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In null-hypothesis significance testing, the p-value [note 1] is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. [2] [3] A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis.
The values within the table are the probabilities corresponding to the table type. These probabilities are calculations of the area under the normal curve from the starting point (0 for cumulative from mean , negative infinity for cumulative and positive infinity for complementary cumulative ) to Z .
Irving Anellis's research shows that C.S. Peirce appears to be the earliest logician (in 1883) to devise a truth table matrix. [4]From the summary of Anellis's paper: [4] In 1997, John Shosky discovered, on the verso of a page of the typed transcript of Bertrand Russell's 1912 lecture on "The Philosophy of Logical Atomism" truth table matrices.
The p-value of the test statistic is computed either numerically or by looking it up in a table. If the p-value is small enough (usually p < 0.05 by convention), then the null hypothesis is rejected, and we conclude that the observed data does not follow the multinomial distribution.
To determine whether a result is statistically significant, a researcher calculates a p-value, which is the probability of observing an effect of the same magnitude or more extreme given that the null hypothesis is true. [5] [12] The null hypothesis is rejected if the p-value is less than (or equal to) a predetermined level, .
Fisher's exact test is a statistical significance test used in the analysis of contingency tables. [1] [2] [3] Although in practice it is employed when sample sizes are small, it is valid for all sample sizes.
These values can be calculated evaluating the quantile function (also known as "inverse CDF" or "ICDF") of the chi-squared distribution; [23] e. g., the χ 2 ICDF for p = 0.05 and df = 7 yields 2.1673 ≈ 2.17 as in the table above, noticing that 1 – p is the p-value from the table.
Chi-squared distribution, showing χ 2 on the x-axis and p-value (right tail probability) on the y-axis.. A chi-squared test (also chi-square or χ 2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large.