AP Statistics Curriculum 2007 IntroDesign - Revision history

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

2020-03-03T19:24:38Z

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

IvoDinov: /* Approach */ added Placebo section

2010-12-28T19:22:06Z

‎Approach: added Placebo section

Jenny: /* Orthogonality */

2010-06-28T18:40:19Z

‎Orthogonality

Jenny: /* Replication */

2010-06-28T18:39:48Z

‎Replication

Jenny: /* Experimental vs. Observational Studies */

2010-06-28T18:37:28Z

‎Experimental vs. Observational Studies

Jenny: /* Randomization */

2010-06-28T18:36:29Z

‎Randomization

Jenny: /* Replication */

2010-06-04T21:04:42Z

‎Replication

Jenny: /* Replication */

2010-06-04T21:04:08Z

‎Replication

Jenny: /* Comparison */

2010-06-04T21:03:33Z

‎Comparison

IvoDinov: /* Design and Experiments */

2010-04-05T15:42:09Z

‎Design and Experiments

← Older revision		Revision as of 19:24, 3 March 2020
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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

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 ===Orthogonality===
 Orthogonality allows division of complex relations and variation into separate (independent/orthogonal) contrasts, or factors, that can be studied efficiently and autonomously. Often, these contrasts may be represented by vectors, where sets of orthogonal contrasts are uncorrelated and may be independently distributed. Independence implies that each orthogonal contrast provides complementary information to other contrasts (i.e., other treatments). The goal is to completely decompose the variance or the relations of the observed measurements into independent components (e.g., like [http://en.wikipedia.org/wiki/Taylor_expansion Taylor expansion] allowing polynomial decomposition of smooth functions, where the polynomial base functions are easy to differentiate, integrate, etc.) This will, of course, allow easier interpretation of the statistical analysis and the findings of the study.
 ==Model Validation==

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 ===Orthogonality===
-Orthogonality allows division of complex relations, variation into separate (independent/orthogonal) contrasts, or factors, that can be studied efficiently and autonomously. Often, these contrasts may be represented by vectors, where sets of orthogonal contrasts are uncorrelated and may be independently distributed. Independence implies that each orthogonal contrast provides complementary information to other contrasts (i.e., other treatments). The goal is to completely decompose the variance or the relations of the observed measurements into independent components (e.g., like [http://en.wikipedia.org/wiki/Taylor_expansion Taylor expansion] allowing polynomial decomposition of smooth functions, where the polynomial base functions are easy to differentiate, integrate, etc.) This will, of course, allow easier interpretation of the statistical analysis and the findings of the study.
+Orthogonality allows division of complex relations and variation into separate (independent/orthogonal) contrasts, or factors, that can be studied efficiently and autonomously. Often, these contrasts may be represented by vectors, where sets of orthogonal contrasts are uncorrelated and may be independently distributed. Independence implies that each orthogonal contrast provides complementary information to other contrasts (i.e., other treatments). The goal is to completely decompose the variance or the relations of the observed measurements into independent components (e.g., like [http://en.wikipedia.org/wiki/Taylor_expansion Taylor expansion] allowing polynomial decomposition of smooth functions, where the polynomial base functions are easy to differentiate, integrate, etc.) This will, of course, allow easier interpretation of the statistical analysis and the findings of the study.
 ==Model Validation==

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 ===Replication===
-All measurements, observations or data collected are subject to variation, as [[SOCR_EduMaterials_Activities_RNG | there are no completely deterministic processes]]. As we try to make inference about the process that generated the observed data (not the sample data itself, even though our statistical analysis are data-driven and based on the observed measurements), the more data we collect (unbiasly) the stronger our inference is likely to be. Therefore, repeated measurements intuitively would allow us to tame the variability associated with the phenomenon we study.
+All measurements, observations or data collected are subject to variation, as [[SOCR_EduMaterials_Activities_RNG | there are no completely deterministic processes]]. As we try to make inference about the process that generated the observed data (not the sample data itself, even though our statistical analysis is data-driven and based on the observed measurements), the more data we collect (unbiased) the stronger our inference is likely to be. Therefore, repeated measurements intuitively would allow it to tame the variability associated with the phenomenon we study.
 ===Blocking===

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 ===Experimental vs. Observational Studies===
-There are many situations, where randomized experiments, albeit desirable, are impractical. And therefore, we can not deduce causality or effects of various treatments on the response measurement. ''Observational studies'' are retrospective or prospective studies where the investigator does not have control over randomization of treatments to subject, or units. In these cases, the subjects or units fall naturally within a treatment group. Examples of such observational studies include [http://www.cancer.org/docroot/PED/ped_10_1.asp studies of smoking effects on cancer] and [[AP_Statistics_Curriculum_2007_IntroDesign#References | use of parachutes to prevent death and major trauma related to gravitational pull]].
+There are many situations, where randomized experiments, albeit desirable, are impractical. Therefore, we cannot deduce causality or effects of various treatments on the response measurement. ''Observational studies'' are retrospective or prospective studies where the investigator does not have control over randomization of treatments to subject, or units. In these cases, the subjects or units fall naturally within a treatment group. Examples of such observational studies include [http://www.cancer.org/docroot/PED/ped_10_1.asp studies of smoking effects on cancer] and [[AP_Statistics_Curriculum_2007_IntroDesign#References | use of parachutes to prevent death and major trauma related to gravitational pull]].
 ===Replication===

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 ===Randomization===
-The second fundamental design principle is randomization. It requires that we make allocation of (controlled variables) treatments to units using some [[SOCR_EduMaterials_Activities_RNG | random mechanism]]. This simply guarantees that the effects resulted are the units, but not incorporated in the model, equidistributed amongst all groups and therefore unlikely to significantly affect our group comparisons at the end of the statistical inference or analysis (as these effects, if present, will be similar within each group).
+The second fundamental design principle is randomization. It requires that we make allocation of (controlled variables) treatments to units using some [[SOCR_EduMaterials_Activities_RNG | random mechanism]]. This simply guarantees that the effects resulted are the units, but not incorporated in the model, equidistributed amongst all groups.  Therefore it is unlikely to significantly affect our group comparisons at the end of the statistical inference or analysis (as these effects, if present, will be similar within each group).
 ===Experimental vs. Observational Studies===

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 ===Comparison===
-To make inference about effects, associations or predictions, one typically has to compare different groups subjected to distinct conditions. This allows contrasting observed responses and underlying group differences that may ultimately lead to inference on relations and influence between controlled and observed variables.
+To make inference about effects, associations or predictions, one typically has to compare different groups subjected to distinct conditions. This allows contrasting observed responses and underlying group differences that may ultimately lead to inference on relationships and influences between controlled and observed variables.
 ===Randomization===

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 [[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Design and Experiments
-==Design and Experiments==
+==Design of Experiments==
 ''Design of experiments'' refers of the blueprint for planning a study or experiment, performing the data collection protocol and controlling the study parameters for accuracy and consistency. Design of experiments only makes sense in studies where variation, chance and uncertainly are present and unavoidable. Data, or information, is typically collected in regard to a specific process or phenomenon being studied to investigate the effects of some controlled variables (independent variables or predictors) on other observed measurements (responses or dependent variables). Both types of variables are associated with specific observational units (living beings, components, objects, materials, etc.)