T Test Formula Correlation. T score r n 2 1 r 2 displaystyle t text score frac r sqrt n 2 sqrt 1 r 2 where r is the pearson correlation coefficient. In this formula t is the t value x1 and x2 are the means of the two groups being compared s2 is the pooled standard error of the two groups and n1 and n2 are the number of observations in each of the groups.
Again like the null and alternative hypotheses the formula for computing the t is identical to the formula used in the two independent groups situation. T test value is calculated using the formula given below. T score r n 2 1 r 2 displaystyle t text score frac r sqrt n 2 sqrt 1 r 2 where r is the pearson correlation coefficient.
Computational formula for paired samples t test calculation of the se d for the correlated samples t test requires finding the pearson product moment correlation r 12 between the two sets of scores.
The formula for the test statistic is t r n 2 1 r2 t r n 2 1 r 2. Therefore the absolute t test value of the sample is 3 61 which is less than the critical value 3 69 at 99 5 confidence interval with a degree of freedom of 9. The value of the test statistic t is shown in the computer or calculator output along with the p value. The student s t test is shown below.
