AP Statistics Curriculum 2007 Fisher F - Revision history

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

2020-03-03T16:57:52Z

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

JayZzz: /* Fisher's F Distribution */

2011-07-18T22:48:57Z

‎Fisher's F Distribution

JayZzz at 04:36, 7 July 2011

2011-07-07T04:36:50Z

JayZzz at 04:24, 7 July 2011

2011-07-07T04:24:18Z

JayZzz at 06:21, 3 July 2011

2011-07-03T06:21:03Z

JayZzz at 06:20, 3 July 2011

2011-07-03T06:20:47Z

JayZzz at 06:20, 3 July 2011

2011-07-03T06:20:11Z

JayZzz: Created page with '== General Advance-Placement (AP) Statistics Curriculum - Fisher's F Distribution== ===Fisher's F Distribution=== Commonly used as the null di…'

2011-07-02T22:31:32Z

Created page with '== General Advance-Placement (AP) Statistics Curriculum - Fisher's F Distribution== ===Fisher's F Distribution=== Commonly used as the null di…'

New page

==[[AP_Statistics_Curriculum_2007 | General Advance-Placement (AP) Statistics Curriculum]] - Fisher's F Distribution==

===Fisher's F Distribution===
Commonly used as the null distribution of a test statistic, such as in analysis of variance [http://en.wikipedia.org/wiki/Anova (ANOVA)]. Relationship to the [http://wiki.stat.ucla.edu/socr/index.php/AP_Statistics_Curriculum_2007_StudentsT t-distribution] and [beta Distribution].

'''PDF''': 
<math>\frac{\sqrt{\frac{(d_1\,x)^{d_1}\,\,d_2^{d_2}}
{(d_1\,x+d_2)^{d_1+d_2}}}}
{x\,\mathrm{B}\!\left(\frac{d_1}{2},\frac{d_2}{2}\right)}\!</math>

'''CDF''': 
<math>I_{\frac{d_1 x}{d_1 x + d_2}}(d_1/2, d_2/2)\!</math>

'''Mean''': 
<math>\frac{d_2}{d_2-2}\!</math> for <math>d_2 > 2</math>

'''Median''': 
None

'''Variance''': 
<math>\frac{2\,d_2^2\,(d_1+d_2-2)}{d_1 (d_2-2)^2 (d_2-4)}\!</math> for <math>d_2 > 4</math>

'''Support''': 
<math>x \in [0, +\infty)\!</math>

'''1st Moment''': 

'''2nd Moment''': 

'''Kth Moment''':

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 ===Fisher's F Distribution===
-Commonly used as the null distribution of a test statistic, such as in analysis of variance [http://en.wikipedia.org/wiki/Anova (ANOVA)]. Relationship to the [http://wiki.stat.ucla.edu/socr/index.php/AP_Statistics_Curriculum_2007_StudentsT t-distribution] and [beta Distribution].
+Commonly used as the null distribution of a test statistic, such as in analysis of variance [http://wiki.stat.ucla.edu/socr/index.php/AP_Statistics_Curriculum_2007_ANOVA_1Way ANOVA]. Relationship to the [http://wiki.stat.ucla.edu/socr/index.php/AP_Statistics_Curriculum_2007_StudentsT t-distribution] and [http://wiki.stat.ucla.edu/socr/index.php/AP_Statistics_Curriculum_2007_Beta beta Distribution].
 '''PDF''': <br>

@@ Line 17: / Line 17: @@
 '''Median''': <br>
 None
 '''Variance''': <br>

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 '''Support''': <br>
 <math>x \in [0, +\infty)\!</math>
 ===Applications===

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−	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php/~~AP_Statistics_Curriculum_2007_Cauchy~~}}	+	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php/AP_Statistics_Curriculum_2007_Fisher_F}}

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	SOCR F-Distribution Calculator (http://socr.ucla.edu/htmls/dist/Fisher_Distribution.html)		SOCR F-Distribution Calculator (http://socr.ucla.edu/htmls/dist/Fisher_Distribution.html)
		+
		+	<hr>
		+	* SOCR Home page: http://www.socr.ucla.edu
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 <math>x \in [0, +\infty)\!</math>
-'''1st Moment''': <br>
+===Applications===
-'''2nd Moment''': <br>
+{| class="wikitable"
-'''Kth Moment''': <br>
+First, we find the F-ratio: