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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.
These values can be calculated evaluating the quantile function (also known as "inverse CDF" or "ICDF") of the chi-squared distribution; [24] 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.
Thus an approximate p-value can be obtained from a normal probability table. For example, if z = 2.2 is observed and a two-sided p-value is desired to test the null hypothesis that =, the p-value is 2 Φ(−2.2) = 0.028, where Φ is the standard normal cumulative distribution function.
In 2016, the American Statistical Association (ASA) published a statement on p-values, saying that "the widespread use of 'statistical significance' (generally interpreted as 'p ≤ 0.05') as a license for making a claim of a scientific finding (or implied truth) leads to considerable distortion of the scientific process". [57]
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 p-value is not the probability that the observed effects were produced by random chance alone. [2] The p-value is computed under the assumption that a certain model, usually the null hypothesis, is true. This means that the p-value is a statement about the relation of the data to that hypothesis. [2]
The last line describes the omnibus F test for model fit. The interpretation is that the null hypothesis is rejected (P = 0.02692<0.05, α=0.05). So Either β1 or β2 appears to be non-zero (or perhaps both). Note that the conclusion from Coefficients: table is that only β1 is significant (P-Value shown on Pr(>|t|) column is 4.37e-05 << 0.001).
If the resulting p-value of Levene's test is less than some significance level (typically 0.05), the obtained differences in sample variances are unlikely to have occurred based on random sampling from a population with equal variances. Thus, the null hypothesis of equal variances is rejected and it is concluded that there is a difference ...