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The coefficients for the linear regression specify the slope and intercept of the line that joins the two group means, as illustrated in the graph. The intercept is 2 and the slope is 4. Compare the result from the linear regression to the result from the t-test. From the t-test, the difference between the group means is 6-2=4.
Another application of paired difference testing arises when comparing two groups in a set of observational data, with the goal being to isolate the effect of one factor of interest from the effects of other factors that may play a role. For example, suppose teachers adopt one of two different approaches, denoted "A" and "B", to teaching a ...
Siegel–Tukey test, named after Sidney Siegel and John Tukey, is a non-parametric test which may be applied to data measured at least on an ordinal scale. It tests for differences in scale between two groups. The test is used to determine if one of two groups of data tends to have more widely dispersed values than the other.
Typically, however, the one-way ANOVA is used to test for differences among at least three groups, since the two-group case can be covered by a t-test (Gosset, 1908). When there are only two means to compare, the t-test and the F-test are equivalent; the relation between ANOVA and t is given by F = t 2.
The Wilcoxon signed-rank test is a non-parametric rank test for statistical hypothesis testing used either to test the location of a population based on a sample of data, or to compare the locations of two populations using two matched samples. [1] The one-sample version serves a purpose similar to that of the one-sample Student's t-test. [2]
However, the studentized range distribution used to determine the level of significance of the differences considered in Tukey's test has vastly broader application: It is useful for researchers who have searched their collected data for remarkable differences between groups, but then cannot validly determine how significant their discovered ...
Next, the observations of groups and are pooled, and the difference in sample means is calculated and recorded for every possible way of dividing the pooled values into two groups of size and (i.e., for every permutation of the group labels A and B). The set of these calculated differences is the exact distribution of possible differences (for ...
The choice between these two groups needs to be justified. Parametric tests assume that the data follow a particular distribution, typically a normal distribution, while non-parametric tests make no assumptions about the distribution. [7] Non-parametric tests have the advantage of being more resistant to misbehaviour of the data, such as ...