# AP Statistics Curriculum 2007 IntroVar

(Difference between revisions)
 Revision as of 03:07, 10 February 2008 (view source) (→Approach)← Older edit Revision as of 03:08, 10 February 2008 (view source) (→Model Validation)Newer edit → Line 19: Line 19: * Each model or technique for data exploration, analysis and understanding relies on a set of assumptions, which always need to be validated before the model or analysis tool is employed to study real data (observations or measurements that are perceived or detected by the investigator). * Each model or technique for data exploration, analysis and understanding relies on a set of assumptions, which always need to be validated before the model or analysis tool is employed to study real data (observations or measurements that are perceived or detected by the investigator). - * Such a priori model conjectures or presumptions could take the form of mathematical constraints about the properties of the underlying process, restrictions on the study design or demands on the data acquisition protocol. + * Such prior model conjectures or presumptions could take the form of mathematical constraints about the properties of the underlying process, restrictions on the study design or demands on the data acquisition protocol. - * Common assumptions include (statistical) independence of the measurements, specific limitations on the shape of the distribution that we sample/observe data from, restrictions on the parameters of the process we study, etc. + * Common assumptions include (statistical) independence of the measurements, specific limitations on the shape of the observed distribution, restrictions on the parameters of the processes being studied , etc. ==Computational Resources: Internet-based SOCR Tools== ==Computational Resources: Internet-based SOCR Tools==

## Revision as of 03:08, 10 February 2008

General Advance-Placement (AP) Statistics Curriculum - Introduction to Statistics

## The Nature of Data & Variation

No mater how controlled the environment, the protocol or the design, virtually any repeated measurement, observation, experiment, trial, study or survey is bound to generate data that varies because of intrinsic (internal to the system) or extrinsic (due to the ambient environment) effects.

For example, the UCLA's study of Alzheimer’s disease* analyzed the data of 31 MCI and 34 probable Alzheimer’s disease patients. The investigators made every attempt to control as many variables as possible, yet, the demographic information they collected from the outcomes of the subjects contained unavoidable variation. The same study found variation in the MMSE cognitive scores even in the same subjects.

## Approach

Models & strategies for solving the problem and understanding the data and inference.

• Once we accept that all natural phenomena are inherently variant and there are no completely deterministic processes, we need to look for models and techniques that allow us to study such acquired data in the presence of variation, uncertainty and chance.
• Statistics is the data science that investigates natural processes and allows us to quantify variation to make population inference based on limited observations.

## Model Validation

Checking/affirming underlying assumptions.

• Each model or technique for data exploration, analysis and understanding relies on a set of assumptions, which always need to be validated before the model or analysis tool is employed to study real data (observations or measurements that are perceived or detected by the investigator).
• Such prior model conjectures or presumptions could take the form of mathematical constraints about the properties of the underlying process, restrictions on the study design or demands on the data acquisition protocol.
• Common assumptions include (statistical) independence of the measurements, specific limitations on the shape of the observed distribution, restrictions on the parameters of the processes being studied , etc.

## Examples

Computer simulations and real observed data.

## Hands-on activities

Step-by-step practice problems.