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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.
If the p-value is less than the chosen significance threshold (equivalently, if the observed test statistic is in the critical region), then we say the null hypothesis is rejected at the chosen level of significance. If the p-value is not less than the chosen significance threshold (equivalently, if the observed test statistic is outside the ...
The trade-off of variance-structure misspecification and consistent regression coefficient estimates is loss of efficiency, yielding inflated Wald test p-values as a result of higher variance of standard errors than that of the most optimal. [6]
The statistical significance of each B is tested by the Wald Chi-Square—testing the null that the B coefficient = 0 (the alternate hypothesis is that it does not = 0). p-values lower than alpha are significant, leading to rejection of the null. Here, only the independent variables felony, rehab, employment, are significant ( P-Value<0.05.
The t-test p-value for the difference in means, and the regression p-value for the slope, are both 0.00805. The methods give identical results. The methods give identical results. This example shows that, for the special case of a simple linear regression where there is a single x-variable that has values 0 and 1, the t -test gives the same ...
The Šidák correction is derived by assuming that the individual tests are independent.Let the significance threshold for each test be ; then the probability that at least one of the tests is significant under this threshold is (1 - the probability that none of them are significant).
The residual is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis , where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals .
The cumulative distribution function (shown as F(x)) gives the p values as a function of the q values. The quantile function does the opposite: it gives the q values as a function of the p values. Note that the portion of F(x) in red is a horizontal line segment.