AP Statistics Curriculum 2007 Contingency Indep - Revision history

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

2020-03-03T20:23:59Z

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

Jenny at 21:12, 28 June 2010

2010-06-28T21:12:20Z

Jenny at 21:11, 28 June 2010

2010-06-28T21:11:01Z

Jenny at 17:44, 28 June 2010

2010-06-28T17:44:14Z

IvoDinov: /* Earthquake Insurance Example */ minor table formatting

2009-11-11T08:24:08Z

‎Earthquake Insurance Example: minor table formatting

IvoDinov: /* Motivational example */ minor table formatting

2009-11-11T08:18:12Z

‎Motivational example: minor table formatting

IvoDinov: added a link to the Problems set

2009-10-26T05:25:22Z

added a link to the Problems set

IvoDinov: /* Moths Memory from Caterpillar Stage */

2008-11-05T20:35:07Z

‎Moths Memory from Caterpillar Stage

IvoDinov at 23:36, 11 March 2008

2008-03-11T23:36:35Z

IvoDinov at 23:34, 11 March 2008

2008-03-11T23:34:29Z

← Older revision		Revision as of 20:23, 3 March 2020
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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

−	{{translate\|pageName=http://wiki.~~stat~~.~~ucla~~.edu~~/socr~~/index.php?title=AP_Statistics_Curriculum_2007_Contingency_Indep}}	+	"{{translate\|pageName=http://wiki.socr.umich.edu/index.php?title=AP_Statistics_Curriculum_2007_Contingency_Indep}}

@@ Line 138: / Line 138: @@
 We can also test to see if within each treatment group, there is a strong group separation between the moths that ''avoided the EA odor'' and those that ''did not''. Recall that this can be done by the [[AP_Statistics_Curriculum_2007_NonParam_2MedianPair |sign-test]].
-: '''Controls''':  <math>x_o =25</math>, and <math>P(x_o > 25) =0.230696</math>, when <math>x_o \sim Binomial(N = 46, p = 0.5)</math>. Thus, we can not reject a null hypothesis that the proportions of moths that avoided the odor and those that did not avoid the odor are different (within the '''Control group''').
+: '''Controls''':  <math>x_o =25</math>, and <math>P(x_o > 25) =0.230696</math>, when <math>x_o \sim Binomial(N = 46, p = 0.5)</math>. Thus, we cannot reject a null hypothesis that the proportions of moths that avoided the odor and those that did not avoid the odor are different (within the '''Control group''').
 : Similarly, in the 4<sup>th</sup> group, where larvae are exposed to EA odor paired with electric shock (odor prior to shock), we have: <math>x_o =32</math>, and <math>P(x_o > 32) =0.000056</math>, when <math>x_o \sim Binomial(N = 41, p = 0.5)</math>. Thus, we can reject a null hypothesis that the proportions of moths that avoided the odor and those that did not avoid it are different (within the '''odor+shock treatment group'''). (Recall that in [[AP_Statistics_Curriculum_2007_NonParam_2MedianPair |this non-parametric inference section we discussed these types of calculations]]).

@@ Line 39: / Line 39: @@
 * The Hypotheses:
-: <math>H_o</math>: there is no association between variable 1 and variable 2  (independence)
+: <math>H_o</math>: There is no association between variable 1 and variable 2  (independence)
 :: ''P(BC|CP)=P(BC)'', that is brain-cancer (BC) is independent of cell-phone (CP) usage.
-: <math>H_a</math>: there is an association between variable 1 and variable 2 (dependence)
+: <math>H_a</math>: There is an association between variable 1 and variable 2 (dependence)
 :: <math>P(BC|CP)={P(BC \cap CP) \over P(CP) } \not= P(BC).</math>
@@ Line 75: / Line 75: @@
 ===Earthquake Insurance Example===
-Many factors are considered when purchasing earthquake insurance.  One factor of interest may be location with respect to a major earthquake fault.  Suppose a survey was mailed to California residents in four counties (data shown below).  Is there a statistically significant association between county of residence and purchase of earthquake insurance?  Test using a = 0.05.
+Many factors are considered when purchasing earthquake insurance.  One factor of interest may be location with respect to a major earthquake fault.  Suppose a survey is mailed to California residents in four counties (data shown below).  Is there a statistically significant association between county of residence and purchase of earthquake insurance?  Test using a = 0.05.
 <center>
@@ Line 107: / Line 107: @@
 [[AP_Statistics_Curriculum_2007_Contingency_Indep#References | One study (Blackiston, Casey and Weiss, 2008)]] showed that moths can remember something they learned at caterpillar stage -- an association of an odor with an electric shock. This memory remains even though the metamorphosis decomposes much of their entire (caterpillar) body and reconstitutes it again (as a moth).
-[http://en.wikipedia.org/wiki/Manduca_sexta Tobacco hornworm moth caterpillars] were put into one of 4 treatment groups: ''control'', ''shock'', ''odor'', or ''shock and odor''. Then the moths were observed to see whether they avoided the ''odor''.  If the moths could "remember" the odor association with shock, then one would expect a greater rate of avoidance of odor in the moths in the last group. The empirical results seem to provide evidence in support of this hypothesis. This study employed a classical conditioning to train caterpillars to avoid the ''odor of ethyl acetate (EA)'' by pairing odor with a mild electric shock. The data are included in the table below.
+[http://en.wikipedia.org/wiki/Manduca_sexta Tobacco hornworm moth caterpillars] were put into one of 4 treatment groups: ''control'', ''shock'', ''odor'', or ''shock and odor''. Then the moths were observed to see whether they avoided the ''odor''.  If the moths could "remember" the odor association with shock, then one would expect a greater rate of avoidance of odor in the moths in the last group. The empirical results seem to provide evidence in supporting this hypothesis. This study employed a classical conditioning to train caterpillars to avoid the ''odor of ethyl acetate (EA)'' by pairing odor with a mild electric shock. The data are included in the table below.
 <center>

@@ Line 105: / Line 105: @@
 ===Moths Memory from Caterpillar Stage===
-[[AP_Statistics_Curriculum_2007_Contingency_Indep#References | One study (Blackiston, Casey and Weiss, 2008)]] showed that moths can remember something they learned at caterpillar stage -- an association of an odor with an electric shock. This memory remains even though the metamorphosis decomposing much of their entire (caterpillar) body and reconstituting it again (as a moth).
+[[AP_Statistics_Curriculum_2007_Contingency_Indep#References | One study (Blackiston, Casey and Weiss, 2008)]] showed that moths can remember something they learned at caterpillar stage -- an association of an odor with an electric shock. This memory remains even though the metamorphosis decomposes much of their entire (caterpillar) body and reconstitutes it again (as a moth).
 [http://en.wikipedia.org/wiki/Manduca_sexta Tobacco hornworm moth caterpillars] were put into one of 4 treatment groups: ''control'', ''shock'', ''odor'', or ''shock and odor''. Then the moths were observed to see whether they avoided the ''odor''.  If the moths could "remember" the odor association with shock, then one would expect a greater rate of avoidance of odor in the moths in the last group. The empirical results seem to provide evidence in support of this hypothesis. This study employed a classical conditioning to train caterpillars to avoid the ''odor of ethyl acetate (EA)'' by pairing odor with a mild electric shock. The data are included in the table below.
@@ Line 124: / Line 124: @@
 </center>
-Use the SOCR Chi-square test of association to find out if indeed the data supports a research hypothesis that training memory may proliferate through the transition process of metamorphosis from caterpillar to moth. Also establish that the first three groups don't deviate significantly from the (null hypothesis) 50% avoidance level. Therefore, the moths seem naturally unaffected by the odor itself. You can also show that the '''Shock + Odor''' treatment group has an avoidance of the odor rate significantly higher than 0.5 (given by the null hypothesis).
+Use the SOCR Chi-square test of association to find out if indeed the data support a research hypothesis that training memory may proliferate through the transition process of metamorphosis from caterpillar to moth. Also establish that the first three groups don't deviate significantly from the (null hypothesis) 50% avoidance level. Therefore, the moths seem naturally unaffected by the odor itself. You can also show that the '''Shock + Odor''' treatment group has an avoidance of the odor rate significantly higher than 0.5 (given by the null hypothesis).
 <center>[[Image:SOCR_EBook_Dinov_ChiSquare_030308_Fig4.jpg|500px]]</center>
@@ Line 136: / Line 136: @@
 : ''P-value = 0.029529758678132345'' indicates that there is an association between these two variables.
-We can also test to see if within each treatment group, there is a strong group separation between the moths that ''avoided the EA odor'' and those that ''did not''. Recall that this is can be done by the [[AP_Statistics_Curriculum_2007_NonParam_2MedianPair |sign-test]].
+We can also test to see if within each treatment group, there is a strong group separation between the moths that ''avoided the EA odor'' and those that ''did not''. Recall that this can be done by the [[AP_Statistics_Curriculum_2007_NonParam_2MedianPair |sign-test]].
 : '''Controls''':  <math>x_o =25</math>, and <math>P(x_o > 25) =0.230696</math>, when <math>x_o \sim Binomial(N = 46, p = 0.5)</math>. Thus, we can not reject a null hypothesis that the proportions of moths that avoided the odor and those that did not avoid the odor are different (within the '''Control group''').

@@ Line 80: / Line 80: @@
 {| class="wikitable" style="text-align:center; width:25%" border="1"
 |-
-|  || || colspan=5| '''County'''
+|  colspan=2 rowspan=2 | || colspan=5| '''County'''
 |-
-|  || || '''Contra Costa''' (CC) || '''Santa Clara''' (SC) || '''Los Angeles''' (LA) || '''San Bernardino''' (SB) || '''Total'''
+| '''Contra Costa''' (CC) || '''Santa Clara''' (SC) || '''Los Angeles''' (LA) || '''San Bernardino''' (SB) || '''Total'''
 |-
 | rowspan=3| '''Earthquake Insurance''' || '''Yes''' || 117 || 222 || 133 || 109 || 581

@@ Line 17: / Line 17: @@
 {| class="wikitable" style="text-align:center; width:25%" border="1"
 |-
-|  || || colspan=3| '''Brain cancer'''
+|  colspan=2 rowspan=2| || colspan=3| '''Brain cancer'''
 |-
-|  || || '''Yes''' || '''No''' || '''Total'''
+| '''Yes''' || '''No''' || '''Total'''
 |-
 | rowspan=3| '''Cell Phone Use''' || '''Yes''' || 18 || 80 || 98

@@ Line 155: / Line 155: @@
 * Sample conditions
 ** critical values only work if each expected value > 5
 <hr>

@@ Line 134: / Line 134: @@
 : <math>H_a</math>:  There is an association between ''odor avoidance'' and ''treatment''. The probability of avoiding odor depends on the treatment applied at the larvae stage (before the metamorphosis to moths).
-: ''P-value = 0.029529758678132345'' indicates that there is a strong association between these two variables.
+: ''P-value = 0.029529758678132345'' indicates that there is an association between these two variables.
-Wee can also test to see if within each treatment group, there is a strong group separation between the moths that ''avoided the EA odor'' and those that ''did not''. Recall that this is can be done by the [[AP_Statistics_Curriculum_2007_NonParam_2MedianPair |sign-test]].
+We can also test to see if within each treatment group, there is a strong group separation between the moths that ''avoided the EA odor'' and those that ''did not''. Recall that this is can be done by the [[AP_Statistics_Curriculum_2007_NonParam_2MedianPair |sign-test]].
-: '''Controls''':  <math>x_o =25</math>, and <math>P(x_o > 25) =0.230696</math>, when <math>x_o \sim Binomial(N = 46, p = 0.5)</math>. Thus, we can not reject a null hypothesis that the proportions of moths that avoided the odor (within the Control group) are different.
+: '''Controls''':  <math>x_o =25</math>, and <math>P(x_o > 25) =0.230696</math>, when <math>x_o \sim Binomial(N = 46, p = 0.5)</math>. Thus, we can not reject a null hypothesis that the proportions of moths that avoided the odor and those that did not avoid the odor are different (within the '''Control group''').
-: Similarly, in the 4<sup>th</sup> group, where larvae are exposed to EA odor paired with electric shock (odor prior to shock), we have: <math>x_o =32</math>, and <math>P(x_o > 32) =0.000056</math>, when <math>x_o \sim Binomial(N = 41, p = 0.5)</math>. Thus, we can reject a null hypothesis that the proportions of moths that avoided the odor (within the '''odor+shock treatment group''') are different. (Recall that in [[AP_Statistics_Curriculum_2007_NonParam_2MedianPair |this non-parametric inference section we discussed these types of calculations]]).
+: Similarly, in the 4<sup>th</sup> group, where larvae are exposed to EA odor paired with electric shock (odor prior to shock), we have: <math>x_o =32</math>, and <math>P(x_o > 32) =0.000056</math>, when <math>x_o \sim Binomial(N = 41, p = 0.5)</math>. Thus, we can reject a null hypothesis that the proportions of moths that avoided the odor and those that did not avoid it are different (within the '''odor+shock treatment group'''). (Recall that in [[AP_Statistics_Curriculum_2007_NonParam_2MedianPair |this non-parametric inference section we discussed these types of calculations]]).
 <center>[[Image:SOCR_EBook_Dinov_ChiSquare_030308_Fig5.jpg|500px]]</center>

← Older revision		Revision as of 23:34, 11 March 2008
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	: '''Controls''': <math>x_o =25</math>, and <math>P(x_o > 25) =0.230696</math>, when <math>x_o \sim Binomial(N = 46, p = 0.5)</math>. Thus, we can not reject a null hypothesis that the proportions of moths that avoided the odor (within the Control group) are different.		: '''Controls''': <math>x_o =25</math>, and <math>P(x_o > 25) =0.230696</math>, when <math>x_o \sim Binomial(N = 46, p = 0.5)</math>. Thus, we can not reject a null hypothesis that the proportions of moths that avoided the odor (within the Control group) are different.

−	~~0.32).~~
	: Similarly, in the 4<sup>th</sup> group, where larvae are exposed to EA odor paired with electric shock (odor prior to shock), we have: <math>x_o =32</math>, and <math>P(x_o > 32) =0.000056</math>, when <math>x_o \sim Binomial(N = 41, p = 0.5)</math>. Thus, we can reject a null hypothesis that the proportions of moths that avoided the odor (within the '''odor+shock treatment group''') are different. (Recall that in [[AP_Statistics_Curriculum_2007_NonParam_2MedianPair \|this non-parametric inference section we discussed these types of calculations]]).		: Similarly, in the 4<sup>th</sup> group, where larvae are exposed to EA odor paired with electric shock (odor prior to shock), we have: <math>x_o =32</math>, and <math>P(x_o > 32) =0.000056</math>, when <math>x_o \sim Binomial(N = 41, p = 0.5)</math>. Thus, we can reject a null hypothesis that the proportions of moths that avoided the odor (within the '''odor+shock treatment group''') are different. (Recall that in [[AP_Statistics_Curriculum_2007_NonParam_2MedianPair \|this non-parametric inference section we discussed these types of calculations]]).