Difference between revisions of "Kendall's Tau Test"

Latest revision as of 10:51, 19 August 2020

KENDALLSTAUTEST(Range1, Range2, alpha, NewTableFlag)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Range1} is the array of x values.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Range2} is the array of y values.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle alpha} is the value from 0 to 1.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle NewTableFlag} is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube.

DESCRIPTION

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.
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.

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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x_i)} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (y_i)} are unique.

concordant if  $(x_{i}>x_{j})$  & Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (y_i > y_j)}
 or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x_i < x_j)}
 & Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (y_i < y_j)}

discordant if Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x_i > x_j)}
 & Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (y_i < y_j)}
 or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x_i < x_j)}
 & Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (y_i > y_j)}

neither if Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x_i = x_j)}
 or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (y_i = y_j)}
 (i.e. ties are not counted).

The Kendall's Tau statistic is:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau=1-\frac{4D}{n(n-1)}} .

C is the number of concordant pairs.
D is the number of discordant pairs.

RESULT

If number of values in a set is <15, critical tables are used to calculate Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau} .
If number of values in a set is >=15, Normal approximation is used for calculation.

* If Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau}
 > critical value from the Kendall's Tau Critical table, then reject the null hypothesis that there is no correlation.
* else if, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau}
 <critical value, correlation exists.

EXAMPLE

Spreadsheet
	A	B
1	80	5
2	78	23
3	60	25
4	53	48
5	85	17
6	84	8
7	73	4
8	79	26
9	81	11
10	75	19
11	68	14
12	72	35
13	58	29
14	92	3
15	65	24

=KENDALLSTAUTEST(A1:A15,B1:B15, 0.05, true)

KENDALL'S TAU TEST USING NORMAL APPROXIMATION
RANGE1 SORT	RANGE2 SORT	CONCORDANT	DISCORDANT
53	48	0	14
58	29	1	12
60	25	2	10
65	24	2	9
68	14	5	5
72	35	0	9
73	4	7	1
75	19	2	5
78	23	1	5
79	26	0	5
80	5	3	1
81	11	1	2
84	8	1	1
85	17	0	1
92	3	0	0

SUMMARY
VARIABLE	RESULT
COUNT	15
C	105
SUM CONCORDANT	25
SUM DISCORDANT	80
KENDALL'S TAU	-0.52381
STDERROR	0.19245
Z-VALUE	-2.7218
ZCRITICAL	1.95996
P-VALUE	0.00649
RESULT	REJECT NULL HYPOTHESIS, NO CORRELATION

CONCLUSION: REJECT NULL HYPOTHESIS, NO CORRELATION

@@ 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.<br></br>
-==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.
-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.<br></br>
+==='''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, 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.
+ * '''else if, <math>\tau</math> <critical value, correlation exists.
+==='''EXAMPLE===
+{| class="wikitable"
+|+Spreadsheet
+|-
+! !! A !! B
+|-
+! 1
+| 80 || 5
+|-
+! 2
+| 78 || 23
+|-
+! 3
+| 60 || 25
+|-
+! 4
+| 53 || 48
+|-
+! 5
+| 85 || 17
+|-
+! 6
+| 84 || 8
+|-
+! 7
+| 73 || 4
+|-
+! 8
+| 79 || 26
+|-
+! 9
+| 81 || 11
+|-
+! 10
+| 75 || 19
+|-
+! 11
+| 68 || 14
+|-
+! 12
+| 72 || 35
+|-
+! 13
+| 58 || 29
+|-
+! 14
+| 92 || 3
+|-
+! 15
+| 65 || 24
+|}
+='''KENDALLSTAUTEST(A1:A15,B1:B15, 0.05, true)
+{| class="wikitable"
+|+KENDALL'S TAU TEST USING NORMAL APPROXIMATION
+|-
+!RANGE1 SORT!!RANGE2 SORT!!CONCORDANT !!DISCORDANT
+|-
+|53||48||0||14
+|-
+|58||29||1||12
+|-
+|60||25||2||10
+|-
+|65||24||2||9
+|-
+|68||14||5||5
+|-
+|72||35||0||9
+|-
+|73||4||7||1
+|-
+|75||19||2||5
+|-
+|78||23||1||5
+|-
+|79||26||0||5
+|-
+|80||5||3||1
+|-
+|81||11||1||2
+|-
+|84||8||1||1
+|-
+|85||17||0||1
+|-
+|92||3||0||0
+|}
+{| class="wikitable"
+|+SUMMARY
+|-
+!VARIABLE       !!RESULT
+|-
+|COUNT          || 15
+|-
+|C              || 105
+|-
+|SUM CONCORDANT || 25
+|-
+|SUM DISCORDANT || 80
+|-
+|KENDALL'S TAU  || -0.52381
+|-
+|STDERROR       || 0.19245
+|-
+|Z-VALUE        || -2.7218
+|-
+|ZCRITICAL      || 1.95996
+|-
+|P-VALUE        || 0.00649
+|-
+|RESULT         || REJECT NULL HYPOTHESIS, NO CORRELATION
+|}
+*'''CONCLUSION:''' REJECT NULL HYPOTHESIS, NO CORRELATION

Difference between revisions of "Kendall's Tau Test"

Latest revision as of 10:51, 19 August 2020

DESCRIPTION

RESULT

EXAMPLE

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	A	B
1	80	5
2	78	23
3	60	25
4	53	48
5	85	17
6	84	8
7	73	4
8	79	26
9	81	11
10	75	19
11	68	14
12	72	35
13	58	29
14	92	3
15	65	24

RANGE1 SORT	RANGE2 SORT	CONCORDANT	DISCORDANT
53	48	0	14
58	29	1	12
60	25	2	10
65	24	2	9
68	14	5	5
72	35	0	9
73	4	7	1
75	19	2	5
78	23	1	5
79	26	0	5
80	5	3	1
81	11	1	2
84	8	1	1
85	17	0	1
92	3	0	0

	A	B
1	80	5
2	78	23
3	60	25
4	53	48
5	85	17
6	84	8
7	73	4
8	79	26
9	81	11
10	75	19
11	68	14
12	72	35
13	58	29
14	92	3
15	65	24

RANGE1 SORT	RANGE2 SORT	CONCORDANT	DISCORDANT
53	48	0	14
58	29	1	12
60	25	2	10
65	24	2	9
68	14	5	5
72	35	0	9
73	4	7	1
75	19	2	5
78	23	1	5
79	26	0	5
80	5	3	1
81	11	1	2
84	8	1	1
85	17	0	1
92	3	0	0

	A	B
1	80	5
2	78	23
3	60	25
4	53	48
5	85	17
6	84	8
7	73	4
8	79	26
9	81	11
10	75	19
11	68	14
12	72	35
13	58	29
14	92	3
15	65	24

RANGE1 SORT	RANGE2 SORT	CONCORDANT	DISCORDANT
53	48	0	14
58	29	1	12
60	25	2	10
65	24	2	9
68	14	5	5
72	35	0	9
73	4	7	1
75	19	2	5
78	23	1	5
79	26	0	5
80	5	3	1
81	11	1	2
84	8	1	1
85	17	0	1
92	3	0	0