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Student's t-test assumes that the sample means being compared for two populations are normally distributed, and that the populations have equal variances.Welch's t-test is designed for unequal population variances, but the assumption of normality is maintained. [1]
Student's t-test is a statistical test used to test whether the difference between the response of two groups is statistically significant or not. It is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis.
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For example, if the mean height in a population of 21-year-old men is 1.75 meters, and one randomly chosen man is 1.80 meters tall, then the "error" is 0.05 meters; if the randomly chosen man is 1.70 meters tall, then the "error" is −0.05 meters.
Most frequently, t statistics are used in Student's t-tests, a form of statistical hypothesis testing, and in the computation of certain confidence intervals. The key property of the t statistic is that it is a pivotal quantity – while defined in terms of the sample mean, its sampling distribution does not depend on the population parameters, and thus it can be used regardless of what these ...
The standard deviation is the square root of the variance. When individual determinations of an age are not of equal significance, it is better to use a weighted mean to obtain an "average" age, as follows: x ¯ ∗ = ∑ i = 1 N w i x i ∑ i = 1 N w i . {\displaystyle {\overline {x}}^{*}={\frac {\sum _{i=1}^{N}w_{i}x_{i}}{\sum _{i=1}^{N}w_{i}}}.}
Heteroskedasticity-consistent standard errors that differ from classical standard errors may indicate model misspecification. Substituting heteroskedasticity-consistent standard errors does not resolve this misspecification, which may lead to bias in the coefficients. In most situations, the problem should be found and fixed. [5]