that in some cases statistical results may be used as evidence to seemingly opposite theses. However, most of the time, common principles of logic allow us to disambiguate the obtained statistical inference.
Approach
When presented with a problem, data and statistical inference about a phenomenon, one needs to assess critically the validity of the assumptions, accuracy of the models and correctness of the interpretation of the thesis. There are many so called paradoxes, where one can easily be convinced of an erroneous conclusion, because the underlying principles are violated (e.g., Simpson's paradox, the Birthday paradox, etc.) Critical evaluation of the design of the experiment, the data collection and measurements and the validity of the analysis strategy should lead to correct inference and interpretation in most cases.
Examples of Common Causes for Data Misinterpretation
Unrepresentative Samples
These are collections of data measurement or observations that do not adequately describe the natural process or phenomenon being studied. The phrase garbage-in, garbage-out refers to this situation and implies that none of the conclusions or the inference based on such unrepresentative samples should be trusted. In general, collecting a population representative sample is a hard experimental design problem.
- Self-selection - voluntary response samples, where the respondents, units or participants decide themselves whether to be included in the sample, survey or experiment.
- Non-sampling errors (e.g., non-response bias) are errors in the data collection that are not due to the process of sampling or the study design.
Sampling errors
Sampling errors arise from a decision to use a sample rather than measure the entire population.
Samples of small sizes
Loaded questions in surveys or polls
Misleading Graphs
Look at the quantitative information represented in a chart or plot, not at the shape, orientation, relation or pattern represented by the graph.
- Partial Pictures
- Deliberate Distortions
- Scale breaks and axes scaling
Inappropriate estimates or statistics
Erroneous population parameter estimates (intentionally or most likely unintentionally). The source of the data and the method for parameter estimation should be carefully reviewed to avoid bias and misinterpretation of data, results and to guarantee robust inference.
Computational Resources: Internet-based SOCR Tools
Examples & Hands-on Activities
References
- TBD
- SOCR Home page: http://www.socr.ucla.edu
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