I don't know how to decide to choose between pair and Independent to compare mean of two groups. Here is the excersise from a book:
DS 9.2.1 shows the data obtained from a paired
experiment performed to examine which of two assembly
methods is quicker on average. A random sample of 35
workers on an assembly line were selected and all were
timed while they assembled an item in the standard
manner (method A) and while they assembled an item in
the new manner (method B). The times in seconds are
recorded. Analyze the data set and present your
conclusions on how the new assembly method differs
from the standard assembly method. Why are the two
data samples paired? Why did the experimenter decide to
perform a paired experiment rather than an unpaired
experiment?
First i think it bases on split or not the group. But, in the second problem, they still split, but its still paired sample
A new teaching method for a calculus class is being
evaluated. A set of 80 students is formed into 40 pairs,
where the two-pair members have roughly equal
mathematics test scores. The pairs are then randomly
split, with one member being assigned to section A where
the standard teaching method is used and with one
member being assigned to section B where the new
teaching method is tried. At the end of the course all the
students take the same exam and their scores are shown in
DS 9.2.4. Analyze the data and present your conclusions
regarding how the new teaching method compares with
the standard approach. Why is this a paired experiment?
Why was it decided to perform a paired experiment rather
than an unpaired experiment?
I don't know how to answer two last question. And in fact how to choose between paired and independent. Pls help me make it clearly
You choose a paired experiment when you have reason to believe that for each pair, the distributions for each sample in the pair are the same under the null hypothesis that the two treatments have the same effect. (Note that the distribution does not have to be the same between different pairs though, e.g. they could have different means). If you cannot use a paired experiment then you do an unpaired experiment, under the hypothesis that the two groups were sampled from the same population distribution under the null hypothesis that the two treatments have the same effect. The paired experiment design gives stronger statistical results when it can be used. In this case, you can use paired experiment design in both cases because the same factory worker uses both procedures in the first case, and the paired students have nearly identical previous scores in the second case.