AP Statistics Curriculum 2007 IntroTools

General Advance-Placement (AP) Statistics Curriculum - Statistics with Tools

Statistics with Tools (Calculators and Computers)

A critical component in any data analysis or process understanding protocol is that one needs to develop a model that has a compact analytical representation (e.g., formulas, symbolic equations, etc.) The model is used to study the process theoretically. Emperical validation of the model is carried by pluggin in data and actually testing the model. This validation stop may be done manually by computing the model prediction or model inference from recorded measurements. This typically may be done by hand only for small number of observations (<10). In practice, most of the time, we use or write algorithms and computer programs that automate these calculations for better efficiency, accuracy and consistency in applying the model to larger datasets.

There are a number of statistical software tools (programs) that one can employ for data analysis and statistical processing. Some of these are: SAS, SYSTAT, SPSS, R, SOCR.

Approach & Model Validation

Before any statistical analysis tool is employed to analyze a dataset, one needs to carefully review the prerequisites and assumptions that this model demands about the data and study design.

For example, if we measure the weight and height of students and want to study gender, age or race differences or association between weight and height, we need to make sure our sample size is large enough, these weight and height measurements are random (i.e., we do not have repeated measurements of the same student or twin-measurements) and that the students we can measure are a representative sample of the population that we are making inference about (e.g., 8^th-grade students).

In this example, suppose we record the following 6 pairs of {weight (kg), height (cm)}:

Student Index	1	2	3	4	5	6
Weight	60	75	58	67	56	80
Height	167	175	152	172	166	175

We can easily compute the average weight (66 kg) and height (167 cm) using the sample mean-formula. We can also compute these averages using the SOCR Charts, or any other statistical package, as shown in the image below.

Computational Resources: Internet-based SOCR Tools

Several of the SOCR tools and resources will be shown later to be useful in a variety of sitiations. Here is just a list of these with one example of each:

• SOCR Charts and Histogram Charts Activity
• SOCR Analyses and Simple Linear Regression Activity
• SOCR Modeler and Random Number Generation Activity

Hands-on Examples & Activities

• As part of a AP_Statistics_Curriculum_2007_IntroTools#References brain imaging study of Alzheimer's disease *, the investigators collected the following data.

Let's try to plot some of this data and perhaps apply a simple linear regression analysis to tease out the relations between average brain volume (MEAN) and age (AGE).

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References

• Mega MS, Dinov, ID, Thompson, P, Manese, M, Lindshield, C, Moussai, J, Tran, N, Olsen, K, Felix, J, Zoumalan, C, Woods, RP, Toga, AW, Mazziotta, JC. Automated Brain Tissue Assessment in the Elderly and Demented Population: Construction and Validation of a Sub-Volume Probabilistic Brain Atlas, NeuroImage, 26(4), 1009-1018, 2005.

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

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