SOCR EduMaterials Activities QQChart - Revision history

IvoDinov at 22:06, 1 July 2009

2009-07-01T22:06:57Z

IvoDinov at 05:06, 30 June 2009

2009-06-30T05:06:06Z

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2009-06-30T04:53:18Z

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IvoDinov: /* Background */

2009-06-30T04:50:33Z

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PriscillaChui: /* Description */

2008-05-11T19:18:20Z

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PriscillaChui at 20:48, 7 September 2007

2007-09-07T20:48:14Z

PriscillaChui at 06:53, 7 September 2007

2007-09-07T06:53:22Z

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== QUANTILE-QUANTILE CHARTS ==

==Background ==

Quantile-Quantile Charts, or QQ Charts, are plots in which observed values are plotted against theoretical quantiles. From the plotted points, a line of good fit is drawn to show the behavior of the data values against the theoretical distribution.

For references, visit [http://www.statsoft.com/textbook/glosq.html QQ Charts] and [http://www.dreamcalc.com/dchelp/userguide_graphing_examples.htm Examples].

== Description ==

Go to the [http://socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts] and select Line Charts from the items located on the left, then select the demonstration for QQ Charts:

<center>[[Image:SOCR_Activities_QQCharts_Chui_090607_Fig1.jpg|400px]]</center>

The image above is a demonstration of a simple QQ Chart. Both demonstrations are similar because they both show specific data values by plotted points and a line of good fit is drawn to show the behavior of the data.

== Applications ==

One of the most persuasive elements when proposing data and literature to others is a well-designed chart presentation.

For QQ Charts, they may be applied to any data values that consist of observed values and theoretical values such as experiments. Suppose scientists developed theoretical values for water consumption among athletic males by age and weight. They then obtain a sample of the population of males and observed the water consumption for each patient. Graphing these values will allow the scientists to draw a line of good fit and help decide the acceptability of their theories.

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← Older revision		Revision as of 22:06, 1 July 2009
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−	== ~~QUANTILE~~-~~QUANTILE CHARTS~~ ==	+	== [[SOCR_EduMaterials_ChartsActivities\| Charts Activities]] - Quantile-Quantile Plot ==

	== Summary==		== Summary==

← Older revision		Revision as of 05:06, 30 June 2009
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	For QQ Charts, they may be applied to any data values that consist of observed values and theoretical values such as experiments. Suppose scientists developed theoretical values for water consumption among athletic males by age and weight. They then obtain a sample of the population of males and observed the water consumption for each patient. Graphing these values will allow the scientists to draw a line of good fit and help decide the acceptability of their theories.		For QQ Charts, they may be applied to any data values that consist of observed values and theoretical values such as experiments. Suppose scientists developed theoretical values for water consumption among athletic males by age and weight. They then obtain a sample of the population of males and observed the water consumption for each patient. Graphing these values will allow the scientists to draw a line of good fit and help decide the acceptability of their theories.
		+
		+	== See also==
		+	[[SOCR_EduMaterials_Activities_PowerTransformFamily_Graphs\| Power Transform Activity/Applet]].

	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_BallotExperiment}}		{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_BallotExperiment}}

@@ Line 13: / Line 13: @@
 If F() is a [[AP_Statistics_Curriculum_2007_Distrib_RV#Probability_density.2Fmass_and_.28cumulative.29_distribution_functions | cumulative distribution function]], then a quantile (q), also known as a percentile, is defined as a solution to the equation
-: ''F(q) = p'', that is, <math>q = F^{−1}(p)</math>,
+: ''F(q) = p'', that is, <math>q=F^{-1}(p)</math>,
 where p is a given probability. For instance, the median is a <math>50^{th}</math> percentile, is obtained when ''p = 0.5''. So, to generate a QQ plot, we need to invert the CDF, F. For the Normal and many other distributions, the inverse CDF is known in closed form. SOCR implements and exact and approximate methods for computing the inverse CDF function.
 For a given column of data (n = sample size), the following protocol is used to check for normality using [http://socr.ucla.edu/htmls/chart/QQNormalPlotDemo1_Chart.html SOCR QQ Normal Plot]:
 * Column 1: Sort the ''data'' from smallest to largest (column 1).
-* Column 2: Generate the column of ''Normal'' probabilities containing <math>{1\over n+1}, {2\over n+1}, \cdots, {n\over n+1}</math>, n is the number of observations.
+* Column 2: Generate the column of ''Normal'' quantiles using these n probability values: <math>{1\over n+1}, {2\over n+1}, \cdots, {n\over n+1}</math>, where n is the number of observations.
 * Draw a scatter plot of Column 2 (X axis) vs. Column 1 (Y axis).

← Older revision		Revision as of 19:18, 11 May 2008
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	The image above is a demonstration of a simple QQ Chart. Both demonstrations are similar because they both show specific data values by plotted points and a line of good fit is drawn to show the behavior of the data.		The image above is a demonstration of a simple QQ Chart. Both demonstrations are similar because they both show specific data values by plotted points and a line of good fit is drawn to show the behavior of the data.
		+
		+	== Examples & Exercises==
		+	*'''Exercise 1:''' What is the main difference between QQ Charts and other types of charts?

	== Data Type and Format ==		== Data Type and Format ==

← Older revision		Revision as of 19:17, 11 May 2008
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	== QUANTILE-QUANTILE CHARTS ==		== QUANTILE-QUANTILE CHARTS ==
		+
		+	== Summary==
		+	This activity describes the need, general methods and SOCR utilities for QQ charts. The simulated data may then be easily copied and pasted in different SOCR [http://www.socr.ucla.edu/htmls/SOCR_Analyses.html Analyses] or [http://www.socr.ucla.edu/htmls/SOCR_Charts.html Graphing] tools for further interrogation.
		+
		+	==Goals==
		+	The purpose of this activity is to:
		+	*show users how SOCR QQ charts are plotted and what conclusions may be drawn

	==Background ==		==Background ==

@@ Line 10: / Line 10: @@
 ==Background ==
-Quantile-Quantile Charts, or QQ Charts, are plots in which observed values are plotted against theoretical quantiles. From the plotted points, a line of good fit is drawn to show the behavior of the data values against the theoretical distribution.
+Quantile-Quantile Charts, or QQ Charts, are plots in which observed values are plotted against theoretical quantiles. From the plotted points, a line of good fit is drawn to show the behavior of the data values against the theoretical distribution. For references, visit [http://www.statsoft.com/textbook/glosq.html QQ Charts] and [http://www.dreamcalc.com/dchelp/userguide_graphing_examples.htm Examples].
-For references, visit [http://www.statsoft.com/textbook/glosq.html QQ Charts] and [http://www.dreamcalc.com/dchelp/userguide_graphing_examples.htm Examples].
+If F() is a [[AP_Statistics_Curriculum_2007_Distrib_RV#Probability_density.2Fmass_and_.28cumulative.29_distribution_functions | cumulative distribution function]], then a quantile (q), also known as a percentile, is defined as a solution to the equation
 == Description ==

← Older revision		Revision as of 20:48, 7 September 2007
Line 14:		Line 14:

	The image above is a demonstration of a simple QQ Chart. Both demonstrations are similar because they both show specific data values by plotted points and a line of good fit is drawn to show the behavior of the data.		The image above is a demonstration of a simple QQ Chart. Both demonstrations are similar because they both show specific data values by plotted points and a line of good fit is drawn to show the behavior of the data.
		+
		+	== Data Type and Format ==
		+
		+	By clicking '''Data''' between the ''Graph'' and ''Mapping'' button, it allows users to input or vary the values of the data set. There is one type of value allowed in QQ Charts which are numerical or quantitative variables. The image below demonstrates how these values are listed to the corresponding order:
		+
		+	<center>[[Image:SOCR_Activities_QQCharts_Chui_090707_Fig2.jpg\|400px]]</center>

	== Applications ==		== Applications ==