AP Statistics Curriculum 2007 IntroTools - Revision history

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

2020-03-03T16:35:50Z

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

IvoDinov: /* Data Plots */

2013-04-05T15:54:25Z

‎Data Plots

IvoDinov: /* Approach & Model Validation */

2013-04-03T15:47:40Z

‎Approach & Model Validation

IvoDinov: /* Approach & Model Validation */

2013-04-03T15:45:51Z

‎Approach & Model Validation

IvoDinov: /* Approach & Model Validation */

2013-04-03T15:43:52Z

‎Approach & Model Validation

Jenny: /* Statistical Analysis */

2010-06-28T18:46:41Z

‎Statistical Analysis

Jenny: /* Data Plots */

2010-06-28T18:45:13Z

‎Data Plots

Jenny: /* Data and Study Design */

2010-06-28T18:44:30Z

‎Data and Study Design

Jenny: /* Computational Resources: Internet-based SOCR Tools */

2010-06-28T18:43:54Z

‎Computational Resources: Internet-based SOCR Tools

Jenny at 18:41, 28 June 2010

2010-06-28T18:41:59Z

← Older revision		Revision as of 16:35, 3 March 2020
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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

−	{{translate\|pageName=http://wiki.~~stat~~.~~ucla~~.edu~~/socr~~/index.php?title=AP_Statistics_Curriculum_2007_IntroTools}}	+	"{{translate\|pageName=http://wiki.socr.umich.edu/index.php?title=AP_Statistics_Curriculum_2007_IntroTools}}

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 ===Data Plots===
-Let's first try to plot some of these data. Suppose we take a smaller fraction of the entire dataset. [[AP_Statistics_Curriculum_2007_IntroTools_Data1 | You can find a fragment of 21 rows and 3 columns of measurements here]]. This number is large enough to require computer software to graph the data. In column 1, this data subset includes an index of the region (blob) and in column 2, a pair of MEAN & Standard Deviation for the intensities over the blob (within the Left Occipital lobe). Now go to [http://www.socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts] and select the ''StatisticalBarChardDemo1'' Chart (under ''BarCharts'' --> ''CategoryPlot''), see figure below). '''Clear''' the default data and '''Paste''' in [[AP_Statistics_Curriculum_2007_IntroTools_Data1 | this data segment]]. '''Map''' the first column (C1) to ''Series'' and the second column (C2) to ''Categories'' and click '''UPDATE''' to redraw the graph with the new data. This plot shows the relations between the means and standard deviations of the intensities in the 21 regions (blobs, rows in table). We see that there is variation in both means and standard deviations (error bars on the box plots).
+Let's first try to plot some of these data. Suppose we take a smaller fraction of the entire dataset. [[AP_Statistics_Curriculum_2007_IntroTools_Data1 | You can find a fragment of 21 rows and 3 columns of measurements here]]. This number is large enough to require computer software to graph the data. In column 1, this data subset includes an index of the region (blob) and in column 2, a pair of MEAN & Standard Deviation for the intensities over the blob (within the Left Occipital lobe). Now go to [http://www.socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts] and select the ''StatisticalBarChartDemo1'' Chart (under ''BarCharts'' --> ''CategoryPlot''), see figure below). '''Clear''' the default data and '''Paste''' in [[AP_Statistics_Curriculum_2007_IntroTools_Data1 | this data segment]]. '''Map''' the first column (C1) to ''Series'' and the second column (C2) to ''Categories'' and click '''UPDATE''' to redraw the graph with the new data. This plot shows the relations between the means and standard deviations of the intensities in the 21 regions (blobs, rows in table). We see that there is variation in both means and standard deviations (error bars on the box plots).
 <center>[[Image:SOCR_EBook_Dinov_IntroTools_061707_Fig2.png|400px]]</center>

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 We can easily compute the average weight (66 kg) and height (167 cm) using the [http://en.wikipedia.org/wiki/Sample_mean sample mean-formula]. We can also compute these averages using the [http://www.socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts (BarChart3DDemo1)], or any other statistical package, as shown in the image below.
-<center>[[Image:SOCR_EBook_Dinov_IntroTools_061707_Fig1.png|400px]]</center>
+<center>[[Image:SOCR_EBook_Dinov_IntroTools_061707_Fig1.png|300px]]
 You can see a [[SOCR_Data_Dinov_020108_HeightsWeights | large dataset of human weights and heights here]].

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 |}
-We can easily compute the average weight (66 kg) and height (167 cm) using the [http://en.wikipedia.org/wiki/Sample_mean sample mean-formula]. We can also compute these averages using the [http://www.socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts], or any other statistical package, as shown in the image below.
+We can easily compute the average weight (66 kg) and height (167 cm) using the [http://en.wikipedia.org/wiki/Sample_mean sample mean-formula]. We can also compute these averages using the [http://www.socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts (BarChart3DDemo1)], or any other statistical package, as shown in the image below.
 <center>[[Image:SOCR_EBook_Dinov_IntroTools_061707_Fig1.png|400px]]</center>

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 {| align="center" border="1"
 |-
-| Student Index || 1 || 2 || 3 || 4 || 5 || 6
+| Student_Index || 1 || 2 || 3 || 4 || 5 || 6
 |-
 | Weight || 60 || 75 || 58 || 67|| 56 || 80

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 ===Statistical Analysis===
-Now we can demonstrate the use of [http://www.socr.ucla.edu/htmls/SOCR_Analyses.html SOCR Analyses] to look for Left-Right hemispheric (HEMISPHERE) effects of the average MRI intensities (MEAN) in one Region of Interest (Occipital lobe, ROI=2). For this, we can apply simple Paired T-test. This analysis is justified as the average intensities will follow [[EBook#Chapter_V:_Normal_Probability_Distribution |Normal Distribution]] by the [[SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem | Central Limit Theorem]] and because the left and right hemispheric observations are naturally paired.
+Now we can demonstrate the use of [http://www.socr.ucla.edu/htmls/SOCR_Analyses.html SOCR Analyses] to look for Left-Right hemispheric (HEMISPHERE) effects of the average MRI intensities (MEAN) in one Region of Interest (Occipital lobe, ROI=2). For this, we can apply simple Paired T-test. This analysis is justified as the average intensities that will follow [[EBook#Chapter_V:_Normal_Probability_Distribution |Normal Distribution]] by the [[SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem | Central Limit Theorem]]  because the left and right hemispheric observations are naturally paired.
-* Copy in your mouse buffer the 6<sup>th</sup> (MEAN), 8<sup>th</sup> (HEMISPHERE) and 9<sup>th</sup> (ROI) columns of the [http://www.stat.ucla.edu/~dinov/courses_students.dir/04/Spring/Stat233.dir/HWs.dir/AD_NeuroPsychImagingData1.html following data table]. You can paste these three columns in Excel, or any other spreadsheet program, and reorder the rows first by ROI and then by HEMISPHERE. This will give you [[AP_Statistics_Curriculum_2007_IntroTools_Data | an exert of 240 rows of measurements]] (MEAN) for ROI=2 (Occipital lobe) for each of the two hemispheres. The break down of this number of observations is as follows 240 = 2(hemispheres) * 3 (3D spatial locations, blobs) * 40 (Patients).
+* Copy in your mouse buffer the 6<sup>th</sup> (MEAN), 8<sup>th</sup> (HEMISPHERE) and 9<sup>th</sup> (ROI) columns of the [http://www.stat.ucla.edu/~dinov/courses_students.dir/04/Spring/Stat233.dir/HWs.dir/AD_NeuroPsychImagingData1.html following data table]. You can paste these three columns in Excel, or any other spreadsheet program, and reorder the rows first by ROI and then by HEMISPHERE. This will give you [[AP_Statistics_Curriculum_2007_IntroTools_Data | an exert of 240 rows of measurements]] (MEAN) for ROI=2 (Occipital lobe) for each of the two hemispheres. The breakdown of this number of observations is as follows 240 = 2(hemispheres) * 3 (3D spatial locations, blobs) * 40 (Patients).
 * Copy [[AP_Statistics_Curriculum_2007_IntroTools_Data | these 240 Rows]] and paste them in the Paired T-test Analysis under [http://www.socr.ucla.edu/htmls/SOCR_Analyses.html SOCR Analyses]. Map the MEAN and HEMISPHERE columns to '''Dependent''' and '''Independent''' variables and then click '''Calculate'''. The results indicate that there are significant differences between the Left and Right Occipital mean intensities for these 40 subjects.

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 ==Hands-on Examples & Activities==
 ===Data and Study Design===
-As part of a [[AP_Statistics_Curriculum_2007_IntroTools#References | brain imaging study of Alzheimer's disease *]], the investigators collected the [http://www.stat.ucla.edu/~dinov/courses_students.dir/04/Spring/Stat233.dir/HWs.dir/AD_NeuroPsychImagingData1.html following data]. We will now demonstrate how computer programs, software tools and resources, like [[SOCR]], can help in statistically analyzing larger datasets (certainly  data size over 10 are difficult to calculate by hand correctly). In this case we'll work with 240 measurements derived from data acquired by [[AP_Statistics_Curriculum_2007_IntroTools#References | this study]].
+As part of a [[AP_Statistics_Curriculum_2007_IntroTools#References | brain imaging study of Alzheimer's disease *]], the investigators collected the [http://www.stat.ucla.edu/~dinov/courses_students.dir/04/Spring/Stat233.dir/HWs.dir/AD_NeuroPsychImagingData1.html following data]. We will now demonstrate how computer programs, software tools and resources, like [[SOCR]], can help in statistically analyzing larger datasets (certainly  data size over 10 is difficult to calculate by hand correctly). In this case we'll work with 240 measurements derived from data acquired by [[AP_Statistics_Curriculum_2007_IntroTools#References | this study]].
 ===Data Plots===

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 ==Computational Resources: Internet-based SOCR Tools==
-Several of the [[SOCR]] tools and resources will be shown later to be useful in  a variety of situations. Here is just a list of these with one example of each:
+Several of the [[SOCR]] tools and resources will be shown later, and will be useful in  a various situations. Here is just a list of tools with one example of each:
 * [http://www.socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts] and [[SOCR_EduMaterials_Activities_Histogram_Graphs | Histogram Charts Activity]]
 * [http://www.socr.ucla.edu/htmls/SOCR_Analyses.html SOCR Analyses] and [[SOCR_EduMaterials_AnalysisActivities_SLR | Simple Linear Regression Activity]]

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 ==Statistics with Tools (Calculators and Computers)==
-A critical component in any data analysis or process understanding approach is the development of a model. Models have compact analytical representations (e.g., formulas, symbolic equations, etc.) The model is frequently used to study the process theoretically. Empirical validation of the model is carried by plugging in data and actually testing the model. This validation step 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 write (or use existent) algorithms and computer programs that automate these calculations for better efficiency, accuracy and consistency in applying the model to larger datasets.
+A critical component in any data analysis or process understanding approach is the development of a model. Models have compact analytical representations (e.g., formulas, symbolic equations, etc.) The model is frequently used to study the process theoretically. Empirical validation of the model is carried by plugging in data and actually testing the model. This validation step 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 write (or use existent) algorithms and computer programs that automate these calculations for greater efficiency, accuracy and consistency in applying the model to larger datasets.
 There are a number of [http://en.wikipedia.org/wiki/List_of_statistical_packages statistical software tools (programs) that one can employ for data analysis and statistical processing]. Some of these are: [http://www.sas.com SAS], [http://www.systat.com SYSTAT], [http://www.spss.com SPSS], [http://www.r-project.org R], [[SOCR]], etc.