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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.
The test statistic for comparing two means is a T. The T score is a ratio of how the groups differ as compared to how the observations within groups vary. \[T = \frac{(\bar{x}_1 - \bar{x}_2) - 0}{s_{\textit{pool}} \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}\] where \(s_{\textit{pool}}\) is the pooled standard deviation between the two groups:
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.
23 Απρ 2022 · Summary for inference of the difference of two means. When considering the difference of two means, there are two common cases: the two samples are paired or they are independent. (There are instances where the data are neither paired nor independent.)
Sometimes we want to compare a sample mean with a known population mean \((\mu_0)\) or some other fixed comparison value. For example, we would like to know whether the reported support by friends unt_freunde differs significantly from the midpoint of the 7-point-Likert scale \((\mu_0=4)\) .
4 Μαΐ 2021 · In my notes, I am looking at a hypothesis testing of a test statistic distributed under the t-distribution because the population SD isn't known. The t score was computed for the test statistic, $\mu$, to be $t = -1.31$.
Learn the general approach to significance testing, including how to test a null hypothesis and calculate and interpret a p -value. Learn how to compare a normally distributed sample mean with an expected value for a given hypothesis, assuming that you know the variance of the distribution the data are sampled from.
