Difference between revisions of "SOCR EduMaterials Activities ConfidenceIntervals"

From SOCR
Jump to: navigation, search
(See also: added a link to general CI activity)
 
(6 intermediate revisions by 3 users not shown)
Line 1: Line 1:
== [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities ]] - SOCR COnfidence Intervals Activity ==
+
== [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities ]] - SOCR Confidence Intervals Activity ==
  
== URL Go to: http://www.socr.ucla.edu/htmls/SOCR_Experiments.html ==
+
Go to the [http://socr.ucla.edu/htmls/exp/Confidence_Interval_Experiment.html SOCR Confidence Interval applet]. Choose the '''Confidence Interval (CI) Experiment'''. In this [[Help_pages_for_SOCR_Experiments | experiment]] you will investigate the empirical properties of the sample-size, confidence level, the size of the constructed confidence interval and the practical utilization of Confidence Intervals in statistical data analysis
 
 
* '''To begin''': Choose the Confidence Interval (CI) Experiment. In this [[Help_pages_for_SOCR_Experiments | experiment]] you will investigate the emperical properties of the sample-size, confidence level, the size of the constructed confidence interval and the practical utilization of Confidence Intervals in statistical data analysis
 
 
<center>[[Image:SOCR_Activities_CI_Dinov_092206_Fig1.jpg|300px]]</center>
 
<center>[[Image:SOCR_Activities_CI_Dinov_092206_Fig1.jpg|300px]]</center>
  
* '''Exercise 1''': Chose the confidence level (α), the sample-size and the number of experiments (see the image below). Click on the <nowiki><STEP></nowiki> button - this performs one set of experiments (20 in this case). Each experiment consist of generating a random sample of the given size (5, in this case) from the standard Normal Distribution, N(0,1). The samples along with the constructed confidence intervals are then displayed. Notice the ixperiments that have a green dot below the corresponding confidence intervals. These are the cases where the <i>parameter</i> being estimated by the confidence interval (population mean, in this case) is outside the corresponding confidence interval (above the right-CI-limit, or below the left-CI-limit).  
+
===Exercise 1===
 +
Chose the confidence level (α), the sample-size and the number of experiments (see the image below). Click on the <nowiki><STEP></nowiki> button - this performs one set of experiments (20 in this case). Each experiment consist of generating a random sample of the given size (5, in this case) from the standard Normal Distribution, N(0,1). The samples along with the constructed confidence intervals are then displayed. Notice the experiments that have a green dot below the corresponding confidence intervals. These are the cases where the <i>parameter</i> being estimated by the confidence interval (population mean, in this case) is outside the corresponding confidence interval (above the right-CI-limit, or below the left-CI-limit).  
  
You can use the <nowiki><SHAPSHOT></nowiki> button to save as a JPEG image the state of your SOCR experiment on your local computer. The <nowiki><RUN></nowiki> allows you to sequantially run large number of sets of experiments (determined by the <nowiki><Number of Experiments></nowiki> selection) and monitor the results. Also, the text-area on the bottom of the applet summarizes the results of these sexperiments.
+
You can use the <nowiki><SHAPSHOT></nowiki> button to save as a JPEG image the state of your SOCR experiment on your local computer. The <nowiki><RUN></nowiki> allows you to sequantially run large number of sets of experiments (determined by the <nowiki><Number of Experiments></nowiki> selection) and monitor the results. Also, the text-area on the bottom of the applet summarizes the results of these experiments.
  
 
<center>[[Image:SOCR_Activities_CI_Dinov_092206_Fig2.jpg|300px]]</center>
 
<center>[[Image:SOCR_Activities_CI_Dinov_092206_Fig2.jpg|300px]]</center>
 
   
 
   
* '''Question 1''': Would you get the same results (what are the results?) if you did this again? If someone else did this? Explain!
+
====Question 1====
 +
Would you get the same results (what are the results?) if you did this again? If someone else did this? Explain!
  
  
* '''Exercise 2''': Now change the sample-size (from 5 to 35) and press <nowiki><STEP></nowiki>, or <nowiki><RUN></nowiki>. You will notice that the result of the experiment changes significantly (e.g., we have 35 randomly sampled observations plotted in each of the 20 experiments). Also, observe the new summary statistics on the bottom.
+
===Exercise 2===
 +
Now change the sample-size (from 5 to 35) and press <nowiki><STEP></nowiki>, or <nowiki><RUN></nowiki>. You will notice that the result of the experiment changes significantly (e.g., we have 35 randomly sampled observations plotted in each of the 20 experiments). Also, observe the new summary statistics on the bottom.
  
 
<center>[[Image:SOCR_Activities_CI_Dinov_092206_Fig3.jpg|300px]]</center>
 
<center>[[Image:SOCR_Activities_CI_Dinov_092206_Fig3.jpg|300px]]</center>
  
+
====Question 2====
* '''Question 2''': Does the fact that we increased (to 35) the sample-size caused the lack of green-dots (indicators of CIs that do not contain the estimated parameter, μ=0) on this outcome?
+
Does the fact that we increased (to 35) the sample-size caused the lack of green-dots (indicators of CIs that do not contain the estimated parameter, μ=0) on this outcome?
 
How are the CI widths effected by this sample-size increase? Is there a theoretical reason for this observation? Explain! Are we more or less likely to get extreme observations now (sample-size=35) than before (when the sample-size=5)?
 
How are the CI widths effected by this sample-size increase? Is there a theoretical reason for this observation? Explain! Are we more or less likely to get extreme observations now (sample-size=35) than before (when the sample-size=5)?
  
* '''Exercise 3''': Finally try changing the alpha-level (α) and the number of experiments? What effects can you predict?
+
===Exercise 3===Finally try changing the alpha-level (α) and the number of experiments? What effects can you predict?
  
 
<center>[[Image:SOCR_Activities_CI_Dinov_092206_Fig4.jpg|300px]]</center>
 
<center>[[Image:SOCR_Activities_CI_Dinov_092206_Fig4.jpg|300px]]</center>
  
* '''Question 3''': Do you expect an effect on the amount or frequency of the green-dots, when y ou alter the values for α and number of experiments?  
+
====Question 3====
 +
Do you expect an effect on the amount or frequency of the green-dots, when y ou alter the values for α and number of experiments?  
 +
 
 +
===See also===
 +
* [[SOCR_EduMaterials_Activities_CoinfidenceIntervalExperiment | Another SOCR Confidence Interval Activity]].
 +
* [[SOCR_EduMaterials_Activities_General_CI_Experiment | General SOCR Confidence Interval Activity]].
  
 
<hr>
 
<hr>

Latest revision as of 01:03, 24 November 2009

SOCR Educational Materials - Activities - SOCR Confidence Intervals Activity

Go to the SOCR Confidence Interval applet. Choose the Confidence Interval (CI) Experiment. In this experiment you will investigate the empirical properties of the sample-size, confidence level, the size of the constructed confidence interval and the practical utilization of Confidence Intervals in statistical data analysis

SOCR Activities CI Dinov 092206 Fig1.jpg

Exercise 1

Chose the confidence level (α), the sample-size and the number of experiments (see the image below). Click on the <STEP> button - this performs one set of experiments (20 in this case). Each experiment consist of generating a random sample of the given size (5, in this case) from the standard Normal Distribution, N(0,1). The samples along with the constructed confidence intervals are then displayed. Notice the experiments that have a green dot below the corresponding confidence intervals. These are the cases where the parameter being estimated by the confidence interval (population mean, in this case) is outside the corresponding confidence interval (above the right-CI-limit, or below the left-CI-limit).

You can use the <SHAPSHOT> button to save as a JPEG image the state of your SOCR experiment on your local computer. The <RUN> allows you to sequantially run large number of sets of experiments (determined by the <Number of Experiments> selection) and monitor the results. Also, the text-area on the bottom of the applet summarizes the results of these experiments.

SOCR Activities CI Dinov 092206 Fig2.jpg

Question 1

Would you get the same results (what are the results?) if you did this again? If someone else did this? Explain!


Exercise 2

Now change the sample-size (from 5 to 35) and press <STEP>, or <RUN>. You will notice that the result of the experiment changes significantly (e.g., we have 35 randomly sampled observations plotted in each of the 20 experiments). Also, observe the new summary statistics on the bottom.

SOCR Activities CI Dinov 092206 Fig3.jpg

Question 2

Does the fact that we increased (to 35) the sample-size caused the lack of green-dots (indicators of CIs that do not contain the estimated parameter, μ=0) on this outcome? How are the CI widths effected by this sample-size increase? Is there a theoretical reason for this observation? Explain! Are we more or less likely to get extreme observations now (sample-size=35) than before (when the sample-size=5)?

===Exercise 3===Finally try changing the alpha-level (α) and the number of experiments? What effects can you predict?

SOCR Activities CI Dinov 092206 Fig4.jpg

Question 3

Do you expect an effect on the amount or frequency of the green-dots, when y ou alter the values for α and number of experiments?

See also




Translate this page:

(default)
Uk flag.gif

Deutsch
De flag.gif

Español
Es flag.gif

Français
Fr flag.gif

Italiano
It flag.gif

Português
Pt flag.gif

日本語
Jp flag.gif

България
Bg flag.gif

الامارات العربية المتحدة
Ae flag.gif

Suomi
Fi flag.gif

इस भाषा में
In flag.gif

Norge
No flag.png

한국어
Kr flag.gif

中文
Cn flag.gif

繁体中文
Cn flag.gif

Русский
Ru flag.gif

Nederlands
Nl flag.gif

Ελληνικά
Gr flag.gif

Hrvatska
Hr flag.gif

Česká republika
Cz flag.gif

Danmark
Dk flag.gif

Polska
Pl flag.png

România
Ro flag.png

Sverige
Se flag.gif