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. A t-value of 0 indicates that the sample results exactly equal the null hypothesis.
As the difference between the sample data and the null hypothesis increases, the absolute value of the t-value increases. Assume that we perform a t-test and it calculates a t-value of 2 for our sample data. What does that even mean? I might as well have told you that our data equal 2 fizbins! We need a larger context in which we can place individual t-values before we can interpret them. This is where t-distributions come in. When you perform a t-test for a single study, you obtain a single t-value.
However, if we drew multiple random samples of the same size from the same population and performed the same t-test, we would obtain many t-values and we could plot a distribution of all of them.
This type of distribution is known as a sampling distribution. Fortunately, the properties of t-distributions are well understood in statistics, so we can plot them without having to collect many samples! A specific t-distribution is defined by its degrees of freedom DF , a value closely related to sample size.
Therefore, different t-distributions exist for every sample size. T-distributions assume that you draw repeated random samples from a population where the null hypothesis is true.
You place the t-value from your study in the t-distribution to determine how consistent your results are with the null hypothesis. The graph above shows a t-distribution that has 20 degrees of freedom, which corresponds to a sample size of 21 in a one-sample t-test.
It is a symmetric, bell-shaped distribution that is similar to the normal distribution, but with thicker tails. This graph plots the probability density function PDF , which describes the likelihood of each t-value. The peak of the graph is right at zero, which indicates that obtaining a sample value close to the null hypothesis is the most likely.
That makes sense because t-distributions assume that the null hypothesis is true. T-values become less likely as you get further away from zero in either direction. In other words, when the null hypothesis is true, you are less likely to obtain a sample that is very different from the null hypothesis.
Ewa Galant Ewa Galant 31 1 1 gold badge 1 1 silver badge 2 2 bronze badges. Obviously, this is just a rule-of-thumb Add a comment. Active Oldest Votes. Here is an example from wikipedia that shows how the t distribution changes with increasing df: Here the Density of the t-distribution is red for 1, 2, 3, 5, 10, and 30 df compared to the standard normal distribution which is blue.
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Post as a guest Name. Email Required, but never shown. Featured on Meta. Now live: A fully responsive profile. Version labels for answers. Linked It appears in many contexts, such as measuring protein expression, the quantity of drug delivered by a medication or the weight of cereal in your cereal box. The concepts underlying this test are an important foundation for future columns in which we will discuss the comparisons across samples that are ubiquitous in the scientific literature.
Krzywinski, M. Methods 10 , — Download references. You can also search for this author in PubMed Google Scholar. Worksheets illustrate calculations that support statements in the column or provide interactive versions of its figures. Please note that the workbook requires that macros be enabled. XLSM kb. Reprints and Permissions. Significance, P values and t -tests.
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Download PDF. Subjects Publishing Research data Statistical methods. The P value reported by tests is a probabilistic significance, not a biological one. You have full access to this article via your institution. Figure 1: The mechanism of statistical testing. Full size image.
Figure 2: Repeated independent observations are used to estimate the s. Figure 3: The t and normal distributions. References 1 Krzywinski, M. View author publications.
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