Respuesta :
Answer:
b. observing different participants one time in each group
[tex]SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 [/tex]
If we analyze the formula for the sum of squares between we see that we are subtracting the mean for each group minus the grand mean. But in order to find the mean of each group we just need to observe just one time the dependent variable of interest for each group.
Step-by-step explanation:
Previous concepts
Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"
Solution to the problem
If we assume that we have [tex]p[/tex] groups and on each group from [tex]j=1,\dots,p[/tex] we have [tex]n_j[/tex] individuals on each group we can define the following formulas of variation:
[tex]SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 [/tex]
[tex]SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 [/tex]
If we analyze the formula for the sum of squares between we see that we are subtracting the mean for each group minus the grand mean. But in order to find the mean of each group we just need to observe just one time the dependent variable of interest for each group.
For this reason the best option on this case is:
b. observing different participants one time in each group
[tex]SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 [/tex]
And we have this property :
[tex]SST=SS_{between}+SS_{within}[/tex]
Answer:
b. observing different participants one time in each group
Step-by-step explanation:
Between-subjects or groups design is a common experimental design used in psychology and other social science fields. Between-subjects is a type of experimental design in which the subjects of an experiment are assigned to different groups or conditions or participants in which each subject is being tested base on only one of the experimental conditions at a time. In Between-subjects experimental study, participants can be part of the treatment group or the control group, but cannot be part of both. A complete new group is required for each group, If more than one treatment is tested. The other way of assigning test to participants is Within-subjects design.
The major difference between Between-subjects design and Within-subjects design is that in Within-subjects design, the same participants test all the conditions of the experiment while in Between-subjects design different participants test each condition of the experiment.
