In statistics, the phi coefficient (or mean square contingency coefficient and denoted by φ or rφ) is a for two binary variables. In machine learning, it is known as the Matthews correlation coefficient (MCC) and used as a measure of the quality of binary (two-class) classifications, introduced by biochemist Brian W. Matthews in 1975. Introduced by Karl Pearson, and also known as the Yule phi coefficient from its introduction by Udny Yule in 1912 this measure is similar to the Pearson correlation coefficient in its interpretation. In fact, a Pearson correlation coefficient estimated for two binary variables will return the phi coefficient. Two binary variables are considered positively associated if most of the data falls along the diagonal cells. In contrast, two binary variables are con
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| rdfs:label
| - Coeficiente phi (es)
- 파이 계수 (ko)
- Phi coefficient (en)
- Współczynnik fi (pl)
- Phi相關係數 (zh)
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| - 파이 계수(pi係數)는 통계학에서 두 변인이 모두 질적으로 양분될수있는 경우에 적용되는 상관 계수이다. (ko)
- 在統計學裡，「Phi相關係數」（英語：Phi coefficient）（符號表示為： 或 ）是測量兩個二元變數（英語：binary variables or dichotomous variables）之間相關性的工具，由卡爾·皮爾森所發明 。他也發明了與Phi相關係數有密切關聯的皮爾森卡方檢定（英語：Pearson's chi-squared test。一般所稱的卡方檢定，若未明指種類，即指此），以及發明了測量兩個連續變數之間相關程度的皮爾森積差相關係數（英語：Pearson's r。一般所稱的相關係數，若未明指種類，即指此）。 Phi 相關係數在機器學習的領域又稱為。 (zh)
- En estadística, el coeficiente phi φ o rφ, también llamado coeficiente de correlación de Mathews es una medida de la asociación entre dos variables binarias. Esta medida es similar al coeficiente de correlación de Pearson en su interpretación. De hecho, un coeficiente de correlación de Pearson estimado para dos variables binarias nos dará el coeficiente phi. El coeficiente phi también relacionado con el estadístico de chi-cuadrado para una tabla de contingencia de a 2×2. (es)
- In statistics, the phi coefficient (or mean square contingency coefficient and denoted by φ or rφ) is a for two binary variables. In machine learning, it is known as the Matthews correlation coefficient (MCC) and used as a measure of the quality of binary (two-class) classifications, introduced by biochemist Brian W. Matthews in 1975. Introduced by Karl Pearson, and also known as the Yule phi coefficient from its introduction by Udny Yule in 1912 this measure is similar to the Pearson correlation coefficient in its interpretation. In fact, a Pearson correlation coefficient estimated for two binary variables will return the phi coefficient. Two binary variables are considered positively associated if most of the data falls along the diagonal cells. In contrast, two binary variables are con (en)
- Współczynnik fi (ϕ) – jedna z miar zależności, będąca współczynnikiem korelacji liniowej Pearsona dla dwóch zmiennych, z których obydwie są nominalne oraz dychotomiczne. Współczynnik fi można policzyć na dwa sposoby: używając wzoru na współczynnik fi albo (podobnie jak ma to miejsce w przypadku korelacji punktowo-dwuseryjnej) zrekodować zmienne nominalne, żeby przyjmowały wartości 0 i 1 (jest to tzw. dummy coding), a następnie policzyć dla nich współczynnik korelacji liniowej Pearsona. Rozwinięciem współczynnika fi jest współczynnik V Craméra. (pl)
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| - The article only ever talks about the 2x2 case and binary variables. How does the phi coefficient extend to other cases? (en)
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| - In order to have an overall understanding of your prediction, you decide to take advantage of common statistical scores, such as accuracy, and F1 score.
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However, even if accuracy and F1 score are widely employed in statistics, both can be misleading, since they do not fully consider the size of the four classes of the confusion matrix in their final score computation.
Suppose, for example, you have a very imbalanced validation set made of 100 elements, 95 of which are positive elements, and only 5 are negative elements . And suppose also you made some mistakes in designing and training your machine learning classifier, and now you have an algorithm which always predicts positive. Imagine that you are not aware of this issue.
By applying your only-positive predictor to your imbalanced validation set, therefore, you obtain values for the confusion matrix categories:
: TP = 95, FP = 5; TN = 0, FN = 0.
These values lead to the following performance scores: accuracy = 95%, and F1 score = 97.44%. By reading these over-optimistic scores, then you will be very happy and will think that your machine learning algorithm is doing an excellent job. Obviously, you would be on the wrong track.
On the contrary, to avoid these dangerous misleading illusions, there is another performance score that you can exploit: the Matthews correlation coefficient [40] .
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By considering the proportion of each class of the confusion matrix in its formula, its score is high only if your classifier is doing well on both the negative and the positive elements.
In the example above, the MCC score would be undefined . By checking this value, instead of accuracy and F1 score, you would then be able to notice that your classifier is going in the wrong direction, and you would become aware that there are issues you ought to solve before proceeding.
Consider this other example. You ran a classification on the same dataset which led to the following values for the confusion matrix categories:
: TP = 90, FP = 4; TN = 1, FN = 5.
In this example, the classifier has performed well in classifying positive instances, but was not able to correctly recognize negative data elements. Again, the resulting F1 score and accuracy scores would be extremely high: accuracy = 91%, and F1 score = 95.24%. Similarly to the previous case, if a researcher analyzed only these two score indicators, without considering the MCC, they would wrongly think the algorithm is performing quite well in its task, and would have the illusion of being successful.
On the other hand, checking the Matthews correlation coefficient would be pivotal once again. In this example, the value of the MCC would be 0.14 , indicating that the algorithm is performing similarly to random guessing. Acting as an alarm, the MCC would be able to inform the data mining practitioner that the statistical model is performing poorly.
For these reasons, we strongly encourage to evaluate each test performance through the Matthews correlation coefficient , instead of the accuracy and the F1 score, for any binary classification problem. (en)
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| - Ten quick tips for machine learning in computational biology (en)
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| - En estadística, el coeficiente phi φ o rφ, también llamado coeficiente de correlación de Mathews es una medida de la asociación entre dos variables binarias. Esta medida es similar al coeficiente de correlación de Pearson en su interpretación. De hecho, un coeficiente de correlación de Pearson estimado para dos variables binarias nos dará el coeficiente phi. El coeficiente phi también relacionado con el estadístico de chi-cuadrado para una tabla de contingencia de a 2×2. Donde n es el total del número de observaciones. Se considera que dos variables binarias están positivamente asociadas si la mayor parte de los datos caen dentro de las celdas diagonales. Por el contrario, dos variables binarias se consideran negativamente asociadas si la mayoría de los datos se salen de la diagonal. Si tenemos una tabla de 2×2 para dos variables aleatorias, x e y donde n11, n10, n01, n00, son "cuentas no negativas celdad celda" que se suman a n, el número total de observaciones. El coeficiente phi que describe la asociación de x e y es (es)
- In statistics, the phi coefficient (or mean square contingency coefficient and denoted by φ or rφ) is a for two binary variables. In machine learning, it is known as the Matthews correlation coefficient (MCC) and used as a measure of the quality of binary (two-class) classifications, introduced by biochemist Brian W. Matthews in 1975. Introduced by Karl Pearson, and also known as the Yule phi coefficient from its introduction by Udny Yule in 1912 this measure is similar to the Pearson correlation coefficient in its interpretation. In fact, a Pearson correlation coefficient estimated for two binary variables will return the phi coefficient. Two binary variables are considered positively associated if most of the data falls along the diagonal cells. In contrast, two binary variables are considered negatively associated if most of the data falls off the diagonal. If we have a 2×2 table for two random variables x and y where n11, n10, n01, n00, are non-negative counts of numbers of observations that sum to n, the total number of observations. The phi coefficient that describes the association of x and y is Phi is related to the point-biserial correlation coefficient and Cohen's d and estimates the extent of the relationship between two variables (2×2). The phi coefficient can also be expressed using only , , , and , as (en)
- 파이 계수(pi係數)는 통계학에서 두 변인이 모두 질적으로 양분될수있는 경우에 적용되는 상관 계수이다. (ko)
- Współczynnik fi (ϕ) – jedna z miar zależności, będąca współczynnikiem korelacji liniowej Pearsona dla dwóch zmiennych, z których obydwie są nominalne oraz dychotomiczne. Współczynnik fi można policzyć na dwa sposoby: używając wzoru na współczynnik fi albo (podobnie jak ma to miejsce w przypadku korelacji punktowo-dwuseryjnej) zrekodować zmienne nominalne, żeby przyjmowały wartości 0 i 1 (jest to tzw. dummy coding), a następnie policzyć dla nich współczynnik korelacji liniowej Pearsona. Przykład zastosowania: związek między płcią (wartości: kobieta i mężczyzna) a trybem studiów (wartości: stacjonarne i niestacjonarne). Rozwinięciem współczynnika fi jest współczynnik V Craméra. (pl)
- 在統計學裡，「Phi相關係數」（英語：Phi coefficient）（符號表示為： 或 ）是測量兩個二元變數（英語：binary variables or dichotomous variables）之間相關性的工具，由卡爾·皮爾森所發明 。他也發明了與Phi相關係數有密切關聯的皮爾森卡方檢定（英語：Pearson's chi-squared test。一般所稱的卡方檢定，若未明指種類，即指此），以及發明了測量兩個連續變數之間相關程度的皮爾森積差相關係數（英語：Pearson's r。一般所稱的相關係數，若未明指種類，即指此）。 Phi 相關係數在機器學習的領域又稱為。 (zh)
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