The Art of Statistics: Learning from Data

by David Spiegelhalter

t-statistic, is a major focus of attention, since it is the link that tells us whether the association between an explanatory variable and the response is statistically significant. The t-value is a special case of what is known as a Student’s t-statistic. ‘Student’ was the pseudonym of William Gosset, who developed the method in 1908 while on secondment at University College London from the Guinness brewery in Dublin – they wanted to preserve their employee’s anonymity. The t-value is simply the estimate/standard error (this can be checked for the numbers in Table 10.5), and so can be interpreted as how far the estimate is away from 0, measured in the number of standard errors. Given a t-value and the sample size, the software can provide a precise P-value; for large samples, t-values greater than 2 or less than −2 correspond to P < 0.05, although these thresholds will be larger for smaller sample sizes. R uses a simple star system for P-values, from one * indicating P < 0.05, up to three stars *** indicating P < 0.001. In Table 10.5 the t-values are so large that the P-values are vanishingly small.

T value is students coeeficient and is inversely proportion to p value