Kendall's Tau Test
KENDALLSTAUTEST(Range1, Range2, alpha, NewTableFlag)
- 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.
is the array of x values.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 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)}
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 (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
| 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)
| 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 |
| 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