Statistics - Revision history

Adamcolton: /* Proportions */

2013-10-15T18:46:01Z

Proportions

← Older revision		Revision as of 18:46, 15 October 2013
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	For H<sub>0</sub>: p<sub>1</sub> = p<sub>2</sub>, H<sub>1</sub>: p<sub>1</sub> ? p<sub>2</sub>		For H<sub>0</sub>: p<sub>1</sub> = p<sub>2</sub>, H<sub>1</sub>: p<sub>1</sub> ? p<sub>2</sub>
	Z = (p<sub>1</sub> - p<sub>2</sub>) / [ (p<sub>p</sub>(1-p<sub>p</sub>))*(1/n<sub>1</sub> + 1/n<sub>2</sub> ]		Z = (p<sub>1</sub> - p<sub>2</sub>) / [ (p<sub>p</sub>(1-p<sub>p</sub>))*(1/n<sub>1</sub> + 1/n<sub>2</sub>) ]
	* p<sub>p</sub>: Pooled proportion. Total passes over population.		* p<sub>p</sub>: Pooled proportion. Total passes over population.
	* Z is two tailed		* Z is two tailed

2013-09-18T20:23:12Z

Proportions

← Older revision		Revision as of 20:23, 18 September 2013
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	For H<sub>0</sub>: p<sub>1</sub> = p<sub>2</sub>, H<sub>1</sub>: p<sub>1</sub> ? p<sub>2</sub>		For H<sub>0</sub>: p<sub>1</sub> = p<sub>2</sub>, H<sub>1</sub>: p<sub>1</sub> ? p<sub>2</sub>
	Z = (p<sub>1</sub> - p<sub>2</sub>) / [ (p<sub>p</sub>(1-p<sub>p</sub>))/n<sub>1</sub> + ~~(p<sub>p</sub>(~~1~~-p<sub>p</sub>))~~/n<sub>2</sub> ]		Z = (p<sub>1</sub> - p<sub>2</sub>) / [ (p<sub>p</sub>(1-p<sub>p</sub>))*(1/n<sub>1</sub> + 1/n<sub>2</sub> ]
	* p<sub>p</sub>: Pooled proportion. Total passes over population.		* p<sub>p</sub>: Pooled proportion. Total passes over population.
	* Z is two tailed		* Z is two tailed

			This is useful for paralytics, when comparing two different populations.

	== Student's T Test ==		== Student's T Test ==

2013-04-08T20:00:26Z

Confidence Interval

← Older revision		Revision as of 20:00, 8 April 2013
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	* s: standard deviation		* s: standard deviation
	* n: sample size		* n: sample size

	$
	~~\newcommand{\Re}{\mathrm{Re}\,}~~
	~~\newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg\| {#5} \right)}~~
	$


	[[Category:Notes]]		[[Category:Notes]]

2013-04-08T20:00:07Z

Confidence Interval

← Older revision		Revision as of 20:00, 8 April 2013
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	* s: standard deviation		* s: standard deviation
	* n: sample size		* n: sample size

			$
			\newcommand{\Re}{\mathrm{Re}\,}
			\newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg\| {#5} \right)}
			$


	[[Category:Notes]]		[[Category:Notes]]

2013-04-08T19:40:36Z

T Distribution

← Older revision		Revision as of 19:40, 8 April 2013
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	* Z is two tailed		* Z is two tailed

	== T ~~Distribution~~ ==		== Student's T Test ==
	t = n^.5 * (x - μ) / s		t = n^.5 * (x - μ) / s
	* x: sample mean (really should be x-bar)		* x: sample mean (really should be x-bar)
	* μ: population mean		* μ: population mean
	* s: sample standard deviation		* s: sample standard deviation
			* n: sample size

			=== Confidence Interval ===
			CI = x ± ( t <sub> α/2 , df</sub>)(s / n<sup>0.5</sup>)
			* x: mean (x bar)
			* t: this needs to be [http://easycalculation.com/statistics/t-distribution-critical-value-table.php looked-up] in a table
			* s: standard deviation
	* n: sample size		* n: sample size


	[[Category:Notes]]		[[Category:Notes]]

2013-04-08T19:13:44Z

Proportions

← Older revision		Revision as of 19:13, 8 April 2013
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	* p<sub>p</sub>: Pooled proportion. Total passes over population.		* p<sub>p</sub>: Pooled proportion. Total passes over population.
	* Z is two tailed		* Z is two tailed

			== T Distribution ==
			t = n^.5 * (x - μ) / s
			* x: sample mean (really should be x-bar)
			* μ: population mean
			* s: sample standard deviation
			* n: sample size


	[[Category:Notes]]		[[Category:Notes]]

2013-04-08T18:50:30Z

Chi-Squared

2013-04-08T14:58:46Z

Proportions

← Older revision		Revision as of 14:58, 8 April 2013
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	=== Proportions ===		=== Proportions ===
	For H<sub>0</sub>: p = π<sub>0</sub>, H<sub>1</sub> ~~π<sub>0</sub>~~ > π<sub>0</sub>		For H<sub>0</sub>: p = π<sub>0</sub>, H<sub>1</sub> p > π<sub>0</sub>
	z = (p-π<sub>0</sub>) / [ (π<sub>0</sub>(1-π<sub>0</sub>)) / n ]<sup>0.5</sup>		Z = (p-π<sub>0</sub>) / [ (π<sub>0</sub>(1-π<sub>0</sub>)) / n ]<sup>0.5</sup>
	* p: proportion observed		* p: proportion observed
	* π<sub>0</sub>: proportion expected (being tested)		* π<sub>0</sub>: proportion expected (being tested)
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	* Z is single tailed		* Z is single tailed

	~~When looking up the~~ Z ~~value, be sure to include if it~~ is ~~one or~~ two tailed		For H<sub>0</sub>: p<sub>1</sub> = p<sub>2</sub>, H<sub>1</sub>: p<sub>1</sub> ? p<sub>2</sub>
			Z = (p<sub>1</sub> - p<sub>2</sub>) / [ (p<sub>p</sub>(1-p<sub>p</sub>))/n<sub>1</sub> + (p<sub>p</sub>(1-p<sub>p</sub>))/n<sub>2</sub> ]
			* p<sub>p</sub>: Pooled proportion. Total passes over population.
			* Z is two tailed


	[[Category:Notes]]		[[Category:Notes]]

2013-04-08T14:49:44Z

McNemar's Test for Matched Pairs

@@ Line 144: / Line 144: @@
 |}
    x<sup>2</sup> = (b-c)<sup>2</sup> / (b+c)
 [[Category:Notes]]

2013-04-08T14:36:31Z

McNemar's Test for Matched Pairs

← Older revision		Revision as of 14:36, 8 April 2013
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	=== McNemar's Test for Matched Pairs ===		=== McNemar's Test for Matched Pairs ===
	A Type of Chi-squared test. Takes 2x2 Chi data but computes X with		A Type of Chi-squared test. Takes 2x2 Chi data but computes X with

			Given:
			{\| class="wikitable"
			\|a
			\|b
			\|-
			\|c
			\|d
			\|}
	x<sup>2</sup> = (b-c)<sup>2</sup> / (b+c)		x<sup>2</sup> = (b-c)<sup>2</sup> / (b+c)

	[[Category:Notes]]		[[Category:Notes]]