| 1 | """ |
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| 2 | Contingency table contains conditional distributions. Unless explicitly |
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| 3 | 'normalized', they contain absolute frequencies, that is, the number of |
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| 4 | instances with a particular combination of two variables' values. If they are |
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| 5 | normalized by dividing each cell by the row sum, the represent conditional |
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| 6 | probabilities of the column variable (here denoted as ``innerVariable``) |
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| 7 | conditioned by the row variable (``outerVariable``). |
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| 8 | |
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| 9 | Contingency matrices are usually constructed for discrete variables. Matrices |
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| 10 | for continuous variables have certain limitations described in a :ref:`separate |
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| 11 | section <contcont>`. |
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| 12 | |
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| 13 | The example below loads the monks-1 data set and prints out the conditional |
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| 14 | class distribution given the value of `e`. |
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| 15 | |
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| 16 | .. _statistics-contingency: code/statistics-contingency.py |
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| 17 | |
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| 18 | part of `statistics-contingency`_ (uses monks-1.tab) |
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| 19 | |
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| 20 | .. literalinclude:: code/statistics-contingency.py |
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| 21 | :lines: 1-7 |
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| 22 | |
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| 23 | This code prints out:: |
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| 24 | |
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| 25 | 1 <0.000, 108.000> |
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| 26 | 2 <72.000, 36.000> |
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| 27 | 3 <72.000, 36.000> |
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| 28 | 4 <72.000, 36.000> |
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| 29 | |
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| 30 | Contingencies behave like lists of distributions (in this case, class |
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| 31 | distributions) indexed by values (of `e`, in this |
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| 32 | example). Distributions are, in turn indexed by values (class values, |
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| 33 | here). The variable `e` from the above example is called the outer |
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| 34 | variable, and the class is the inner. This can also be reversed. It is |
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| 35 | also possible to use features for both, outer and inner variable, so |
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| 36 | the table shows distributions of one variable's values given the |
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| 37 | value of another. There is a corresponding hierarchy of classes: |
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| 38 | :obj:`Table` is a base class for :obj:`VarVar` (both |
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| 39 | variables are attributes) and :obj:`Class` (one variable is |
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| 40 | the class). The latter is the base class for |
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| 41 | :obj:`VarClass` and :obj:`ClassVar`. |
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| 42 | |
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| 43 | The most commonly used of the above classes is :obj:`VarClass` which |
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| 44 | can compute and store conditional probabilities of classes given the feature value. |
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| 45 | |
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| 46 | Contingency matrices |
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| 47 | ==================== |
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| 48 | |
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| 49 | .. class:: Table |
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| 50 | |
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| 51 | Provides a base class for storing and manipulating contingency |
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| 52 | matrices. Although it is not abstract, it is seldom used directly but rather |
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| 53 | through more convenient derived classes described below. |
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| 54 | |
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| 55 | .. attribute:: outerVariable |
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| 56 | |
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| 57 | Outer variable (:class:`Orange.data.variable.Variable`) whose values are |
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| 58 | used as the first, outer index. |
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| 59 | |
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| 60 | .. attribute:: innerVariable |
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| 61 | |
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| 62 | Inner variable(:class:`Orange.data.variable.Variable`), whose values are |
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| 63 | used as the second, inner index. |
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| 64 | |
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| 65 | .. attribute:: outerDistribution |
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| 66 | |
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| 67 | The marginal distribution (:class:`Distribution`) of the outer variable. |
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| 68 | |
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| 69 | .. attribute:: innerDistribution |
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| 70 | |
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| 71 | The marginal distribution (:class:`Distribution`) of the inner variable. |
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| 72 | |
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| 73 | .. attribute:: innerDistributionUnknown |
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| 74 | |
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| 75 | The distribution (:class:`distribution.Distribution`) of the inner variable for |
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| 76 | instances for which the outer variable was undefined. This is the |
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| 77 | difference between the ``innerDistribution`` and (unconditional) |
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| 78 | distribution of inner variable. |
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| 79 | |
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| 80 | .. attribute:: varType |
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| 81 | |
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| 82 | The type of the outer variable (:obj:`Orange.data.Type`, usually |
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| 83 | :obj:`Orange.data.variable.Discrete` or |
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| 84 | :obj:`Orange.data.variable.Continuous`); equals |
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| 85 | ``outerVariable.varType`` and ``outerDistribution.varType``. |
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| 86 | |
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| 87 | .. method:: __init__(outer_variable, inner_variable) |
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| 88 | |
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| 89 | Construct an instance of contingency table for the given pair of |
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| 90 | variables. |
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| 91 | |
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| 92 | :param outer_variable: Descriptor of the outer variable |
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| 93 | :type outer_variable: Orange.data.variable.Variable |
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| 94 | :param outer_variable: Descriptor of the inner variable |
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| 95 | :type inner_variable: Orange.data.variable.Variable |
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| 96 | |
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| 97 | .. method:: add(outer_value, inner_value[, weight=1]) |
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| 98 | |
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| 99 | Add an element to the contingency table by adding ``weight`` to the |
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| 100 | corresponding cell. |
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| 101 | |
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| 102 | :param outer_value: The value for the outer variable |
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| 103 | :type outer_value: int, float, string or :obj:`Orange.data.Value` |
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| 104 | :param inner_value: The value for the inner variable |
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| 105 | :type inner_value: int, float, string or :obj:`Orange.data.Value` |
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| 106 | :param weight: Instance weight |
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| 107 | :type weight: float |
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| 108 | |
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| 109 | .. method:: normalize() |
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| 110 | |
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| 111 | Normalize all distributions (rows) in the table to sum to ``1``:: |
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| 112 | |
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| 113 | >>> cont.normalize() |
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| 114 | >>> for val, dist in cont.items(): |
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| 115 | print val, dist |
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| 116 | |
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| 117 | Output: :: |
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| 118 | |
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| 119 | 1 <0.000, 1.000> |
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| 120 | 2 <0.667, 0.333> |
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| 121 | 3 <0.667, 0.333> |
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| 122 | 4 <0.667, 0.333> |
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| 123 | |
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| 124 | .. note:: |
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| 125 | |
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| 126 | This method does not change the ``innerDistribution`` or |
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| 127 | ``outerDistribution``. |
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| 128 | |
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| 129 | With respect to indexing, contingency table is a cross between dictionary |
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| 130 | and a list. It supports standard dictionary methods ``keys``, ``values`` and |
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| 131 | ``items``. :: |
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| 132 | |
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| 133 | >> print cont.keys() |
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| 134 | ['1', '2', '3', '4'] |
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| 135 | >>> print cont.values() |
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| 136 | [<0.000, 108.000>, <72.000, 36.000>, <72.000, 36.000>, <72.000, 36.000>] |
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| 137 | >>> print cont.items() |
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| 138 | [('1', <0.000, 108.000>), ('2', <72.000, 36.000>), |
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| 139 | ('3', <72.000, 36.000>), ('4', <72.000, 36.000>)] |
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| 140 | |
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| 141 | Although keys returned by the above functions are strings, contingency can |
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| 142 | be indexed by anything that can be converted into values of the outer |
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| 143 | variable: strings, numbers or instances of ``Orange.data.Value``. :: |
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| 144 | |
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| 145 | >>> print cont[0] |
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| 146 | <0.000, 108.000> |
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| 147 | >>> print cont["1"] |
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| 148 | <0.000, 108.000> |
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| 149 | >>> print cont[orange.Value(data.domain["e"], "1")] |
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| 150 | |
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| 151 | The length of the table equals the number of values of the outer |
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| 152 | variable. However, iterating through contingency |
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| 153 | does not return keys, as with dictionaries, but distributions. :: |
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| 154 | |
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| 155 | >>> for i in cont: |
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| 156 | ... print i |
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| 157 | <0.000, 108.000> |
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| 158 | <72.000, 36.000> |
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| 159 | <72.000, 36.000> |
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| 160 | <72.000, 36.000> |
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| 161 | <72.000, 36.000> |
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| 162 | |
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| 163 | |
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| 164 | .. class:: Class |
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| 165 | |
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| 166 | An abstract base class for contingency matrices that contain the class, |
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| 167 | either as the inner or the outer variable. |
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| 168 | |
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| 169 | .. attribute:: classVar (read only) |
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| 170 | |
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| 171 | The class attribute descriptor; always equal to either |
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| 172 | :obj:`Table.innerVariable` or :obj:``Table.outerVariable``. |
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| 173 | |
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| 174 | .. attribute:: variable |
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| 175 | |
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| 176 | Variable; always equal either to either ``innerVariable`` or ``outerVariable`` |
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| 177 | |
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| 178 | .. method:: add_var_class(variable_value, class_value[, weight=1]) |
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| 179 | |
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| 180 | Add an element to contingency by increasing the corresponding count. The |
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| 181 | difference between this and :obj:`Table.add` is that the variable |
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| 182 | value is always the first argument and class value the second, |
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| 183 | regardless of which one is inner and which one is outer. |
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| 184 | |
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| 185 | :param variable_value: Variable value |
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| 186 | :type variable_value: int, float, string or :obj:`Orange.data.Value` |
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| 187 | :param class_value: Class value |
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| 188 | :type class_value: int, float, string or :obj:`Orange.data.Value` |
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| 189 | :param weight: Instance weight |
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| 190 | :type weight: float |
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| 191 | |
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| 192 | |
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| 193 | .. class:: VarClass |
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| 194 | |
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| 195 | A class derived from :obj:`Class` in which the variable is |
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| 196 | used as :obj:`Table.outerVariable` and class as the |
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| 197 | :obj:`Table.innerVariable`. This form is a form suitable for |
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| 198 | computation of conditional class probabilities given the variable value. |
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| 199 | |
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| 200 | Calling :obj:`VarClass.add_var_class(v, c)` is equivalent to |
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| 201 | :obj:`Table.add(v, c)`. Similar as :obj:`Table`, |
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| 202 | :obj:`VarClass` can compute contingency from instances. |
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| 203 | |
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| 204 | .. method:: __init__(feature, class_variable) |
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| 205 | |
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| 206 | Construct an instance of :obj:`VarClass` for the given pair of |
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| 207 | variables. Inherited from :obj:`Table`. |
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| 208 | |
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| 209 | :param feature: Outer variable |
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| 210 | :type feature: Orange.data.variable.Variable |
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| 211 | :param class_attribute: Class variable; used as ``innerVariable`` |
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| 212 | :type class_attribute: Orange.data.variable.Variable |
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| 213 | |
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| 214 | .. method:: __init__(feature, data[, weightId]) |
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| 215 | |
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| 216 | Compute the contingency table from data. |
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| 217 | |
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| 218 | :param feature: Outer variable |
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| 219 | :type feature: Orange.data.variable.Variable |
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| 220 | :param data: A set of instances |
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| 221 | :type data: Orange.data.Table |
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| 222 | :param weightId: meta attribute with weights of instances |
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| 223 | :type weightId: int |
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| 224 | |
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| 225 | .. method:: p_class(value) |
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| 226 | |
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| 227 | Return the probability distribution of classes given the value of the |
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| 228 | variable. |
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| 229 | |
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| 230 | :param value: The value of the variable |
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| 231 | :type value: int, float, string or :obj:`Orange.data.Value` |
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| 232 | :rtype: Orange.statistics.distribution.Distribution |
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| 233 | |
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| 234 | |
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| 235 | .. method:: p_class(value, class_value) |
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| 236 | |
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| 237 | Returns the conditional probability of the class_value given the |
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| 238 | feature value, p(class_value|value) (note the order of arguments!) |
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| 239 | |
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| 240 | :param value: The value of the variable |
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| 241 | :type value: int, float, string or :obj:`Orange.data.Value` |
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| 242 | :param class_value: The class value |
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| 243 | :type value: int, float, string or :obj:`Orange.data.Value` |
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| 244 | :rtype: float |
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| 245 | |
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| 246 | .. _statistics-contingency3.py: code/statistics-contingency3.py |
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| 247 | |
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| 248 | part of `statistics-contingency3.py`_ (uses monks-1.tab) |
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| 249 | |
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| 250 | .. literalinclude:: code/statistics-contingency3.py |
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| 251 | :lines: 1-23 |
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| 252 | |
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| 253 | The inner and the outer variable and their relations to the class are |
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| 254 | as follows:: |
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| 255 | |
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| 256 | Inner variable: y |
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| 257 | Outer variable: e |
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| 258 | |
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| 259 | Class variable: y |
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| 260 | Feature: e |
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| 261 | |
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| 262 | Distributions are normalized, and probabilities are elements from the |
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| 263 | normalized distributions. Knowing that the target concept is |
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| 264 | y := (e=1) or (a=b), distributions are as expected: when e equals 1, class 1 |
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| 265 | has a 100% probability, while for the rest, probability is one third, which |
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| 266 | agrees with a probability that two three-valued independent features |
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| 267 | have the same value. :: |
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| 268 | |
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| 269 | Distributions: |
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| 270 | p(.|1) = <0.000, 1.000> |
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| 271 | p(.|2) = <0.662, 0.338> |
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| 272 | p(.|3) = <0.659, 0.341> |
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| 273 | p(.|4) = <0.669, 0.331> |
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| 274 | |
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| 275 | Probabilities of class '1' |
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| 276 | p(1|1) = 1.000 |
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| 277 | p(1|2) = 0.338 |
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| 278 | p(1|3) = 0.341 |
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| 279 | p(1|4) = 0.331 |
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| 280 | |
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| 281 | Distributions from a matrix computed manually: |
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| 282 | p(.|1) = <0.000, 1.000> |
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| 283 | p(.|2) = <0.662, 0.338> |
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| 284 | p(.|3) = <0.659, 0.341> |
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| 285 | p(.|4) = <0.669, 0.331> |
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| 286 | |
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| 287 | |
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| 288 | .. class:: ClassVar |
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| 289 | |
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| 290 | :obj:`ClassVar` is similar to :obj:`VarClass` except |
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| 291 | that the class is outside and the variable is inside. This form of |
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| 292 | contingency table is suitable for computing conditional probabilities of |
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| 293 | variable given the class. All methods get the two arguments in the same |
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| 294 | order as :obj:`VarClass`. |
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| 295 | |
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| 296 | .. method:: __init__(feature, class_variable) |
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| 297 | |
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| 298 | Construct an instance of :obj:`VarClass` for the given pair of |
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| 299 | variables. Inherited from :obj:`Table`, except for the reversed |
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| 300 | order of arguments. |
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| 301 | |
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| 302 | :param feature: Outer variable |
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| 303 | :type feature: Orange.data.variable.Variable |
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| 304 | :param class_variable: Class variable |
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| 305 | :type class_variable: Orange.data.variable.Variable |
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| 306 | |
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| 307 | .. method:: __init__(feature, data[, weightId]) |
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| 308 | |
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| 309 | Compute contingency table from the data. |
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| 310 | |
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| 311 | :param feature: Descriptor of the outer variable |
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| 312 | :type feature: Orange.data.variable.Variable |
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| 313 | :param data: A set of instances |
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| 314 | :type data: Orange.data.Table |
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| 315 | :param weightId: meta attribute with weights of instances |
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| 316 | :type weightId: int |
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| 317 | |
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| 318 | .. method:: p_attr(class_value) |
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| 319 | |
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| 320 | Return the probability distribution of variable given the class. |
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| 321 | |
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| 322 | :param class_value: The value of the variable |
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| 323 | :type class_value: int, float, string or :obj:`Orange.data.Value` |
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| 324 | :rtype: Orange.statistics.distribution.Distribution |
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| 325 | |
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| 326 | .. method:: p_attr(value, class_value) |
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| 327 | |
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| 328 | Returns the conditional probability of the value given the |
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| 329 | class, p(value|class_value). |
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| 330 | |
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| 331 | :param value: Value of the variable |
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| 332 | :type value: int, float, string or :obj:`Orange.data.Value` |
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| 333 | :param class_value: Class value |
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| 334 | :type value: int, float, string or :obj:`Orange.data.Value` |
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| 335 | :rtype: float |
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| 336 | |
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| 337 | .. _statistics-contingency4.py: code/statistics-contingency4.py |
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| 338 | |
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| 339 | .. literalinclude:: code/statistics-contingency4.py |
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| 340 | :lines: 1-27 |
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| 341 | |
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| 342 | part of the output from `statistics-contingency4.py`_ (uses monk1.tab) |
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| 343 | |
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| 344 | The role of the feature and the class are reversed compared to |
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| 345 | :obj:`ClassVar`:: |
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| 346 | |
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| 347 | Inner variable: e |
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| 348 | Outer variable: y |
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| 349 | |
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| 350 | Class variable: y |
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| 351 | Feature: e |
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| 352 | |
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| 353 | Distributions given the class can be printed out by calling :meth:`p_attr`. |
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| 354 | |
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| 355 | part of `statistics-contingency4.py`_ (uses monks-1.tab) |
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| 356 | |
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| 357 | .. literalinclude:: code/statistics-contingency4.py |
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| 358 | :lines: 30-31 |
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| 359 | |
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| 360 | will print:: |
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| 361 | p(.|0) = <0.000, 0.333, 0.333, 0.333> |
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| 362 | p(.|1) = <0.500, 0.167, 0.167, 0.167> |
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| 363 | |
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| 364 | If the class value is '0', the attribute `e` cannot be `1` (the first |
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| 365 | value), while distribution across other values is uniform. If the class |
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| 366 | value is `1`, `e` is `1` for exactly half of instances, and distribution of |
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| 367 | other values is again uniform. |
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| 368 | |
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| 369 | .. class:: VarVar |
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| 370 | |
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| 371 | Contingency table in which none of the variables is the class. The class |
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| 372 | is derived from :obj:`Table`, and adds an additional constructor and |
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| 373 | method for getting conditional probabilities. |
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| 374 | |
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| 375 | .. method:: VarVar(outer_variable, inner_variable) |
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| 376 | |
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| 377 | Inherited from :obj:`Table`. |
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| 378 | |
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| 379 | .. method:: __init__(outer_variable, inner_variable, data[, weightId]) |
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| 380 | |
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| 381 | Compute the contingency from the given instances. |
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| 382 | |
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| 383 | :param outer_variable: Outer variable |
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| 384 | :type outer_variable: Orange.data.variable.Variable |
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| 385 | :param inner_variable: Inner variable |
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| 386 | :type inner_variable: Orange.data.variable.Variable |
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| 387 | :param data: A set of instances |
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| 388 | :type data: Orange.data.Table |
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| 389 | :param weightId: meta attribute with weights of instances |
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| 390 | :type weightId: int |
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| 391 | |
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| 392 | .. method:: p_attr(outer_value) |
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| 393 | |
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| 394 | Return the probability distribution of the inner variable given the |
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| 395 | outer variable value. |
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| 396 | |
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| 397 | :param outer_value: The value of the outer variable |
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| 398 | :type outer_value: int, float, string or :obj:`Orange.data.Value` |
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| 399 | :rtype: Orange.statistics.distribution.Distribution |
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| 400 | |
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| 401 | .. method:: p_attr(outer_value, inner_value) |
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| 402 | |
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| 403 | Return the conditional probability of the inner_value |
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| 404 | given the outer_value. |
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| 405 | |
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| 406 | :param outer_value: The value of the outer variable |
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| 407 | :type outer_value: int, float, string or :obj:`Orange.data.Value` |
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| 408 | :param inner_value: The value of the inner variable |
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| 409 | :type inner_value: int, float, string or :obj:`Orange.data.Value` |
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| 410 | :rtype: float |
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| 411 | |
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| 412 | The following example investigates which material is used for |
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| 413 | bridges of different lengths. |
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| 414 | |
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| 415 | .. _statistics-contingency5.py: code/statistics-contingency5.py |
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| 416 | |
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| 417 | part of `statistics-contingency5.py`_ (uses bridges.tab) |
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| 418 | |
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| 419 | .. literalinclude:: code/statistics-contingency5.py |
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| 420 | :lines: 1-17 |
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| 421 | |
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| 422 | Short bridges are mostly wooden or iron, and the longer (and most of the |
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| 423 | middle sized) are made from steel:: |
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| 424 | |
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| 425 | SHORT: |
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| 426 | WOOD (56%) |
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| 427 | IRON (44%) |
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| 428 | |
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| 429 | MEDIUM: |
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| 430 | WOOD (9%) |
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| 431 | IRON (11%) |
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| 432 | STEEL (79%) |
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| 433 | |
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| 434 | LONG: |
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| 435 | STEEL (100%) |
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| 436 | |
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| 437 | As all other contingency tables, this one can also be computed "manually". |
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| 438 | |
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| 439 | .. literalinclude:: code/statistics-contingency5.py |
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| 440 | :lines: 18- |
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| 441 | |
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| 442 | |
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| 443 | Contingencies for entire domain |
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| 444 | =============================== |
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| 445 | |
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| 446 | A list of contingency tables, either :obj:`VarClass` or |
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| 447 | :obj:`ClassVar`. |
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| 448 | |
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| 449 | .. class:: Domain |
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| 450 | |
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| 451 | .. method:: __init__(data[, weightId=0, classOuter=0|1]) |
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| 452 | |
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| 453 | Compute a list of contingency tables. |
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| 454 | |
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| 455 | :param data: A set of instances |
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| 456 | :type data: Orange.data.Table |
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| 457 | :param weightId: meta attribute with weights of instances |
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| 458 | :type weightId: int |
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| 459 | :param classOuter: `True`, if class is the outer variable |
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| 460 | :type classOuter: bool |
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| 461 | |
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| 462 | .. note:: |
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| 463 | |
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| 464 | ``classIsOuter`` cannot be given as positional argument, |
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| 465 | but needs to be passed by keyword. |
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| 466 | |
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| 467 | .. attribute:: classIsOuter (read only) |
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| 468 | |
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| 469 | Tells whether the class is the outer or the inner variable. |
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| 470 | |
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| 471 | .. attribute:: classes |
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| 472 | |
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| 473 | Contains the distribution of class values on the entire dataset. |
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| 474 | |
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| 475 | .. method:: normalize() |
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| 476 | |
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| 477 | Call normalize for all contingencies. |
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| 478 | |
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| 479 | The following script prints the contingency tables for features |
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| 480 | "a", "b" and "e" for the dataset Monk 1. |
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| 481 | |
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| 482 | .. _statistics-contingency8: code/statistics-contingency8.py |
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| 483 | |
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| 484 | part of `statistics-contingency8`_ (uses monks-1.tab) |
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| 485 | |
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| 486 | .. literalinclude:: code/statistics-contingency8.py |
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| 487 | :lines: 9 |
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| 488 | |
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| 489 | Contingency tables of type :obj:`VarClass` give |
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| 490 | the conditional distributions of classes, given the value of the variable. |
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| 491 | |
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| 492 | .. _statistics-contingency8: code/statistics-contingency8.py |
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| 493 | |
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| 494 | part of `statistics-contingency8`_ (uses monks-1.tab) |
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| 495 | |
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| 496 | .. literalinclude:: code/statistics-contingency8.py |
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| 497 | :lines: 12- |
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| 498 | |
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| 499 | |
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| 500 | .. _contcont: |
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| 501 | |
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| 502 | Contingency tables for continuous variables |
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| 503 | =========================================== |
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| 504 | |
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| 505 | If the outer variable is continuous, the index must be one of the |
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| 506 | values that do exist in the contingency table; other values raise an |
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| 507 | exception:: |
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| 508 | |
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| 509 | .. _statistics-contingency6: code/statistics-contingency6.py |
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| 510 | |
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| 511 | part of `statistics-contingency6`_ (uses monks-1.tab) |
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| 512 | |
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| 513 | .. literalinclude:: code/statistics-contingency6.py |
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| 514 | :lines: 1-4,17- |
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| 515 | |
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| 516 | Since even rounding can be a problem, the only safe way to get the key |
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| 517 | is to take it from from the contingencies' ``keys``. |
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| 518 | |
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| 519 | Contingency tables with discrete outer variable and continuous inner variables |
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| 520 | are more useful, since methods :obj:`ContingencyClassVar.p_class` |
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| 521 | and :obj:`ContingencyVarClass.p_attr` use the primitive density estimation |
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| 522 | provided by :obj:`Orange.statistics.distribution.Distribution`. |
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| 523 | |
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| 524 | For example, :obj:`ClassVar` on the iris dataset can return the |
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| 525 | probability of the sepal length 5.5 for different classes:: |
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| 526 | |
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| 527 | .. _statistics-contingency7: code/statistics-contingency7.py |
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| 528 | |
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| 529 | part of `statistics-contingency7`_ (uses iris.tab) |
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| 530 | |
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| 531 | .. literalinclude:: code/statistics-contingency7.py |
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| 532 | |
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| 533 | The script outputs:: |
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| 534 | |
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| 535 | Estimated frequencies for e=5.5 |
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| 536 | f(5.5|Iris-setosa) = 2.000 |
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| 537 | f(5.5|Iris-versicolor) = 5.000 |
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| 538 | f(5.5|Iris-virginica) = 1.000 |
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| 539 | |
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| 540 | """ |
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| 541 | |
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| 542 | from Orange.core import Contingency as Table |
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| 543 | from Orange.core import ContingencyAttrAttr as VarVar |
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| 544 | from Orange.core import ContingencyClass as Class |
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| 545 | from Orange.core import ContingencyAttrClass as VarClass |
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| 546 | from Orange.core import ContingencyClassAttr as ClassVar |
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| 547 | |
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| 548 | from Orange.core import DomainContingency as Domain |
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