Kendall's Tau Test - Revision history

Sahiti at 15:51, 19 August 2020

2020-08-19T15:51:54Z

Sahiti at 15:49, 19 August 2020

2020-08-19T15:49:38Z

Sahiti at 15:48, 19 August 2020

2020-08-19T15:48:00Z

Sahiti at 15:47, 19 August 2020

2020-08-19T15:47:24Z

Sahiti at 15:46, 19 August 2020

2020-08-19T15:46:27Z

Sahiti: /* Example */

2017-05-03T15:10:24Z

Example

Sahiti at 15:09, 3 May 2017

2017-05-03T15:09:32Z

Sahiti: /* Example */

2017-05-03T15:08:56Z

Example

Sahiti: /* Example */

2017-05-03T15:08:07Z

Example

Sahiti: /* Example */

2017-05-03T15:02:29Z

Example

@@ Line 11: / Line 11: @@
 *'''It will be low when observations have a dissimilar rank between the two variables.
-'''Let (x1, y1), (x2, y2), …, (xn, yn) be a set of observations of the joint random variables X and Y respectively,
+'''Let (x1, y1), (x2, y2), …, (xn, yn) be a set of observations of the joint random variables X and Y respectively, such that all the values of <math>(x_i)</math> and <math>(y_i)</math> are unique.
   '''concordant if <math>(x_i > x_j)</math> & <math>(y_i > y_j)</math> or <math>(x_i < x_j)</math> & <math>(y_i < y_j)</math>
   '''discordant if <math>(x_i > x_j)</math> & <math>(y_i < y_j)</math> or <math>(x_i < x_j)</math> & <math>(y_i > y_j)</math>

@@ Line 1: / Line 1: @@
-<div style="font-size:25px">'''KENDALLSTAUTEST(Range1,Range2,alpha,NewTableFlag)'''</div>
+<div style="font-size:25px">'''KENDALLSTAUTEST(Range1, Range2, alpha, NewTableFlag)'''</div>
 *'''<math>Range1</math> is the array of x values.
 *'''<math>Range2</math> is the array of y values.
@@ Line 6: / Line 6: @@
 ==='''DESCRIPTION===
-* '''It is a statistic test used to measure the ordinal association between two measured quantities.
+*'''It is a statistic test used to measure the ordinal association between two measured quantities.
-* '''It is a measure of rank correlation: the similarity of the orderings of the data when ranked by each of the quantities.
+*'''It is a measure of rank correlation: the similarity of the orderings of the data when ranked by each of the quantities.
-* '''Kendall correlation between two variables will be high when observations have a similar rank.
+*'''Kendall correlation between two variables will be high when observations have a similar rank.
-* '''It will be low when observations have a dissimilar rank between the two variables.
+*'''It will be low when observations have a dissimilar rank between the two variables.
 '''Let (x1, y1), (x2, y2), …, (xn, yn) be a set of observations of the joint random variables X and Y respectively,

@@ Line 3: / Line 3: @@
 *'''<math>Range2</math> is the array of y values.
 *'''<math>alpha</math>  is the value from 0 to 1.
-*'''<math>NewTableFlag</math> is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube.
+*'''<math>NewTableFlag</math> is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube.<br></br>
 ==='''DESCRIPTION===
@@ Line 20: / Line 20: @@
 :<math>\tau=1-\frac{4D}{n(n-1)}</math>.
 * '''C is the number of concordant pairs.
-* '''D is the number of discordant pairs.
+* '''D is the number of discordant pairs.<br></br>
 ==='''RESULT===

@@ Line 13: / Line 13: @@
 '''Let (x1, y1), (x2, y2), …, (xn, yn) be a set of observations of the joint random variables X and Y respectively,
 such that all the values of <math>(x_i)</math> and <math>(y_i)</math> are unique.
-  * '''concordant if <math>(x_i > x_j)</math> & <math>(y_i > y_j)</math> or <math>(x_i < x_j)</math> & <math>(y_i < y_j)</math>
+  '''concordant if <math>(x_i > x_j)</math> & <math>(y_i > y_j)</math> or <math>(x_i < x_j)</math> & <math>(y_i < y_j)</math>
-  * '''discordant if <math>(x_i > x_j)</math> & <math>(y_i < y_j)</math> or <math>(x_i < x_j)</math> & <math>(y_i > y_j)</math>
+  '''discordant if <math>(x_i > x_j)</math> & <math>(y_i < y_j)</math> or <math>(x_i < x_j)</math> & <math>(y_i > y_j)</math>
-  * '''neither if <math>(x_i = x_j)</math> or <math>(y_i = y_j)</math> (i.e. ties are not counted).
+  '''neither if <math>(x_i = x_j)</math> or <math>(y_i = y_j)</math> (i.e. ties are not counted).
 '''The Kendall's Tau statistic is:

@@ Line 1: / Line 1: @@
-<div style="font-size:25px">'''KENDALLSTAUTEST(Range1,Range2,alpha,NewTableFlag)'''</div><br/>
+<div style="font-size:25px">'''KENDALLSTAUTEST(Range1,Range2,alpha,NewTableFlag)'''</div>
-*<math>Range1</math> is the array of x values.
+*'''<math>Range1</math> is the array of x values.
-*<math>Range2</math> is the array of y values.
+*'''<math>Range2</math> is the array of y values.
-*<math>alpha</math>  is the value from 0 to 1.
+*'''<math>alpha</math>  is the value from 0 to 1.
-*<math>NewTableFlag</math> is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube.
+*'''<math>NewTableFlag</math> is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube.
-==Description==
+==='''DESCRIPTION===
-* It is a statistic test used to measure the ordinal association between two measured quantities.
+* '''It is a statistic test used to measure the ordinal association between two measured quantities.
-* It is a measure of rank correlation: the similarity of the orderings of the data when ranked by each of the quantities.
+* '''It is a measure of rank correlation: the similarity of the orderings of the data when ranked by each of the quantities.
-* Kendall correlation between two variables will be high when observations have a similar rank.
+* '''Kendall correlation between two variables will be high when observations have a similar rank.
-* It will be low when observations have a dissimilar rank between the two variables.
+* '''It will be low when observations have a dissimilar rank between the two variables.
-Let (x1, y1), (x2, y2), …, (xn, yn) be a set of observations of the joint random variables X and Y respectively,
+'''Let (x1, y1), (x2, y2), …, (xn, yn) be a set of observations of the joint random variables X and Y respectively,
 such that all the values of <math>(x_i)</math> and <math>(y_i)</math> are unique.
-  * concordant if <math>(x_i > x_j)</math> & <math>(y_i > y_j)</math> or <math>(x_i < x_j)</math> & <math>(y_i < y_j)</math>
+  * '''concordant if <math>(x_i > x_j)</math> & <math>(y_i > y_j)</math> or <math>(x_i < x_j)</math> & <math>(y_i < y_j)</math>
-  * discordant if <math>(x_i > x_j)</math> & <math>(y_i < y_j)</math> or <math>(x_i < x_j)</math> & <math>(y_i > y_j)</math>
+  * '''discordant if <math>(x_i > x_j)</math> & <math>(y_i < y_j)</math> or <math>(x_i < x_j)</math> & <math>(y_i > y_j)</math>
-  * neither if <math>(x_i = x_j)</math> or <math>(y_i = y_j)</math> (i.e. ties are not counted).
+  * '''neither if <math>(x_i = x_j)</math> or <math>(y_i = y_j)</math> (i.e. ties are not counted).
-The Kendall's Tau statistic is:
+'''The Kendall's Tau statistic is:
-<math>\tau=1-\frac{4D}{n(n-1)}</math>.
+:<math>\tau=1-\frac{4D}{n(n-1)}</math>.
-* C is the number of concordant pairs.
+* '''C is the number of concordant pairs.
-* D is the number of discordant pairs.
+* '''D is the number of discordant pairs.
-==Result==
+==='''RESULT===
-* If number of values in a set is <15, critical tables are used to calculate <math>\tau</math>.
+* '''If number of values in a set is <15, critical tables are used to calculate <math>\tau</math>.
-* If number of values in a set is >=15, Normal approximation is used for calculation.
+* '''If number of values in a set is >=15, Normal approximation is used for calculation.
-  * If <math>\tau</math> > critical value from the Kendall's Tau Critical table, then reject the null hypothesis that there is no correlation.
+  * '''If <math>\tau</math> > critical value from the Kendall's Tau Critical table, then reject the null hypothesis that there is no correlation.
-  * else if <math>\tau</math> <critical value, correlation exists.
+  * '''else if, <math>\tau</math> <critical value, correlation exists.
-==Example==
+==='''EXAMPLE===
 {| class="wikitable"
 |+Spreadsheet
@@ Line 79: / Line 79: @@
 | 65 || 24
 |}
-=KENDALLSTAUTEST(A1:A15,B1:B15,0.05,true)
+='''KENDALLSTAUTEST(A1:A15,B1:B15, 0.05, true)
 {| class="wikitable"
 |+KENDALL'S TAU TEST USING NORMAL APPROXIMATION
@@ Line 115: / Line 116: @@
 |92||3||0||0
 |}
 {| class="wikitable"
 |+SUMMARY

← Older revision		Revision as of 15:10, 3 May 2017
Line 140:		Line 140:
	\|RESULT \|\| REJECT NULL HYPOTHESIS, NO CORRELATION		\|RESULT \|\| REJECT NULL HYPOTHESIS, NO CORRELATION
	\|}		\|}
		+	*'''CONCLUSION:''' REJECT NULL HYPOTHESIS, NO CORRELATION

@@ Line 118: / Line 118: @@
 |+SUMMARY
 |-
-!VARIABLE!!RESULT
+!VARIABLE       !!RESULT
 |-
 |COUNT          || 15

@@ Line 120: / Line 120: @@
 !VARIABLE!!RESULT
 |-
-|COUNT|| 15
+|COUNT          || 15
 |-
-|C|| 105
+|C              || 105
 |-
 |SUM CONCORDANT || 25
@@ Line 128: / Line 128: @@
 |SUM DISCORDANT || 80
 |-
-|KENDALL'S TAU || -0.52381
+|KENDALL'S TAU  || -0.52381
 |-
-|STDERROR || 0.19245
+|STDERROR       || 0.19245
 |-
-|Z-VALUE || -2.7218
+|Z-VALUE        || -2.7218
 |-
-|ZCRITICAL || 1.95996
+|ZCRITICAL      || 1.95996
 |-
-|P-VALUE|| 0.00649
+|P-VALUE        || 0.00649
 |-
-|RESULT || REJECT NULL HYPOTHESIS, NO CORRELATION
+|RESULT         || REJECT NULL HYPOTHESIS, NO CORRELATION
 |}

@@ Line 67: / Line 67: @@
 | 68 || 14
 |-
-! 112
+! 12
 | 72 || 35
 |-
@@ Line 78: / Line 78: @@
 ! 15
 | 65 || 24
 |}