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The t.test function in R is used to perform a t-test, which is a statistical test to compare the means of two groups and determine if they are significantly different from each other or to test if the mean of a sample is equal to a certain value.
In fact, the t-value that the t-test relies on is a ratio between the signal (difference between mean (\(\bar{x}\)) and threshold (\(\mu_{0}\))) and noise (variability, standard error of the mean (\(s/ \sqrt{n}\))): \[t = \frac{\bar{x}-\mu_{0}} {s/ \sqrt{n}}\]
Two-sample t-tests: Compare the means of two groups under the assumption that both samples are random, independent, and normally distributed with unknown but equal variances. Paired t-tests: Compare the means of two sets of paired samples, taken from two populations with unknown variance.
The one-sample t-test checks if the known mean is statistically correct, based on a sample average and sample standard deviation. The null hypothesis assumes that the known mean is correct. The statistical decision will be based on the difference between the known mean and the sample average.
Use this test if you know that the two populations' variances are the same (or very similar). Two-sample t-test formula (with equal variances): t = \frac {\bar {x}_1 - \bar {x}_2 - \Delta} {s_p \cdot \sqrt {\frac {1} {n_1} +\frac {1} {n_2} }} t = sp ⋅ n11 + n21xˉ1 − xˉ2 − Δ.
31 Ιαν 2020 · What is the difference between a one-sample t-test and a paired t-test? A one-sample t-test is used to compare a single population to a standard value (for example, to determine whether the average lifespan of a specific town is different from the country average).
20 Απρ 2016 · Understanding t-Tests: t-values and t-distributions. T-tests are handy hypothesis tests in statistics when you want to compare means. You can compare a sample mean to a hypothesized or target value using a one-sample t-test. You can compare the means of two groups with a two-sample t-test.
