Compute chi^2-statistic for test on proportions as the categorical variable (Chi2Score)

class cerebstats.stat_scores.chi2Score.Chi2Score(*args: Any, **kwargs: Any)

Compute chi2-statistic for chi squared Test of proportions.

For any two-way contingency tables.

Possibilities for categorical variable, A	Possibilities for categorical variable, B
	Yes	No
a1	\(O_{00}\)	\(O_{01}\)
a2	\(O_{10}\)	\(O_{11}\)

Definitions	Interpretation
\(r\)	number of row variables
\(c\)	number of column variables
\(O_{ij}\)	observed count for a cell in \(i^{th}\) row, \(j^{th}\) column
\(R_{i}\)	total observations in \(i^{th}\) row, \(\sum_{\forall j \in c} O_{ij}\)
\(C_{j}\)	total observations in \(j^{th}\) column, \(\sum_{\forall i \in r} O_{ij}\)
\(n\)	total count for entire table \(\sum_{\forall i \in r} R_i\) or \(\sum_{\forall j \in c} C_j\)
\(E_{ij}\)	expected count for a cell in \(i^{th}\) row, \(j^{th}\) column \(E_{ij} = \frac{R_i C_j}{n}\)
test-statistic	\(\chi^2 = \sum_{\forall i,j} \frac{(O_{ij}-E_{ij})^2}{E_{ij}}\)
\(df\)	degrees of freedom, \(df = (r-1)(c-1)\)

Special note. For the case of 2 x 2 table like below

Possibilities for categorical variable, A row-1	Possibilities for categorical variable, B		Total R1
	column-1 A	column-2 B
row-2	C	D	R2
Total	C1	C2	N

Notice that for 2 x 2, \(df = 1\) and its test statictic can calculated with the shortcut formula

\(\chi^2 = \frac{ N(AD-BC)^2 }{ R_1 R_2 C_1 C_2 }\)

This class uses scipy.stats.chi2_contingency. chi2_contingency is a special case of chisquare as demonstrated below

obs = np.array([ [129, 49], [150, 29], [137, 39] ])
chi2, p, df, expected = scipy.stats.chi2_contingency( obs )
chi2_, p_ = scipy.stats.chisquare( obs.ravel(), f_exp=expected.ravel(), ddof=obs.size-1-df )
chi2 == chi2_ == 6.69
True
p == p2 == 0.03
True

Use Case:

x = Chi2ScoreForProportionChi2Test.compute( observation, prediction )
score = Chi2ScoreForProportionChi2Test(x)

Note: As part of the SciUnit framework this custom TScore should have the following methods,

• compute() (class method)

• sort_key() (property)

• __str__()

classmethod compute(observation, prediction)

Argument	Value type
first argument |dictionary; observation/experimental data must |must have keys “sample_size” and “success_numbers”
second argument |dictionary; model prediction must also have keys |”sample_size” and “success_numbers”

Note:

• for a 2 x 2 table, the value for the key “success_numbers is a number for both observation and prediction

• for a 2 x k table, the values for the keys “success_numbers” (both observation and prediction) is either a list or an array.

• chi squared tests by nature are two-sided so there is not option for one-sidedness.