Similar to the one-sample t-test, individuals who first encounter this test may wonder about the plausibility of its assumptions. This is a type of two-sample test used to compare two sample means, where a large t-value suggests that the samples are very different, and a small t-value suggests that they are similar. The Student’s t-test assumes that the variances of two populations are equal and asks whether their means differ significantly. The name “Student” refers to the pseudonym of the author who first proposed the test in an academic journal, and does not refer to the fact it is one of the most commonly taught tests in statistics courses (although the latter is also true). How to Calculate T Using a Student’s T-TestĪ Student’s t-test is used for test statistics that follow a Student’s t-distribution under the null hypothesis that two populations have equal means. Thus, the test statistic t is equal to the difference between the sample mean x̄ and the population mean μ, divided by the standard error s / √n. Where: x̄ = sample mean μ = population mean s = sample standard deviation n = sample size To calculate the t value using a one-sample t-test, use the following formula: Then, you may well consider doing a one-sample t-test to examine whether the average blood lead level of a sample of individuals was above that medically acceptable limit. It often does make sense to use a one-sample t-test if you have a particular interest in whether a sample’s mean is different from some reference value that is determined to be substantively important for other reasons.įor example, let’s suppose that 5 micrograms of lead per liter of blood is the maximum safe amount, according to most medical references. Those who first encounter this test often wonder why they would use it, since the population mean is often not known (and the data is often collected to determine the population mean in the first place). How to Calculate T Using a One-Sample T-TestĪ one-sample t-test, or single-sample test, is used to compare a sample mean to a population mean when the null hypothesis is that the sample mean is equal to the population mean.
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