AP Statistics Curriculum 2007 IntroUses - Revision history

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Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/"

IvoDinov: /* Approach */

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‎Approach

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‎Approach

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‎Misleading Graphs

Jenny: /* Samples of Small Sizes */

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‎Samples of Small Sizes

Jenny at 18:29, 28 June 2010

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Jenny: /* Samples of Small Sizes */

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‎Samples of Small Sizes

Jenny: /* Uses and Abuses of Statistics */

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‎Uses and Abuses of Statistics

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‎Uses and Abuses of Statistics

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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

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 ==Approach==
-When presented with a problem, data and statistical inference about a phenomenon, one needs to critically assess 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 by 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, data collection, measurements and validity of the analysis strategy should lead to the correct inference and interpretation in most cases.
+When presented with a problem, data and statistical inference about a phenomenon, one needs to critically assess 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 by 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, data collection, measurements and validity of the analysis strategy should lead to the correct inference and interpretation in most cases.
 Suppose we stidy the success rates for treatments involving both ''small'' and ''large'' kidney stones -- treatment ''A'' includes all open procedures and treatment ''B'' is percutaneous nephrolithotomy:

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 ==Approach==
 When presented with a problem, data and statistical inference about a phenomenon, one needs to critically assess 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 by 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, data collection, measurements and validity of the analysis strategy should lead to the correct inference and interpretation in most cases.
 In summary, one must:

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 * Deliberate Distortions
 * Scale breaks and axes scaling
 ===Inappropriate estimates or statistics===

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 ===Samples of Small Sizes===
-Small sample sizes may significantly distort the interpretation of the data, or results, because a small-sample data [[EBook#Chapter_II:_Describing.2C_Exploring.2C_and_Comparing_Data | distribution may have completely different characteristics]] from the native population where the sample is drawn from (e.g., center, spread, shape, etc.) For example, use the [[SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem | SOCR CLT activity]] to sample small samples from varieties of distributions and compare the sample-histogram against the population distribution. Their characteristics will be mostly similar, but sometimes they will be drastically different.
+Small sample sizes may significantly distort the interpretation of the data, or results, because a small-sample data [[EBook#Chapter_II:_Describing.2C_Exploring.2C_and_Comparing_Data | distribution may have completely different characteristics]] from the native population where the sample is drawn from (e.g., center, spread, shape, etc.) For example, use the [[SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem | SOCR CLT activity]] to sample small samples from varieties of distributions and compare the sample-histogram against the population distribution. Their characteristics will be mostly similar, but sometimes drastically different.
 ===Loaded Questions in Surveys or Polls===

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 ==Approach==
-When presented with a problem, data and statistical inference about a phenomenon, one needs to critically assess 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 by 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, data collection, measurements and 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 critically assess 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 by 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, data collection, measurements and validity of the analysis strategy should lead to the correct inference and interpretation in most cases.
 In summary, one must:
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 ==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.
+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 part of experimental design.
-* '''Self-Selection''' - voluntary response samples, where the respondents, units or participants decide themselves whether to be included in the sample, survey or experiment.
+* '''Self-Selection''' - voluntary response samples, where the respondents, units or participants decide whether to be 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.
+Sampling errors arise from a decision of using  a sample rather than measuring the entire population.
 ===Samples of Small Sizes===
-Small sample sizes may significantly distort the interpretation of the data, or results, because a small-sample data [[EBook#Chapter_II:_Describing.2C_Exploring.2C_and_Comparing_Data | distribution may have completely different characteristics]] from the native population which the sample is drawn from (e.g., center, spread, shape, etc.) For example, use the [[SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem | SOCR CLT activity]] to sample small samples from varieties of distributions and compare the sample-histogram against the population distribution. Their characteristics will be mostly similar, but sometimes they will be drastically different.
+Small sample sizes may significantly distort the interpretation of the data, or results, because a small-sample data [[EBook#Chapter_II:_Describing.2C_Exploring.2C_and_Comparing_Data | distribution may have completely different characteristics]] from the native population where the sample is drawn from (e.g., center, spread, shape, etc.) For example, use the [[SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem | SOCR CLT activity]] to sample small samples from varieties of distributions and compare the sample-histogram against the population distribution. Their characteristics will be mostly similar, but sometimes they will be drastically different.
 ===Loaded Questions in Surveys or Polls===

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 ==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 treat 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]. Since statistics provides tools for data understanding where no other science can, one should be prepared to treat 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 varyious interpretations.
-This possibility of multiple interpretations may be viewed by some as detrimental or inconsistent. 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 these. However, most of the time, common [http://en.wikipedia.org/wiki/Logic principles of logic] allow us to disambiguate the obtained statistical inference. [[AP_Statistics_Curriculum_2007_IntroUses#References | Some appropriate probability and statistics quotes are provided in the references section]].
+This possibility of multiple interpretations may be viewed by some as detrimental or inconsistent. However, some others may 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 the notion that in some cases statistical results may be used as evidence to seemingly opposite these. However, most of the time, common [http://en.wikipedia.org/wiki/Logic principles of logic] allow us to disambiguate the obtained statistical inference. [[AP_Statistics_Curriculum_2007_IntroUses#References | Some appropriate probability and statistics quotes are provided in the references section]].
 ==Approach==
-When presented with a problem, data and statistical inference about a phenomenon, one needs to critically assess 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, data collection, measurements and 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 critically assess 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 by 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, data collection, measurements and validity of the analysis strategy should lead to correct inference and interpretation in most cases.
 In summary, one must:

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 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 detrimental or inconsistent. 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. [[AP_Statistics_Curriculum_2007_IntroUses#References | Some appropriate probability and statistics quotes are provided in the references section]].
+This possibility of multiple interpretations may be viewed by some as detrimental or inconsistent. 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 these. However, most of the time, common [http://en.wikipedia.org/wiki/Logic principles of logic] allow us to disambiguate the obtained statistical inference. [[AP_Statistics_Curriculum_2007_IntroUses#References | Some appropriate probability and statistics quotes are provided in the references section]].
 ==Approach==