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Can I use t test if data is not normally distributed?
For a t-test to be valid on a sample of smaller size, the population distribution would have to be approximately normal. The t-test is invalid for small samples from non-normal distributions, but it is valid for large samples from non-normal distributions.
Does T Test assume normality?
. Since often variances can differ between the two groups being tested, it is generally advisable to allow for this possibility. So, as constructed, the two-sample t-test assumes normality of the variable X in the two groups.
What is asymptotic Ttest?
In statistics: asymptotic theory, or large sample theory, is a framework for assessing properties of estimators and statistical tests. Within this framework, it is often assumed that the sample size n may grow indefinitely; the properties of estimators and tests are then evaluated under the limit of n → ∞.
What happens if the t-test assumes normality?
Of course if X isn’t normally distributed, even if the type 1 error rate for the t-test assuming normality is close to 5%, the test will not be optimally powerful. That is, there will exist alternative tests of the null hypothesis which have greater power to detect alternative hypotheses.
Is the assumption of normality of the error term needed to?
EDIT: Derivation of asymptotic normality of estimator of linear regression only makes use of the mean property: I’m not a statistician, but I’ll try to weigh-in. Note: edited somewhat in response to comments by OP, to make this response more relevant for the linear regression case.
Is the t-test valid when x does not follow a normal distribution?
In fact, as the sample size in the two groups gets large, the t-test is valid (i.e. the type 1 error rate is controlled at 5%) even when X doesn’t follow a normal distribution. I think the most direct route to seeing why this is so, is to recall that the t-test is based on the two groups means and .
How often does the t test reject the null hypothesis?
In particular, we would worry that the t-test will not perform as it should – i.e. that if the null hypothesis is true, it will falsely reject the null 5% of the time (I’m assuming we are using the usual significance level).