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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 p-value for the permutation test is the proportion of the r values generated in step (2) that are larger than the Pearson correlation coefficient that was calculated from the original data. Here "larger" can mean either that the value is larger in magnitude, or larger in signed value, depending on whether a two-sided or one-sided test is ...
In order to calculate the significance of the observed data, i.e. the total probability of observing data as extreme or more extreme if the null hypothesis is true, we have to calculate the values of p for both these tables, and add them together. This gives a one-tailed test, with p approximately 0
The p-value is the probability that a test statistic which is at least as extreme as the one obtained would occur under the null hypothesis. At a significance level of 0.05, a fair coin would be expected to (incorrectly) reject the null hypothesis (that it is fair) in 1 out of 20 tests on average.
Yates's correction should always be applied, as it will tend to improve the accuracy of the p-value obtained. [ citation needed ] However, in situations with large sample sizes, using the correction will have little effect on the value of the test statistic, and hence the p-value.
The Spearman correlation coefficient is often described as being "nonparametric". This can have two meanings. First, a perfect Spearman correlation results when X and Y are related by any monotonic function. Contrast this with the Pearson correlation, which only gives a perfect value when X and Y are related by a linear function.
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.
The Bonferroni correction can also be applied as a p-value adjustment: Using that approach, instead of adjusting the alpha level, each p-value is multiplied by the number of tests (with adjusted p-values that exceed 1 then being reduced to 1), and the alpha level is left unchanged.