Proportion Estimation - Revision history

Rice at 17:43, 18 March 2024

2024-03-18T17:43:00Z

← Older revision		Revision as of 17:43, 18 March 2024
Line 38:		Line 38:
	\widetilde{p} = \frac{y + 2}{n + 4}		\widetilde{p} = \frac{y + 2}{n + 4}
	</math>		</math>

			This essentially adds two samples that fits the traits and two that does
			not into consideration. It doesn't impact large samples but works "well"
			with small samples.

	with standard error		with standard error
Line 45:		Line 49:
	</math>		</math>

	Remember that the confidence interval is ca		Remember that the confidence interval is mean plus or minus standard
			error.

	<math>\widetilde{p}</math> is slightly skewed towards <math>0.5</math>,		<math>\widetilde{p}</math> is slightly skewed towards <math>0.5</math>,
Line 52:		Line 57:
	= Confidence Interval =		= Confidence Interval =

	We use ''normal distribution'' since <math>p</math> is bounded between		We use ''normal distribution'' since <math>p</math> is bounded between 0
	0 and 1, and we don't have extra error from extra parameters such as		and 1, and we don't have extra error from extra parameters such as
	multiple sample mean.		multiple sample mean.

2024-03-16T02:32:48Z

@@ Line 21: / Line 21: @@
 SE = \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}
 </math>
 = Wilson-Adjusted CI for p =
@@ Line 28: / Line 36: @@
 <math>
-\widetilde{p}
+\widetilde{p} = \frac{y + 2}{n + 4}
 </math>
 [[Category:Sample Statistics]]

2024-03-16T02:01:21Z

← Older revision	Revision as of 02:01, 16 March 2024
Line 1:	Line 1:
		Proportion estimation is another common task for sample statistics.

		We have sample proportion

		<math>
		\hat{p} = \frac{y}{n}
		</math>

		where <math>y</math> is the number of subjects in the sample with a
		particular trait, and <math>n</math> is the sample size.

		We have

		<math>
		\mu_\hat{p} = p, \sigma_\hat{p} = \sqrt{\frac{p (1 - p)}{n}}
		</math>

		and standard error

		<math>
		SE = \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}
		</math>

		= Wilson-Adjusted CI for p =

		''Correcting'' the sample proportion narrows the confidence interval. We
		do this with the '''Wilson-Adjusted estimate''' for <math>p</math>

		<math>
		\widetilde{p}
		</math>

		[[Category:Sample Statistics]]

2024-03-16T02:01:02Z

Blanked the page

← Older revision		Revision as of 02:01, 16 March 2024
Line 1:		Line 1:
	~~Proportion estimation is another common task for sample statistics.~~

	~~We have sample proportion~~

	~~<math>~~
	~~\hat{p} = \frac{y}{n}~~
	~~</math>~~

	~~where <math>y</math> is the number of subjects in the sample with a~~
	~~particular trait, and <math>n</math> is the sample size.~~

	~~We have~~

	~~<math>~~
	~~\mu_\hat{p} = p, \sigma_\hat{p} = \sqrt{\frac{p (1 - p)}{n}}~~
	~~</math>~~

	~~and standard error~~

	~~<math>~~
	~~SE = \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}~~
	~~</math>~~

	~~= Wilson-Adjusted CI for p =~~

	~~''Correcting'' the sample proportion narrows the confidence interval. We~~
	~~do this with the '''Wilson-Adjusted estimate''' for <math>p</math>~~

	~~<math>~~
	~~\widetilde{p}~~
	~~</math>~~

	~~[[Category:Sample Statistics]]~~

2024-03-16T02:00:59Z

← Older revision		Revision as of 02:00, 16 March 2024
Line 1:		Line 1:
	Proportion estimation is another common task for sample statistics.		Proportion estimation is another common task for sample statistics.

			We have sample proportion

	<math>		<math>
Line 18:		Line 20:
	<math>		<math>
	SE = \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}		SE = \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}
			</math>

			= Wilson-Adjusted CI for p =

			''Correcting'' the sample proportion narrows the confidence interval. We
			do this with the '''Wilson-Adjusted estimate''' for <math>p</math>

			<math>
			\widetilde{p}
	</math>		</math>

	[[Category:Sample Statistics]]		[[Category:Sample Statistics]]

2024-03-16T01:58:39Z

← Older revision	Revision as of 01:58, 16 March 2024
Line 1:	Line 1:
		Proportion estimation is another common task for sample statistics.

		<math>
		\hat{p} = \frac{y}{n}
		</math>

		where <math>y</math> is the number of subjects in the sample with a
		particular trait, and <math>n</math> is the sample size.

		We have

		<math>
		\mu_\hat{p} = p, \sigma_\hat{p} = \sqrt{\frac{p (1 - p)}{n}}
		</math>

		and standard error

		<math>
		SE = \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}
		</math>

		[[Category:Sample Statistics]]

2024-03-16T01:56:03Z

Created blank page

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