<title>Comparing the means of two samples with the Students-t test</title>
<link rel="stylesheet" href="../../../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../../index.html" title="Math Toolkit 2.10.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit 2.11.0">
<link rel="up" href="../st_eg.html" title="Student's t Distribution Examples">
<link rel="prev" href="tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">
<link rel="next" href="paired_st.html" title="Comparing two paired samples with the Student's t distribution">
Our procedure will begin by calculating the t-statistic, assuming equal
variances the needed formulae are:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../../equations/dist_tutorial1.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../../equations/dist_tutorial1.svg"></span>
+
+ </p></blockquote></div>
<p>
where Sp is the "pooled" standard deviation of the two samples,
and <span class="emphasis"><em>v</em></span> is the number of degrees of freedom of the
at the more complex one: that the standard deviations of the two samples
are not equal. In this case the formula for the t-statistic becomes:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../../equations/dist_tutorial2.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../../equations/dist_tutorial2.svg"></span>
+
+ </p></blockquote></div>
<p>
And for the combined degrees of freedom we use the <a href="http://en.wikipedia.org/wiki/Welch-Satterthwaite_equation" target="_top">Welch-Satterthwaite</a>
approximation:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../../equations/dist_tutorial3.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../../equations/dist_tutorial3.svg"></span>
+
+ </p></blockquote></div>
<p>
Note that this is one of the rare situations where the degrees-of-freedom
parameter to the Student's t distribution is a real number, and not an