Results for: NTCIR12-MathWiki-40

Doc 18	0.3516, -4.0000, 10.0000, 0.7033	testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Conjugate_prior.html
Doc 18	0.3516, -4.0000, 10.0000, 0.7033	testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Conjugate_prior.html

Σ_{b} = \frac{1}{C} \sum_{i = 1}^{C} (μ_{i} - μ) {(μ_{i} - μ)}^{T}

Doc 19

0.3409, -7.0000, 10.0000, 0.3409

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Linear_discriminant_analysis.html

\frac{\sqrt{n} (\bar{X} - μ_{0})}{\sqrt{\sum_{i = 1}^{n} {(X_{i} - \bar{X})}^{2} / (n - 1)}}

Doc 12

0.3989, -9.0000, 13.0000, 1.2789

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Degrees_of_freedom_(statistics).html

t score = \frac{(\hat{β} - β_{0}) \sqrt{n - 2}}{\sqrt{SSR / \sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2}}} .

Doc 20

0.3379, -14.0000, 13.0000, 0.6553

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Student's_t-test.html

\sum_{i = 1}^{n} (x_{i} - \bar{x}) (θ - \bar{x}) = 0

Doc 21

0.3280, -3.0000, 12.0000, 0.3280

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Sufficient_statistic.html

σ^{2} = \sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2} / (n - 1)

Doc 22

0.3280, -5.0000, 12.0000, 0.5612

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Weighted_arithmetic_mean.html

ρ \equiv \frac{\sum_{i \neq j} (a_{i j} - \bar{a}) (a_{j i} - \bar{a})}{\sum_{i \neq j} {(a_{i j} - \bar{a})}^{2}}

Doc 23

0.3173, -19.0000, 10.0000, 0.3173

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Reciprocity_(network_science).html

S E_{\hat{β}} = \frac{\sqrt{\frac{1}{n - 2} \sum_{i = 1}^{n} {(y_{i} - {\hat{y}}_{i})}^{2}}}{\sqrt{\sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2}}}

Doc 20

0.3379, -14.0000, 13.0000, 0.6553

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Student's_t-test.html

\hat{β_{1}} = \frac{\sum (x_{i} - \bar{x}) (y_{i} - \bar{y})}{\sum {(x_{i} - \bar{x})}^{2}} and \hat{β_{0}} = \bar{y} - \hat{β_{1}} \bar{x}

Doc 24

0.3173, -25.0000, 10.0000, 0.3173

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Regression_analysis.html

{\hat{σ}}_{i} = \sqrt{\frac{\sum_{k = 1}^{n} {(x_{k} - {\bar{x}}_{i})}^{2}}{n - 1}} {\hat{σ}}_{i, j} = \sqrt{\frac{\sum_{k = 1}^{n} (x_{k} - {\bar{x}}_{i}) (x_{k} - {\bar{x}}_{j})}{n - 1}}

Doc 25

0.3074, -34.0000, 11.0000, 0.3074

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Experimental_uncertainty_analysis.html

σ_{y}^{2} = \frac{1}{n} \sum_{i = 1}^{n} {(y_{i} - \bar{y})}^{2} = (\frac{1}{n} \sum_{i = 1}^{n} y_{i}^{2}) - {\bar{y}}^{2}

Doc 26

0.3043, -20.0000, 11.0000, 0.3043

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Variance.html

s_{M} = \sum_{i = 1}^{m} x_{i}; s_{Σ} = \sqrt{\sum_{i = 1}^{m} {(x_{i} - \bar{x})}^{2}}

Doc 27

0.2938, -14.0000, 10.0000, 0.2938

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Well-behaved_statistic.html

C_{n} = \sum_{i = 1}^{n} (x_{i} - {\bar{x}}_{n}) (y_{i} - {\bar{y}}_{n})

Doc 28

0.2830, -5.0000, 13.0000, 1.0523

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Algorithms_for_calculating_variance.html

q_{j k} = \frac{1}{N} \sum_{i = 1}^{N} (x_{i j} - {\bar{x}}_{j}) (x_{i k} - {\bar{x}}_{k})

Doc 14

0.3880, -9.0000, 12.0000, 1.1873

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Sample_mean_and_sample_covariance.html

q_{j k} = \frac{1}{N - 1} \sum_{i = 1}^{N} (X_{i j} - {\bar{X}}_{j}) (X_{i k} - {\bar{X}}_{k})

Doc 29

0.2830, -13.0000, 12.0000, 0.2830

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Covariance.html

q_{j k} = \frac{1}{N - 1} \sum_{i = 1}^{N} (x_{i j} - {\bar{x}}_{j}) (x_{i k} - {\bar{x}}_{k}),

Doc 14

0.3880, -9.0000, 12.0000, 1.1873

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Sample_mean_and_sample_covariance.html

s^{2} = \frac{\sum_{i = 1}^{n} {(x_{i} - K)}^{2} - {(\sum_{i = 1}^{n} (x_{i} - K))}^{2} / n}{n - 1} .

Doc 28

0.2830, -5.0000, 13.0000, 1.0523

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Algorithms_for_calculating_variance.html

F = \frac{\sum_{j = 1}^{k} n_{j} {({\bar{y}}_{j} - \bar{y})}^{2} / (k - 1)}{\sum_{j = 1}^{k} \sum_{i = 1}^{n_{j}} {(y_{i j} - {\bar{y}}_{j})}^{2} / (n - k)}

Doc 30

0.2750, -33.0000, 12.0000, 0.5259

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Omnibus_test.html

S S_{A B} \equiv \frac{{(\sum_{i j} Y_{i j} ({\bar{Y}}_{i \cdot} - {\bar{Y}}_{\cdot \cdot}) ({\bar{Y}}_{\cdot j} - {\bar{Y}}_{\cdot \cdot}))}^{2}}{\sum_{i} {({\bar{Y}}_{i \cdot} - {\bar{Y}}_{\cdot \cdot})}^{2} \sum_{j} {({\bar{Y}}_{\cdot j} - {\bar{Y}}_{\cdot \cdot})}^{2}}

Doc 31

0.2750, -42.0000, 12.0000, 0.2750

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Tukey's_test_of_additivity.html

\sum_{i = 1}^{n} {(X_{i} - \bar{X})}^{2}

Doc 32

0.2702, 0.0000, 10.0000, 0.5404

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Bias_of_an_estimator.html

\sum_{i = 1}^{n} {(y_{i} - \bar{y})}^{2}

Doc 33

0.2702, 0.0000, 10.0000, 0.2702

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Partition_of_sums_of_squares.html

\frac{\sum_{i = 1}^{n} {(X_{i} - \bar{X})}^{2}}{σ^{2}}

Doc 12

0.3989, -9.0000, 13.0000, 1.2789

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Degrees_of_freedom_(statistics).html

s = \sqrt{\frac{\sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2}}{n - 1}}

Doc 34

0.2702, -7.0000, 10.0000, 0.4472

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Xbar_and_s_chart.html

σ_{X}^{2} = \frac{\sum_{i = 1}^{n} {(X_{i} - \bar{X})}^{2}}{n} .

Doc 35

0.2702, -7.0000, 10.0000, 0.2702

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Kuder–Richardson_Formula_20.html

variance = s^{2} = \frac{\sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2}}{n - 1}

Doc 28

0.2830, -5.0000, 13.0000, 1.0523

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Algorithms_for_calculating_variance.html

q_{x y} = \frac{\sum (x - \bar{x}) (y - \bar{y}) I (x, y)}{\sum I (x, y)}

Doc 36

0.2702, -15.0000, 8.0000, 0.2702

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Gravitational_lensing_formalism.html

\frac{1}{n} \sum_{i = 1}^{n} {(X_{i} - \bar{X})}^{2} < \frac{1}{n} \sum_{i = 1}^{n} {(X_{i} - μ)}^{2},

Doc 32

0.2702, 0.0000, 10.0000, 0.5404

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Bias_of_an_estimator.html

\sum_{i = 1}^{n} {(x_{i} - μ)}^{2} = \sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2} + n {(\bar{x} - μ)}^{2}

Doc 37

0.2702, -20.0000, 10.0000, 0.2702

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Normal_distribution.html

SSE = \sum_{i = 1}^{n} {(X_{i} - \bar{X})}^{2} + \sum_{i = 1}^{n} {(Y_{i} - \bar{Y})}^{2} + \sum_{i = 1}^{n} {(Z_{i} - \bar{Z})}^{2}

Doc 12

0.3989, -9.0000, 13.0000, 1.2789

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Degrees_of_freedom_(statistics).html

\sum_{i = 1}^{n} {(y_{i} - \bar{y})}^{2} = \sum_{i = 1}^{n} {(y_{i} - {\hat{y}}_{i})}^{2} + \sum_{i = 1}^{n} {({\hat{y}}_{i} - \bar{y})}^{2} .

Doc 8

0.4116, -16.0000, 14.0000, 1.1290

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Explained_sum_of_squares.html

C = \frac{{\hat{μ}}_{4}}{{\hat{σ}}^{4}} = \frac{\frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{4}}{{(\frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2})}^{2}},

Doc 38

0.2702, -32.0000, 10.0000, 0.2702

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Jarque–Bera_test.html

s_{n}^{2} = \frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2} = \frac{\sum_{i = 1}^{n} (x_{i}^{2})}{n} - \frac{{(\sum_{i = 1}^{n} x_{i})}^{2}}{n^{2}}

Doc 39

0.2702, -32.0000, 10.0000, 0.2702

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Bessel's_correction.html

= \frac{(n + 1) n}{(n - 1) (n - 2) (n - 3)} \frac{\sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{4}}{k_{2}^{2}} - 3 \frac{{(n - 1)}^{2}}{(n - 2) (n - 3)}

Doc 7

0.5404, -38.0000, 20.0000, 0.8106

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Kurtosis.html

\sum_{i = 1}^{n} {(y_{i} - \bar{y})}^{2} = \sum_{i = 1}^{n} {(y_{i} - {\hat{y}}_{i})}^{2} + \sum_{i = 1}^{n} {({\hat{y}}_{i} - \bar{y})}^{2} + \sum_{i = 1}^{n} 2 ({\hat{y}}_{i} - \bar{y}) (y_{i} - {\hat{y}}_{i}) .

Doc 8

0.4116, -16.0000, 14.0000, 1.1290

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Explained_sum_of_squares.html

{(x_{i} - \bar{x})}^{T} Σ^{- 1} (x_{i} - \bar{x})

Doc 13

0.3880, -8.0000, 13.0000, 2.5851

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Estimation_of_covariance_matrices.html

F = \frac{\sum_{i = 1}^{n} {(\hat{y_{i}} - \bar{y})}^{2} / k}{\sum_{j = 1}^{k} \sum_{i = 1}^{n_{j}} {(y_{i j} - \hat{y_{i}})}^{2} / (n - k - 1)}

Doc 30

0.2750, -33.0000, 12.0000, 0.5259

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Omnibus_test.html

I = \frac{N}{\sum_{i} \sum_{j} w_{i j}} \frac{\sum_{i} \sum_{j} w_{i j} (X_{i} - \bar{X}) (X_{j} - \bar{X})}{\sum_{i} {(X_{i} - \bar{X})}^{2}}

Doc 40

0.2466, -29.0000, 7.0000, 0.4461

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Moran's_I.html

TREND = \frac{\sum_{i = 1}^{\tilde{N}} (i - \tilde{N} / 2) (R R_{i} - ⟨ R R_{i} ⟩)}{\sum_{i = 1}^{\tilde{N}} {(i - \tilde{N} / 2)}^{2}},

Doc 41

0.2466, -30.0000, 8.0000, 0.2466

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Recurrence_quantification_analysis.html

\sqrt{\frac{1}{M N} \sum_{i = 0}^{N - 1} \sum_{j = 0}^{M - 1} {(I_{i j} - \bar{I})}^{2}},

Doc 42

0.2424, -16.0000, 8.0000, 0.2424

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Contrast_(vision).html

= {[\sum_{i = 1}^{N} (x_{i 2} - x_{i 1}) {(x_{i 2} - x_{i 1})}^{'}]}^{- 1} \sum_{i = 1}^{N} (x_{i 2} - x_{i 1}) (y_{i 2} - y_{i 1}) = F D_{T = 2}

Doc 43

0.2337, -36.0000, 10.0000, 0.2337

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Fixed_effects_model.html

K = (N - 1) \frac{\sum_{i = 1}^{g} n_{i} {({\bar{r}}_{i \cdot} - \bar{r})}^{2}}{\sum_{i = 1}^{g} \sum_{j = 1}^{n_{i}} {(r_{i j} - \bar{r})}^{2}},

Doc 44

0.2332, -32.0000, 9.0000, 0.2332

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Kruskal–Wallis_one-way_analysis_of_variance.html

s^{2} = \frac{\sum_{i = 1}^{N} w_{i}}{{(\sum_{i = 1}^{N} w_{i})}^{2} - \sum_{i = 1}^{N} w_{i}^{2}} . \sum_{i = 1}^{N} w_{i} {(x_{i} - {\bar{x}}^{*})}^{2}

Doc 45

0.2332, -34.0000, 9.0000, 0.4351

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Mean_square_weighted_deviation.html

Σ = \frac{\sum_{i = 1}^{N} w_{i}}{{(\sum_{i = 1}^{N} w_{i})}^{2} - \sum_{i = 1}^{N} w_{i}^{2}} \sum_{i = 1}^{N} w_{i} {(𝐱_{i} - μ^{*})}^{T} (𝐱_{i} - μ^{*}) .

Doc 22

0.3280, -5.0000, 12.0000, 0.5612

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Weighted_arithmetic_mean.html

q_{j k} = \frac{\sum_{i = 1}^{N} w_{i}}{{(\sum_{i = 1}^{N} w_{i})}^{2} - \sum_{i = 1}^{N} w_{i}^{2}} \sum_{i = 1}^{N} w_{i} (x_{i j} - {\bar{x}}_{j}) (x_{i k} - {\bar{x}}_{k}) .

Doc 14

0.3880, -9.0000, 12.0000, 1.1873

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Sample_mean_and_sample_covariance.html

\sum_{i = 1}^{n} x_{i}^{2} \sum_{i = 1}^{n} y_{i}^{2} - {(\sum_{i = 1}^{n} x_{i} y_{i})}^{2} \geq 0.

Doc 46

0.2264, -18.0000, 12.0000, 0.2264

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Cauchy–Schwarz_inequality.html

T = \frac{\sum_{i = 1}^{n} {(X_{i} - μ)}^{2}}{n} .

Doc 47

0.2230, -6.0000, 9.0000, 0.4461

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Cramér–Rao_bound.html

Z_{n} = \frac{\sum_{i = 1}^{n} (X_{i} - μ)}{σ \sqrt{n}}

Doc 48

0.2230, -7.0000, 9.0000, 0.2230

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Probability_theory.html

T = \frac{\sum_{i = 1}^{n} {(X_{i} - μ)}^{2}}{n + 2} .

Doc 47

0.2230, -6.0000, 9.0000, 0.4461

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Cramér–Rao_bound.html

s_{p}^{2} = \frac{\sum_{i = 1}^{k} (n_{i} - 1) s_{i}^{2}}{\sum_{i = 1}^{k} n_{i}}

Doc 49

0.2230, -15.0000, 8.0000, 0.4461

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Pooled_variance.html

s_{p}^{2} = \frac{\sum_{i = 1}^{k} (n_{i} - 1) s_{i}^{2}}{\sum_{i = 1}^{k} (n_{i} - 1)}

Doc 49

0.2230, -15.0000, 8.0000, 0.4461

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Pooled_variance.html

\sum {(X_{i} - μ)}^{2} = \sum {(X_{i} - \bar{X})}^{2} + \sum {(\bar{X} - μ)}^{2} + 2 \sum (X_{i} - \bar{X}) (\bar{X} - μ) .

Doc 50

0.2230, -28.0000, 7.0000, 0.3989

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Cochran's_theorem.html

\sum_{i = 1}^{n} {(x_{i} - {\bar{x}}_{n})}^{2}

Doc 28

0.2830, -5.0000, 13.0000, 1.0523

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Algorithms_for_calculating_variance.html

\sqrt{\sum_{i = 1}^{n} {(a_{i} - b_{i})}^{2}} .

Doc 51

0.2184, -2.0000, 10.0000, 0.2184

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Absolute_value.html

d_{j k} = \sqrt{\sum_{i = 1}^{N} {(x_{i j} - x_{i k})}^{2}}

Doc 52

0.2184, -6.0000, 9.0000, 0.2184

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Qualitative_variation.html

\sqrt{{(a_{1} - b_{1})}^{2} + {(a_{2} - b_{2})}^{2} + \dots + {(a_{n} - b_{n})}^{2}} = \sqrt{\sum_{i = 1}^{n} {(a_{i} - b_{i})}^{2}} .

Doc 53

0.2184, -29.0000, 10.0000, 0.2184

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Pythagorean_theorem.html

{\hat{σ}}^{2} = \frac{1}{n} \sum_{i = 1}^{n} {(μ - δ_{i})}^{2} - \frac{1}{n^{2}} \sum_{i = 1}^{n} \sum_{j = 1}^{n} (μ - δ_{i}) (μ - δ_{j}) .

Doc 54

0.2184, -31.0000, 8.0000, 0.2184

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Maximum_likelihood.html

\sum_{i j} {(Y_{i j} - {\bar{Y}}_{i \cdot})}^{2} / (N - K),

Doc 55

0.2018, -6.0000, 9.0000, 0.2018

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/F-test.html

s^{2} = \frac{\sum_{i = 0}^{p} \sum_{j = 1}^{N_{i}} (X_{i j} - \bar{X_{i}})}{n}

Doc 56

0.2018, -12.0000, 8.0000, 0.2018

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Dunnett's_test.html

σ^{2} = \frac{\sum_{i = 1}^{N} w_{i} {(x_{i} - {\bar{x}}^{*})}^{2}}{\sum_{i = 1}^{N} w_{i}}

Doc 45

0.2332, -34.0000, 9.0000, 0.4351

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Mean_square_weighted_deviation.html

r {(Y, \hat{Y})}^{2} = \frac{\sum_{i} {({\hat{Y}}_{i} - \bar{Y})}^{2}}{\sum_{i} {(Y_{i} - \bar{Y})}^{2}}

Doc 4

0.7176, -19.0000, 25.0000, 1.3159

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Pearson_product-moment_correlation_coefficient.html

η^{2} = \frac{\sum_{x} n_{x} {({\bar{y}}_{x} - \bar{y})}^{2}}{\sum_{x, i} {(y_{x i} - \bar{y})}^{2}}

Doc 57

0.1994, -19.0000, 5.0000, 0.1994

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Correlation_ratio.html

S_{3} = \frac{N^{- 1} \sum_{i} {(x_{i} - \bar{x})}^{4}}{{(N^{- 1} \sum_{i} {(x_{i} - \bar{x})}^{2})}^{2}}

Doc 40

0.2466, -29.0000, 7.0000, 0.4461

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Moran's_I.html

\sum_{i} {(Y_{i} - \bar{Y})}^{2} = \sum_{i} {(Y_{i} - {\hat{Y}}_{i})}^{2} + \sum_{i} {({\hat{Y}}_{i} - \bar{Y})}^{2},

Doc 4

0.7176, -19.0000, 25.0000, 1.3159

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Pearson_product-moment_correlation_coefficient.html

1 = \frac{\sum_{i} {(Y_{i} - {\hat{Y}}_{i})}^{2}}{\sum_{i} {(Y_{i} - \bar{Y})}^{2}} + \frac{\sum_{i} {({\hat{Y}}_{i} - \bar{Y})}^{2}}{\sum_{i} {(Y_{i} - \bar{Y})}^{2}} .

Doc 4

0.7176, -19.0000, 25.0000, 1.3159

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Pearson_product-moment_correlation_coefficient.html

μ sig = \frac{\sum_{i = 1}^{n} (X_{i} - f_{i})}{n} μ bkg = \frac{\sum_{i = 1}^{n} (X_{i} - f_{i})}{n}

Doc 58

0.1942, -21.0000, 9.0000, 0.1942

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Signal-to-noise_ratio_(imaging).html

\sum_{i = 1}^{n} {(y_{i} - {\hat{y}}_{i})}^{2} = \sum_{i = 1}^{n} {(y_{i} - \sum_{j = 1}^{K} {\hat{β}}_{j} X_{i j})}^{2} .

Doc 59

0.1942, -23.0000, 9.0000, 0.1942

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Gauss–Markov_theorem.html

\frac{(N - 2 K) {(N - 1)}^{\frac{1}{2}} (N - 2 n)}{{[n K (N - K) (N - n)]}^{\frac{1}{2}} (N - 2)}

Doc 60

0.1942, -26.0000, 7.0000, 0.1942

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Hypergeometric_distribution.html

{\bar{s}}_{i} = \sqrt{\frac{\sum_{j = 1}^{n} {(x_{i j} - {\bar{x}}_{i})}^{2}}{n - 1}}

Doc 34

0.2702, -7.0000, 10.0000, 0.4472

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Xbar_and_s_chart.html

\begin{matrix} (y_{i} - \bar{y}) = (y_{i} - {\hat{y}}_{i}) + ({\hat{y}}_{i} - \bar{y}) . \end{matrix}

Doc 8

0.4116, -16.0000, 14.0000, 1.1290

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Explained_sum_of_squares.html

\sum {(X_{i} - μ)}^{2} = \sum {(X_{i} - \bar{X} + \bar{X} - μ)}^{2}

Doc 50

0.2230, -28.0000, 7.0000, 0.3989

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Cochran's_theorem.html

\sum_{i = 1}^{n} f (x_{i}^{*}) (x_{i} - x_{i - 1})

Doc 61

0.1616, -9.0000, 7.0000, 0.1616

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Antiderivative.html

Γ = \frac{\sum (r_{j} - r_{i}) (s_{j} - s_{i})}{\sum {(r_{j} - r_{i})}^{2}}

Doc 62

0.1575, -12.0000, 6.0000, 0.1575

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Rank_correlation.html

\sum_{i = 1}^{n} x_{i} (1 - k_{i}) {(1 - k_{j})}^{- 1} = 0

Doc 63

0.1452, -12.0000, 7.0000, 0.1452

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Nakayama_lemma.html

\sqrt{(t - p) (t - q) (t - r) (t - s)} .

Doc 64

0.1285, -12.0000, 4.0000, 0.1285

testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Brahmagupta.html