AP Statistics Curriculum 2007 NonParam 2PropIndep - Revision history

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

2020-03-03T19:03:49Z

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

Dinov: /* General McNemar test of marginal homogeneity for a single category */

2014-10-26T15:16:14Z

‎General McNemar test of marginal homogeneity for a single category

Jenny at 17:41, 28 June 2010

2010-06-28T17:41:51Z

IvoDinov: /* Example */ typo

2008-04-29T19:37:10Z

‎Example: typo

IvoDinov at 04:27, 14 April 2008

2008-04-14T04:27:20Z

IvoDinov at 04:24, 14 April 2008

2008-04-14T04:24:53Z

IvoDinov at 04:10, 14 April 2008

2008-04-14T04:10:31Z

IvoDinov at 04:07, 14 April 2008

2008-04-14T04:07:53Z

PriscillaChui: /* General Advance-Placement (AP) Statistics Curriculum - Two-Samples Difference of Proportions */

2008-03-10T23:14:42Z

‎ General Advance-Placement (AP) Statistics Curriculum - Two-Samples Difference of Proportions

PriscillaChui: /* General Advance-Placement (AP) Statistics Curriculum - Two-Samples Difference of Proportions */

2008-03-01T23:10:33Z

‎ General Advance-Placement (AP) Statistics Curriculum - Two-Samples Difference of Proportions

← Older revision		Revision as of 19:03, 3 March 2020
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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

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← Older revision		Revision as of 15:16, 26 October 2014
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	<center>[[Image:SOCR_EBook_Dinov_NonParam_McNemar_041408_Fig1.jpg\|500px]]</center>		<center>[[Image:SOCR_EBook_Dinov_NonParam_McNemar_041408_Fig1.jpg\|500px]]</center>
		+
		+	* [[SMHS_NonParamInference#McNemar_Test\|See also the SMHS Ebook section on the McNemar Test]]

	==References==		==References==

@@ Line 28: / Line 28: @@
 </center>
-'''Marginal homogeneity''' occurs when the row totals are equal to the column totals, ''a'' and ''d'' in each equation can be cancelled; leaving ''b'' equal to ''c'':
+'''Marginal homogeneity''' occurs when the row totals equal to the column totals, ''a'' and ''d'' in each equation can be cancelled; leaving ''b'' equal to ''c'':
 :<math>a+b = a+c \,</math>

@@ Line 20: / Line 20: @@
 |  <math>D^+</math> || <math>D^-</math>|| '''Total'''
 |-
-| rowspan=3| '''Before Treatment''' || <math>D^+</math> ||  a=101 ||  b=59 || a+b=160
+| rowspan=3| '''After Treatment''' || <math>D^+</math> ||  a=101 ||  b=59 || a+b=160
 |-
 |  <math>D^-</math> || c=121 || d=33 || c+d=154

@@ Line 44: / Line 44: @@
 ===General McNemar test of marginal homogeneity for a single category===
-If we have observed measurements on a K-level categorical variable -- e.g., agreement between two evaluators summarized by a K×K classification table, where each row or column contains the number of individuals rated as part of this group by each evaluator. For instance, two instructors may evaluate students as 1=poor, 2=good and 3=excellent. There could be significant differences in the evaluations of the same students by the 2 instructors. Suppose we are interested in whether the proportions of students rated ''excellent'' by the 2 instructors are the same. Then we'll pool the ''poor'' and  ''good'' categories together and form a 2x2 table that we can then use the 2x2 McNemar test statistics on, as shown below.
+If we have observed measurements on a K-level categorical variable -- e.g., agreement between two evaluators summarized by a K×K classification table, where each row or column contains the number of individuals rated as part of this group by each evaluator. For instance, two instructors may evaluate students as 1=poor, 2=good and 3=excellent. There could be significant differences in the evaluations of the same students by the 2 instructors. Suppose we are interested in whether the proportions of students rated ''excellent'' by the 2 instructors are the same. Then we'll pool the ''poor'' and ''good'' categories together and form a 2x2 table that we can then use the 2x2 McNemar test statistics on, as shown below.
 <center>
 {| class="wikitable" title="Title1" style="text-align:center; width:35%" border="1"
 |-
-| || || colspan="4" align="center"|Evaluator 2
+| || || colspan="4" align="center"| Evaluator 2
 |-
 |  || || Poor || Good || Excellent || Total
@@ Line 79: / Line 79: @@
 : <math>x_o^2 = {(b-c)^2 \over b+c} = {(-8)^2 \over 46} = 1.39 \sim \chi_{(df=1)}^2</math>
-: <math>P(\chi_{(df=1)}^2 > 1.39) = 0.238405</math> and therefore, we do not have sufficient evidence to reject a hull hypotheses that the 2evaluators were consistent in their ratings of students.
+: <math>P(\chi_{(df=1)}^2 > 1.39) = 0.238405</math> and therefore, we do not have sufficient evidence to reject a hull hypotheses that the 2 evaluators were consistent in their ratings of students.
 <center>[[Image:SOCR_EBook_Dinov_NonParam_McNemar_041408_Fig1.jpg|500px]]</center>

@@ Line 68: / Line 68: @@
 |  || || Poor || Good or Excellent || Total
 |-
-| rowspan=3 | Evaluator 1 || Poor || 5 || 19 || 24
+| rowspan=3 | Evaluator 1 || Poor || a=5 || b=19 || a+b=24
 |-
-| Good or Excellent || 27 || 49 || 76
+| Good or Excellent || c=27 || d=49 || c+d=76
 |-
-| Total || 32 || 68 || 100
+| Total || a+c=32 || b+d=68 || a+b+c+d=100
 |}
 </center>
@@ Line 78: / Line 78: @@
 To test '''marginal homogeneity''' for one single category (in this case ''poor evaluation'') means to test row/column marginal homogeneity for the first category (poor). This is achieved by collapsing all rows and columns corresponding to the other categories.
 ==References==

@@ Line 47: / Line 47: @@
 <center>
-{| class="wikitable" title="Title1" style="text-align:center; width:75%" border="1"
+{| class="wikitable" title="Title1" style="text-align:center; width:35%" border="1"
 |-
-| || || colspan="3" align="center"|Evaluator 2||
+| || || colspan="4" align="center"|Evaluator 2
 |-
 |  || || Poor || Good || Excellent || Total
@@ Line 62: / Line 62: @@
 |}
-{| class="wikitable" title="Title2" style="text-align:center; width:75%" border="1"
+{| class="wikitable" title="Title2" style="text-align:center; width:35%" border="1"
 |-
-| || || colspan="3" align="center"|Evaluator 2||
+| || || colspan="3" align="center"|Evaluator 2
 |-
 |  || || Poor || Good or Excellent || Total

@@ Line 3: / Line 3: @@
 ===Differences of Proportions of Two Independent Samples===
 If the samples are independent and we are interested in the differences in the proportions of subjects of the same trait (a characteristic of each observation, e.g., gender) we need to use the [[AP_Statistics_Curriculum_2007_Hypothesis_Proportion | standard proportion tests]]
-: For small sample-sizes, we use corrected-proportions (<math>\tilde{p}</math>) that we saw in the [[AP_Statistics_Curriculum_2007_Hypothesis_Proportion | independent sample tests for proportions section]].
+: For small sample-sizes, we use corrected-proportions (<math>\tilde{p}</math>) that we saw in the [[AP_Statistics_Curriculum_2007_Hypothesis_Proportion | ''Independent Sample Tests for Proportions'' section]].
-: For large samples, we can use the raw-sample proportion (<math>\hat{p}</math>) as in the [[AP_Statistics_Curriculum_2007_Hypothesis_Proportion | independent sample tests for proportions section]].
+: For large samples, we can use the raw-sample proportion (<math>\hat{p}</math>) as in the [[AP_Statistics_Curriculum_2007_Hypothesis_Proportion | ''Independent Sample Tests for Proportions'' section]].
 ===Differences of Proportions of Two Paired-Samples===
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 :<math>\chi_o^2 = {(b-c)^2 \over b+c} \sim \chi_{(df=1)}^2</math>
-The marginal frequencies are not homogeneous if the <math>\chi^2</math> result is significant ''p'' < 0.05. If ''b'' and/or ''c'' are small (''b''&nbsp;+&nbsp;''c'' < 20) then  <math>\chi^2</math> is not approximated by the Chi-square distribution and a [[AP_Statistics_Curriculum_2007_NonParam_2MedianPair | sign test]] should instead be used.
+The marginal frequencies are not homogeneous if the <math>\chi^2</math> result is significant ''p'' < 0.05. If ''b'' and/or ''c'' are small (''b''&nbsp;+&nbsp;''c'' < 20) then  <math>\chi^2</math> is not approximated by the Chi-Square Distribution and a [[AP_Statistics_Curriculum_2007_NonParam_2MedianPair | Sign Test]] should instead be used.
 An interesting observation when interpreting McNemar's test is that the elements of the main diagonal contribute no information whatsoever to the decision if (in the above example) pre- or post-treatment condition is more favorable.

← Older revision		Revision as of 23:10, 1 March 2008
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−	===[[AP_Statistics_Curriculum_2007 \| General Advance-Placement (AP) Statistics Curriculum]] - Two-Samples Difference of Proportions===	+	==[[AP_Statistics_Curriculum_2007 \| General Advance-Placement (AP) Statistics Curriculum]] - Two-Samples Difference of Proportions==

	===Differences of Proportions of Two Independent Samples===		===Differences of Proportions of Two Independent Samples===