Some of the birds had one "odd" feather that was different in color or length from the rest of the tail feathers, presumably because it was regrown after being lost. Wiebe and Bortolotti (2002) examined color in the tail feathers of northern flickers. Examples Northern flicker, Colaptes auratus. So the paired t–test is really just one application of the one-sample t–test, but because the paired experimental design is so common, it gets a separate name. Then you use a one-sample t–test to compare the mean difference to 0. The first step in a paired t–test is to calculate the difference for each pair, as shown in the last column above. And it does not assume that the groups are homoscedastic. The paired t–test does not assume that observations within each group are normal, only that the differences are normal. I don't think the test is very sensitive to deviations from normality, so unless the deviation from normality is really obvious, you shouldn't worry about it. If the differences between pairs are severely non-normal, it would be better to use the Wilcoxon signed-rank test. The paired t–test assumes that the differences between pairs are normally distributed you can use the histogram spreadsheet described on that page to check the normality. Because of the paired design of the data, the null hypothesis of a paired t–test is usually expressed in terms of the mean difference. When the mean difference is zero, the means of the two groups must also be equal. The null hypothesis is that the mean difference between paired observations is zero. But if some of your data sets are in pairs, and some are in sets of three or more, you should call all of your tests two-way anovas otherwise people will think you're using two different tests. The paired design is a common one, and if all you're doing is paired designs, you should call your test the paired t–test it will sound familiar to more people. "Paired t–test" is just a different name for "two-way anova without replication, where one nominal variable has just two values" the results are mathematically identical. If you wanted to compare horseshoe crab abundance in 2010, 2011, and 2012, you'd have to do a two-way anova without replication. You can only use the paired t–test when the data are in pairs. For example, if you had multiple counts of horseshoe crabs at each beach in each year, you'd have to do the two-way anova. If you have more than one observation for each combination, you have to use two-way anova with replication. You can only use the paired t–test when there is just one observation for each combination of the nominal values. For the horseshoe crabs, the P value for a two-sample t–test is 0.110, while the paired t–test gives a P value of 0.045. A paired t–test just looks at the differences, so if the two sets of measurements are correlated with each other, the paired t–test will be more powerful than a two-sample t–test. If the difference between years is small relative to the variation within years, it would take a very large sample size to get a significant two-sample t–test comparing the means of the two years. BeachĪs you might expect, there's a lot of variation from one beach to the next. The biological question is whether the number of horseshoe crabs has gone up or down between 20. Each beach has one pair of observations of the measurement variable, one from 2011 and one from 2012. 2012, and the other nominal variable is the name of the beach. The measurement variable is number of horseshoe crabs, one nominal variable is 2011 vs. You can use the paired t–test for other pairs of observations for example, you might sample an ecological measurement variable above and below a source of pollution in several streams.Īs an example, volunteers count the number of breeding horseshoe crabs on beaches on Delaware Bay every year here are data from 20. Sometimes the pairs are spatial rather than temporal, such as left vs. The most common design is that one nominal variable represents individual organisms, while the other is "before" and "after" some treatment. One of the nominal variables has only two values, so that you have multiple pairs of observations. Use the paired t–test when there is one measurement variable and two nominal variables. It tests whether the mean difference in the pairs is different from 0. Use the paired t–test when you have one measurement variable and two nominal variables, one of the nominal variables has only two values, and you only have one observation for each combination of the nominal variables in other words, you have multiple pairs of observations.
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