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One-sample t-tests: Compare the sample mean with a known value, when the variance of the population is unknown; 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
The mathematics involved with calculating the t-statistic is very similar to the one-sample t-test, except the numerator in the fraction is the difference between two means rather than between a mean and a fixed value.
You would create very messy notation using the $\mu$-Notations, whereas $$E\left(X+\frac{1}{2}Y\right)=E(X)+\frac{1}{2}E(Y)$$ is as clear as it can get. Note that the expected value above is potentially unknown, or at least not explicitly given.
In this chapter, you will learn how to compare two mean values from two groups or the same group measured two times using R and RStudio. We will use independent samples t-test and dependent sampled (or paired) t-test to find out if the difference between two mean scores is statistically significant.
Depending on the t-test that you use, you can compare a sample mean to a hypothesized value, the means of two independent samples, or the difference between paired samples. In this post, I show you how t-tests use t-values and t-distributions to calculate probabilities and test hypotheses.
20 Απρ 2016 · Each type of t-test uses a specific procedure to boil all of your sample data down to one value, the t-value. The calculations behind t-values compare your sample mean(s) to the null hypothesis and incorporates both the sample size and the variability in the data.
One-sample: Compares a sample mean to a reference value. Two-sample: Compares two sample means. Paired: Compares the means of matched pairs, such as before and after scores. In this post, you’ll learn about the different types of t tests, when you should use each one, and their assumptions.
