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Does one-sample t-test require normality?
Assumption #4: Your dependent variable should be approximately normally distributed. We talk about the one-sample t-test only requiring approximately normal data because it is quite “robust” to violations of normality, meaning that the assumption can be a little violated and still provide valid results.
Why do we have to assume normal distribution?
No matter what distribution you start with (i.e., no matter what the shape of the population), the distribution of sample means becomes normal as the size of the samples increases. So if we’re going to assume one thing for all situations, it has to be a normal, because the normal is always correct for large samples.
Why we need to meet satisfy the assumptions before using the t tests?
Assumption testing of your chosen analysis allows you to determine if you can correctly draw conclusions from the results of your analysis. You can think of assumptions as the requirements you must fulfill before you can conduct your analysis.
Is the two sample t-test assumes normality?
So, as constructed, the two-sample t-test assumes normality of the variable X in the two groups. On the face of it then, we would worry if, upon inspection of our data, say using histograms, we were to find that our data looked non-normal.
Why do we have to assume normality in sampling?
It seems to me that the only thing that has to be normal is the sampling distribution that is approximatively normal given a large enough sample size, isn’t it?
Is the t-test starting to look more normal?
It is now starting to look more normal, but it is still skewed – the sample mean is occasionally large. Notice that x-axis range is now smaller – the variability of the sample mean is now smaller than with n=3. Lastly, we try n=100:
Is the t test valid when the sample size is large?
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.