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  3. Intro to Statistics with R: Student's T-test
  • 1

    Introduction to t-tests

    Free

    The first part covers z-tests, single sample t-tests, and dependent t-tests. You will learn when to use a z-test, when to use a t-test, and how you can calculate the corresponding test statistic. The focus is on understanding how t-tests are constructed, the intuition and interpretation behind them, and how R can help you to do t-tests more easily.

  • 2

    Independent t-tests

    The independent t-test is one of the most common statistical test that you will encounter. An independent t-test is appropriate when you want to compare two independent samples, so two completely different groups. Common examples are comparisons between men and women, or treatment group vs control group. The example used to explain the theory behind independent t-tests is the working memory training example.

Initializing

Exercise

Understanding the t-distribution

When performing a t-test, you first calculate your t-statistic using the familiar formula:

$$ t = \frac{X - M}{SE} $$

\(X\) is the observed value, \(M\) is the expected value under the null hypothesis (or population mean), and \(SE\) is the standard error. Once you've computed the t-statistic, you then compare it to the so-called critical value, which comes from the relevant t-distribution.

The shape of a t-distribution, and thus the critical value, is determined entirely by its degrees of freedom. To demonstrate this, let's draw some density plots for t-distributions using different degrees of freedom.

Instructions

100 XP
  • Create a vector x that contains a sequence of length 100 between -4 and 4. See ?seq for help.
  • Use dt() to generate t-distributions with 4, 6, 8, 10, and 12 degrees of freedom (in that order). The first argument to dt() is the vector of values at which to evalute the t-distribution (x from above) and the second argument (df) is the degrees of freedom.
  • Plot each of the t-distributions. Once the inital plot() is created, you'll use lines() to plot each additional distribution. The two arguments to lines() are the same as the first two arguments to plot(), except that you'll have to substitute the appropriate y-values. Use the color black for 4 degrees of freedom, red for 6, orange for 8, green for 10, and blue for 12.
  • Add a legend() to your plot. The legend should be situated at the top right corner of your plot and should have the title "t-distributions". This is done by setting the first argument to "topright" and the title argument to "t-distributions".