AP Statistics Curriculum 2007 IntroVar

From Socr

(Difference between revisions)
Jump to: navigation, search
(The Nature of Data & Variation)
(The Nature of Data & Variation)
Line 4: Line 4:
No matter 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.
No matter 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 [[AP_Statistics_Curriculum_2007_IntroVar#References | 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.
+
For example, the UCLA's [[AP_Statistics_Curriculum_2007_IntroVar#References | 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. The table below shows the demographic characteristics for the subjects and patients included in this study, where the following notation is used M: male; F: female; W: white; AA: African American; A: Asian:
-
<center>[[Image:AP_Statistics_Curriculum_2007_IntroVar_Dinov_061407_Fig1.png|500px]]</center>
+
<center>
 +
{| class="wikitable" style="text-align:center; width:75%" border="1"
 +
|-
 +
| '''Variable''' || '''Alzheimer’s disease''' || '''MCI''' || '''Test statistics''' || '''Test score''' || '''P-value'''
 +
|-
 +
| '''Age (years)''' || 76.2 (8.3) range 52–89 || 73.7 (7.4) range 57–84 || Student’s T  || <math>t_o = 1.284</math> || ''p=0.21''
 +
|-
 +
| '''Gender (M:F)''' || 15:19 || 15:16 || Proportion || <math>z_o = -0.345</math>  || ''p=0.733''
 +
|-
 +
| '''Education (years)''' || 14.0 (2.1) range 12–19 || 16.23 (2.7) range 12–20 || Wilcoxon rank sum || <math>w_o = 773.0</math>  || ''p<0.001''
 +
|-
 +
| '''Race (W:AA:A)'''  || 29:1:4 || 26:2:3 || <math>\chi_{(df=2)}^2</math> || <math>\chi_{(df=2)}^2=1.18</math> || 0.55
 +
|-
 +
| '''MMSE''' || 20.9 (6.3) range 4–29 || 28.2 (1.6) range 23–30 || Wilcoxon rank-sum || <math>w_o= 977.5</math>  || ''p<0.001''
 +
|}
 +
</center>
==Approach==
==Approach==

Revision as of 05:03, 7 March 2008

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

Contents

The Nature of Data & Variation

No matter 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. The table below shows the demographic characteristics for the subjects and patients included in this study, where the following notation is used M: male; F: female; W: white; AA: African American; A: Asian:

Variable Alzheimer’s disease MCI Test statistics Test score P-value
Age (years) 76.2 (8.3) range 52–89 73.7 (7.4) range 57–84 Student’s T to = 1.284 p=0.21
Gender (M:F) 15:19 15:16 Proportion zo = − 0.345 p=0.733
Education (years) 14.0 (2.1) range 12–19 16.23 (2.7) range 12–20 Wilcoxon rank sum wo = 773.0 p<0.001
Race (W:AA:A) 29:1:4 26:2:3 \chi_{(df=2)}^2 \chi_{(df=2)}^2=1.18 0.55
MMSE 20.9 (6.3) range 4–29 28.2 (1.6) range 23–30 Wilcoxon rank-sum wo = 977.5 p<0.001

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.

Computational Resources: Internet-based SOCR Tools

Examples

Computer simulations and real observed data.

Hands-on activities

Step-by-step practice problems.


References




Translate this page:

(default)

Deutsch

Español

Français

Italiano

Português

日本語

България

الامارات العربية المتحدة

Suomi

इस भाषा में

Norge

한국어

中文

繁体中文

Русский

Nederlands

Ελληνικά

Hrvatska

Česká republika

Danmark

Polska

România

Sverige

Personal tools