That’s enough to create a graphic of the distribution of the mean, which is: With those assumptions, then all that’s needed to determine the “sampling distribution of the mean” is the sample size (5 students in this case) and standard deviation of the data (let’s say it’s 1 foot). That may seem impossible to do, which is why there are particular assumptions that need to be made to perform a t test. To evaluate this, we need a distribution that shows every possible average value resulting from a sample of five individuals in a population where the true mean is four. Does that mean that the “true” average height of all sixth graders is greater than four feet or did we randomly happen to measure taller than average students? Say that we measure the height of 5 randomly selected sixth graders and the average height is five feet. To do this, t tests rely on an assumed “null hypothesis.” With the above example, the null hypothesis is that the average height is less than or equal to four feet. A t test could be used to answer questions such as, “Is the average height greater than four feet?” How does a t test work?īased on your experiment, t tests make enough assumptions about your experiment to calculate an expected variability, and then they use that to determine if the observed data is statistically significant. The value for comparison could be a fixed value (e.g., 10) or the mean of a second sample.įor example, if your variable of interest is the average height of sixth graders in your region, then you might measure the height of 25 or 30 randomly-selected sixth graders. When should I use a t test?Ī t test is appropriate to use when you’ve collected a small, random sample from some statistical “population” and want to compare the mean from your sample to another value. He wanted to get information out of very small sample sizes (often 3-5) because it took so much effort to brew each keg for his samples. It got its name because a brewer from the Guinness Brewery, William Gosset, published about the method under the pseudonym "Student". Sometimes t tests are called “Student’s” t tests, which is simply a reference to their unusual history. When you have a reasonable-sized sample (over 30 or so observations), the t test can still be used, but other tests that use the normal distribution (the z test) can be used in its place. They use t-distributions to evaluate the expected variability. Some examples are height, gross income, and amount of weight lost on a particular diet.Ī t test tells you if the difference you observe is “surprising” based on the expected difference. In this guide, we’ll lay out everything you need to know about t tests, including providing a simple workflow to determine what t test is appropriate for your particular data or if you’d be better suited using a different model.Ī t test is a statistical technique used to quantify the difference between the mean (average value) of a variable from up to two samples (datasets). All t tests are used as standalone analyses for very simple experiments and research questions as well as to perform individual tests within more complicated statistical models such as linear regression. The characteristics of the data dictate the appropriate type of t test to run. The t test is especially useful when you have a small number of sample observations (under 30 or so), and you want to make conclusions about the larger population. The t test is one of the simplest statistical techniques that is used to evaluate whether there is a statistical difference between the means from up to two different samples.
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