SOCR EduMaterials Activities GeneralCentralLimitTheorem - Revision history

Dinov: added link to CLT animation

2020-02-12T17:10:22Z

added link to CLT animation

IvoDinov: /* References */

2013-05-16T12:23:27Z

‎References

IvoDinov: /* The SOCR CLT Experiment */

2013-05-16T12:21:22Z

‎The SOCR CLT Experiment

IvoDinov at 23:53, 8 August 2009

2009-08-08T23:53:52Z

IvoDinov: /* References */

2009-08-08T23:45:45Z

‎References

IvoDinov: /* SOCR Educational Materials - Activities - SOCR General Central Limit Theorem (CLT) Activity */

2009-06-20T16:37:26Z

‎SOCR Educational Materials - Activities - SOCR General Central Limit Theorem (CLT) Activity

IvoDinov: added references section

2008-08-23T00:33:11Z

added references section

Rgidwani at 19:10, 8 July 2007

2007-07-08T19:10:00Z

IvoDinov: /* Experiment 1 */

2007-06-30T20:48:00Z

‎Experiment 1

IvoDinov at 20:46, 30 June 2007

2007-06-30T20:46:48Z

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 * Show that the variation of the sampling distribution of the mean rapidly decreases as the sample size increases (<math> ~1\over{\sqrt{n}}</math>).
 * Reinforce the concepts of a native distribution, sample, sample distribution, sampling distribution, parameter estimator and data-driven numerical parameter estimate.
 ==The SOCR CLT Experiment==

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 ==References==
-* Dinov, ID, Christou, N and Sanchez, J. (2008) [http://www.amstat.org/publications/jse/v16n2/dinov.html Central Limit Theorem: New SOCR Applet and Demonstration Activity], [http://www.amstat.org/publications/jse/ Journal of Statistics Education], Volume 16, Number 2.
+* Dinov, ID, Christou, N and Sanchez, J. (2008) [http://www.amstat.org/publications/jse/v16n2/dinov.html Central Limit Theorem: New SOCR Applet and Demonstration Activity], [http://www.amstat.org/publications/jse/ Journal of Statistics Education], 16(2):1-15.
 * [[SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem2 | Second SOCR CLT Activity]]
 * [[AP_Statistics_Curriculum_2007_Limits_CLT | EBook CLT Section]]

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 ==The SOCR CLT Experiment==
-To start the this Experiment, go to [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] and select the SOCR Sampling Distribution CLT Experiment from the drop-down list of experiments in the left panel. The image below shows the interface to this experiment. Notice the main control widgets on this image (boxed in blue and pointed to by arrows). The generic control buttons on the top allow you to do one or multiple steps/runs, stop and reset this experiment. The two tabs in the main frame provide graphical access to the results of the experiment (Histograms and Summaries) or the Distribution selection panel (Distributions). Remember that choosing sample-sizes <= 16 will animate the samples (second graphing row), whereas larger sample-sizes (N>20) will only show the updates of the sampling distributions (bottom two graphing rows).
+To start the this Experiment, go to [http://socr.ucla.edu/htmls/exp/Sampling_Distribution_CLT_Experiment.html SOCR Experiments] and select the SOCR Sampling Distribution CLT Experiment from the drop-down list of experiments in the left panel. The image below shows the interface to this experiment. Notice the main control widgets on this image (boxed in blue and pointed to by arrows). The generic control buttons on the top allow you to do one or multiple steps/runs, stop and reset this experiment. The two tabs in the main frame provide graphical access to the results of the experiment (Histograms and Summaries) or the Distribution selection panel (Distributions). Remember that choosing sample-sizes <= 16 will animate the samples (second graphing row), whereas larger sample-sizes (N>20) will only show the updates of the sampling distributions (bottom two graphing rows).
 <center>[[Image:SOCR_Activities_General_CLT_Dinov_012207_Fig1.jpg|400px]]</center>

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 The aims of this activity are to:
 * Provide intuitive notion of sampling from any process with a well-defined distribution.
-* Motivate and facilitate learning of the [http://en.wikipedia.org/wiki/Central_limit_theorem central limit theorem].
+* Motivate and facilitate learning of the [[AP_Statistics_Curriculum_2007_Limits_CLT | CLT]].
 * Empirically validate that sample-averages of random observations (most processes) follow approximately [http://en.wikipedia.org/wiki/Normal_distribution normal distribution].
 * Empirically demonstrate that the ''sample-average'' is special and other [http://en.wikipedia.org/wiki/Point_estimator sample statistics] (e.g., median, variance, range, etc.) generally do not have distributions that are normal.

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 * Dinov, ID, Christou, N and Sanchez, J. (2008) [http://www.amstat.org/publications/jse/v16n2/dinov.html Central Limit Theorem: New SOCR Applet and Demonstration Activity], [http://www.amstat.org/publications/jse/ Journal of Statistics Education], Volume 16, Number 2.
 * [[SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem2 | Second SOCR CLT Activity]]
 * SOCR Home page: http://www.socr.ucla.edu.
 * [http://www.merlot.org/merlot/viewMaterial.htm?id=236831 SOCR CLT Activity at MERLOT].

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 == [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities]] - SOCR General Central Limit Theorem (CLT) Activity ==
-This activity represents a very general demonstration of the the [http://en.wikipedia.org/wiki/Central_limit_theorem Central Limit Theorem (CLT)]. The activity is based on the [http://socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Sampling Distribution CLT Experiment]. This experiment builds upon a [http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/ RVLS CLT applet] by extending the applet functionality and providing the capability of sampling from any [[About_pages_for_SOCR_Distributions | SOCR Distribution]].
+This activity represents a very general demonstration of the [http://en.wikipedia.org/wiki/Central_limit_theorem Central Limit Theorem (CLT)]. The activity is based on the [http://socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Sampling Distribution CLT Experiment]. This experiment builds upon a [http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/ RVLS CLT applet] by extending the applet functionality and providing the capability of sampling from any [[About_pages_for_SOCR_Distributions | SOCR Distribution]].
 ----

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 ===Experiment 1===
-Expand your Experiment panel (right panel) by clicking/dragging the vertical split-pane bar. Choose the two sample sizes for the two statistics to be 10. Press the '''step'''-button a few of times (2-5) to see the experiment run several times. Notice how data is being sampled from the native population (the distribution of the process on the top). For each step, the process of sampling 2 samples of 10 observations will generate 2 sample statistics of the 2 parameters of interest (these are defaulted to ''mean'' and ''variance''). At each step, you can see the plots of all sample values, as well as the computed sample statistics for each parameter. The sample values are shown on the second row graph, below the distribution of the process, and the two sample statistics are plotted on the bottom two rows. If we run this experiment many times, the bottom two graphs/histograms become good approximations to the corresponging sampling distributions. If we did this infinitely many times these two graphs become the sampling distributions of the chosen sample statistics (as the observations/measurements are independent within each sample and between samples). Finally, press the '''Refresh Stats Table''' button on the top to see the sample summary statistics for the native population distribution (row 1), last sample (row 2) and the two sampling distributions, in this case ''mean'' and ''variance'' (rows 3 and 4).
+Expand your Experiment panel (right panel) by clicking/dragging the vertical split-pane bar. Choose the two sample sizes for the two statistics to be 10. Press the '''step'''-button a few of times (2-5) to see the experiment run several times. Notice how data is being sampled from the native population (the distribution of the process on the top). For each step, the process of sampling 2 samples of 10 observations will generate 2 sample statistics of the 2 parameters of interest (these are defaulted to ''mean'' and ''variance''). At each step, you can see the plots of all sample values, as well as the computed sample statistics for each parameter. The sample values are shown on the second row graph, below the distribution of the process, and the two sample statistics are plotted on the bottom two rows. If we run this experiment many times, the bottom two graphs/histograms become good approximations to the corresponding sampling distributions. If we did this infinitely many times these two graphs become the sampling distributions of the chosen sample statistics (as the observations/measurements are independent within each sample and between samples). Finally, press the '''Refresh Stats Table''' button on the top to see the sample summary statistics for the native population distribution (row 1), last sample (row 2) and the two sampling distributions, in this case ''mean'' and ''variance'' (rows 3 and 4).
 <center>[[Image:SOCR_Activities_General_CLT_Dinov_012207_Fig2.jpg|400px]]</center>