SOCR EduMaterials AnalysisActivities KruskalWallis - Revision history

Dinov: /* Result Interpretation */

2014-09-05T21:53:47Z

‎Result Interpretation

IvoDinov at 19:51, 23 January 2009

2009-01-23T19:51:57Z

IvoDinov at 17:52, 3 March 2008

2008-03-03T17:52:59Z

IvoDinov at 17:50, 3 March 2008

2008-03-03T17:50:22Z

IvoDinov at 17:48, 3 March 2008

2008-03-03T17:48:47Z

Annie: /* SOCR Analyses Example on the Kruskal-Wallis Test */

2008-03-03T01:40:10Z

‎SOCR Analyses Example on the Kruskal-Wallis Test

Annie: /* SOCR Analyses Example on the Kruskal-Wallis Test */

2008-03-03T01:38:58Z

‎SOCR Analyses Example on the Kruskal-Wallis Test

Annie: /* SOCR Analyses Example on the Kruskal-Wallis Test */

2008-03-03T01:38:20Z

‎SOCR Analyses Example on the Kruskal-Wallis Test

Annie: /* SOCR Analyses Example on the Kruskal-Wallis Test */

2008-03-03T01:37:23Z

‎SOCR Analyses Example on the Kruskal-Wallis Test

Annie: /* References */

2008-03-03T01:35:18Z

‎References

@@ Line 60: / Line 60: @@
 <br>
 The test statistic that follows Student's t-distribution is:<br>
-:|Ri/ni - Rj/nj| / sqrt(S * S * (N - 1 - T) / (N - k)) / sqrt(1/ni + 1/nj) (or identically)
+::|Ri/ni - Rj/nj| / sqrt(S * S * (N - 1 - T) / (N - k)) / sqrt(1/ni + 1/nj) (or identically)
-:: <math>\sqrt{{1\over n_i} + {1\over n_j}}\times {|{R_i\over n_i} - {R_j\over n_j}| \over ({S^2 (N - 1 - T) \over N - k})^{0.5}}</math>
+:: $$\sqrt{{1\over n_i} + {1\over n_j}}\times {|{R_i\over n_i} - {R_j\over n_j}| \over ({S^2 (N - 1 - T) \over N - k})^{0.5}}$$
-<br>
 It is computed using T and S above. N is the total number of observations.
 <br><br>

@@ Line 1: / Line 1: @@
-==Kruskal-Wallis Test Background==
+==[[SOCR_EduMaterials_AnalysesActivities | SOCR Analysis]] - Kruskal-Wallis Test Background==
 The [[AP_Statistics_Curriculum_2007_NonParam_ANOVA | Kruskal-Wallis Test is a generalization of the Two Independent Sample Wilcoxon Test]]. While the latter one test for two groups, the Kruskal-Wallis Test test multiple groups. Suppose there are k groups, the hypotheses are written as:
@@ Line 9: / Line 9: @@
 or
-'''Alternative Hypothesis H_A''':  The k poputations do not all have identical means. (k is the number of groups here.)
+'''Alternative Hypothesis H_A''':  The k populations do not all have identical means. (k is the number of groups here.)
-Rank sum is employed for hypothese testing. Note that the sample size for each group do not have to be the same.
+Rank sum is employed for hypotheses testing. Note that the sample size for each group do not have to be the same. Go to the [http://www.socr.ucla.edu/htmls/ana/TwoIndependentKruskalWallis_Analysis.html Kruskal-Wallis Test Applet].
 ==SOCR Analyses Example on the Kruskal-Wallis Test==
@@ Line 33: / Line 33: @@
 === The data need to be send to the computer for analysis===
-In the Kruskal-Wallis test, at least two groups need to be included. You can certainly include any two groups, any three groups, or all the avaialble groups, etc., from the data set. The test will only analyze the groups selected. Therefore, you'll need to let the computer know what groups you're choosing. This is done in the "Mapping" panel. Click on the "Mapping" button to include the groups you want.
+In the Kruskal-Wallis test, at least two groups need to be included. You can certainly include any two groups, any three groups, or all the available groups, etc., from the data set. The test will only analyze the groups selected. Therefore, you'll need to let the computer know what groups you're choosing. This is done in the "Mapping" panel. Click on the "Mapping" button to include the groups you want.
 <center>[[Image:SOCR_AnalysisActivities_KruskalWallies_Chu_061407_Fig2A.gif|700px]]</center>
@@ Line 49: / Line 49: @@
-'''Note''': if you happen to click on the "Clear" button in the middle of the procedure, all the data will be cleared out. Simply start over from step 1 and reteive the data by click an '''EXAMPLE''' button.
+'''Note''': if you happen to click on the "Clear" button in the middle of the procedure, all the data will be cleared out. Simply start over from step 1 and retrieve the data by click an '''EXAMPLE''' button.
 ===Result Interpretation===
@@ Line 79: / Line 79: @@
-* These reuslts include the critical value (2.120) and the value of the test statistics (''T=7.487''), which indicate that there is sufficient evidence (at <math>\alpha=0.05</math>) to reject the null hypothesis that the sample centers are equal.
+* These results include the critical value (2.120) and the value of the test statistics (''T=7.487''), which indicate that there is sufficient evidence (at <math>\alpha=0.05</math>) to reject the null hypothesis that the sample centers are equal.
 * Also, the paired-group comparisons (accounting for multiple-testing) indicate the ''normal'' ranges of the rank differences between groups. For instance, ''Group B vs. Group C: 	7.9	>	6.6928'' indicates the range of normal rank differences between groups ''B'' and ''C''.

@@ Line 1: / Line 1: @@
 ==Kruskal-Wallis Test Background==
+The [[AP_Statistics_Curriculum_2007_NonParam_ANOVA | Kruskal-Wallis Test is a generalization of the Two Independent Sample Wilcoxon Test]]. While the latter one test for two groups, the Kruskal-Wallis Test test multiple groups. Suppose there are k groups, the hypotheses are written as:
 '''Null Hypothesis H_0''': All of the k population distribution functions are identical.
@@ Line 15: / Line 14: @@
 ==SOCR Analyses Example on the Kruskal-Wallis Test==
 The example we show here is from "Practical Nonparametric Statistics" by Conover, Second Edition, John Wiley & Sons, 1980. (Page 230)

@@ Line 71: / Line 71: @@
 ::::	|Ri/ni - Rj/nj|                 2.1199 * sqrt(24.9187) * sqrt(1/ni + 1/nj)<br>
 <br>
-::Group A vs. Group B: 	3.1999	<	6.6928    (does not yield rejection of Ho.)
+::Group A vs. Group B: 	3.1999	<	6.6928    (does not yield rejection of Ho)
-::Group A vs. Group C: 	4.7000	<	6.6928    (does not yield rejection of Ho.)
+::Group A vs. Group C: 	4.7000	<	6.6928    (does not yield rejection of Ho)
-::Group A vs. Group D: 	5.7000	<	6.6928    (does not yield rejection of Ho.)
+::Group A vs. Group D: 	5.7000	<	6.6928    (does not yield rejection of Ho)
-::Group B vs. Group C: 	7.9	>	6.6928    (yields rejection of Ho.)
+::'''Group B vs. Group C: 	7.9	>	6.6928    (yields rejection of Ho)'''
-::Group B vs. Group D: 	8.9	>	6.6928    (yields rejection of Ho.)
+::'''Group B vs. Group D: 	8.9	>	6.6928    (yields rejection of Ho)'''
-::Group C vs. Group D: 	1.0	<	6.6928    (does not yield rejection of Ho.)
+::Group C vs. Group D: 	1.0	<	6.6928    (does not yield rejection of Ho)
 Since Group B appears to have different mean ranks than group C and group D, the null hypothesis is rejected.

@@ Line 1: / Line 1: @@
-=== Kruskal-Wallis Test Background===
+==Kruskal-Wallis Test Background==
@@ Line 14: / Line 14: @@
 Rank sum is employed for hypothese testing. Note that the sample size for each group do not have to be the same.
-=== SOCR Analyses Example on the Kruskal-Wallis Test===
+==SOCR Analyses Example on the Kruskal-Wallis Test==
@@ Line 20: / Line 20: @@
-'''Steps:'''
+=='''Steps:'''==
-'''1.''' The data of this example has 4 groups: A, B, C and D. Click on "'''Kruskal-Wallis Test'''" from the conbo box in the left panel.
+=== The data of this example has 4 groups: A, B, C and D. Click on "'''Kruskal-Wallis Test'''" from the conbo box in the left panel===
@@ Line 31: / Line 31: @@
-'''2.'''  Click on "'''Example 2'''" button. than the "Data" button to see the data.
+===Click on "'''Example 2'''" button. than the "Data" button to see the data===
 <center>[[Image:SOCR_AnalysisActivities_KruskalWallies_Chu_061407_Fig2.gif|700px]]</center>
-'''3.''' The data need to be send to the computer for analysis. In the Kruskal-Wallis test, at least two groups need to be included. You can certainly include any two groups, any three groups, or all the avaialble groups, etc., from the data set. The test will only analyze the groups selected. Therefore, you'll need to let the computer know what groups you're choosing. This is done in the "Mapping" panel. Click on the "Mapping" button to include the groups you want.
+=== The data need to be send to the computer for analysis===
 <center>[[Image:SOCR_AnalysisActivities_KruskalWallies_Chu_061407_Fig2A.gif|700px]]</center>
-'''4.''' Next, click on the "'''Calculate'''" button. Now you're ready to see the results. Just click on the "Result" button.
+=== Next, click on the "'''Calculate'''" button===
 Now you're ready to see the results. Just click on the "Result" button.
 <center>[[Image:SOCR_AnalysisActivities_KruskalWallies_Chu_061407_Fig3.gif|700px]]</center>
@@ Line 52: / Line 53: @@
 '''Note''': if you happen to click on the "Clear" button in the middle of the procedure, all the data will be cleared out. Simply start over from step 1 and reteive the data by click an '''EXAMPLE''' button.
-'''3. Result Interpretation'''
+===Result Interpretation===
 * The '''Results''' tab ends with a summary like this:
 ::Significance Level = 0.05<br>
@@ Line 61: / Line 62: @@
 <br>
 The test statistic that follows Student's t-distribution is:<br>
-|Ri/ni - Rj/nj| / (S * S * (N - 1 - T) / (N - k)) / sqrt(1/ni + 1/nj)<br><br>
+:|Ri/ni - Rj/nj| / sqrt(S * S * (N - 1 - T) / (N - k)) / sqrt(1/ni + 1/nj) (or identically)
 It is computed using T and S above. N is the total number of observations.
 <br><br>

@@ Line 64: / Line 64: @@
 And this is computed using T and S above. N is the total number of observations.
 <br><br>
-::Notation: Ri -- Rank of group i; ni -- size of group i.<br>
+::Notation: Ri -- Sum of ranks of group i; ni -- size of group i.<br>
 <br>
 ::::	|Ri/ni - Rj/nj|                 2.1199 * sqrt(24.9187) * sqrt(1/ni + 1/nj)<br>

@@ Line 81: / Line 81: @@
 ==References==
-*{{cite book | author=Conover, WJ. | title=Practical Nonparametric Statistics (2ed ed.) | publisher=John Wiley & Sons | year=1980 }}
+* Conover, WJ (1980). Practical Nonparametric Statistics. John Wiley & Sons. Second Edition.
 <hr>
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