Ttesti

Ttesti refers to a class of statistical procedures used to assess whether the means of two groups differ. In standard English, the term is t-test (also written as t test or Student's t-test). The form “Ttesti” is uncommon and may reflect a typographical variant, a plural in another language, or a misunderstanding of the conventional name. T-tests are parametric tests that rely on an approximately normal distribution of the data and on measurements on a continuous scale.

There are several variants. The one-sample t-test compares the sample mean to a known value (null hypothesis μ = μ0). The independent two-sample t-test compares means from two independent groups, using either equal variances (pooled) or unequal variances (Welch's) assumptions. The paired t-test compares means from paired observations, such as before-and-after measurements. Formulas (simplified): one-sample t = (X̄ − μ0) / (s/√n); independent equal-variance t = (X̄1 − X̄2) / (sp √(1/n1 + 1/n2)); Welch’s t = (X̄1 − X̄2) / √(s1²/n1 + s2²/n2); paired t = d̄ / (sd/√n), where d̄ is the mean difference and sd the standard deviation of differences.

Assumptions include independent observations, scale measurement, and normality of the underlying distribution (especially for small samples). The test yields a t-statistic and a p-value, assessed against a t-distribution with appropriate degrees of freedom. Reported results typically include the t value, degrees of freedom, p-value, and an effect size such as Cohen’s d. If assumptions are violated, nonparametric alternatives like the Mann–Whitney U test or Wilcoxon signed-rank test may be employed. The t-test was developed by William Sealy Gosset under the pseudonym Student in 1908.