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A contrast is defined as the sum of each group mean multiplied by a coefficient for each group (i.e., a signed number, c j). [10] In equation form, = ¯ + ¯ + + ¯ ¯, where L is the weighted sum of group means, the c j coefficients represent the assigned weights of the means (these must sum to 0 for orthogonal contrasts), and ¯ j represents the group means. [8]
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If only a fixed number of pairwise comparisons are to be made, the Tukey–Kramer method will result in a more precise confidence interval. In the general case when many or all contrasts might be of interest, the Scheffé method is more appropriate and will give narrower confidence intervals in the case of a large number of comparisons.
The only difference between the confidence limits for simultaneous comparisons and those for a single comparison is the multiple of the estimated standard deviation. Also note that the sample sizes must be equal when using the studentized range approach.
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Three-component SSIM (3-SSIM) is a form of SSIM that takes into account the fact that the human eye can see differences more precisely on textured or edge regions than on smooth regions. [9] The resulting metric is calculated as a weighted average of SSIM for three categories of regions: edges, textures, and smooth regions.
Dunnett's test's calculation is a procedure that is based on calculating confidence statements about the true or the expected values of the differences ¯ ¯, thus the differences between treatment groups' mean and control group's mean.
The ATE measures the difference in mean (average) outcomes between units assigned to the treatment and units assigned to the control. In a randomized trial (i.e., an experimental study), the average treatment effect can be estimated from a sample using a comparison in mean outcomes for treated and untreated units.