Just basic statisitical questions that I\'ve not quite grasping, an example/ exp

Question

Just basic statisitical questions that I've not quite grasping, an example/ explanation would be greatly appreciated as I already know the answers but do not understand the concept behind them.

Referred to the picture attached: I have been asked which shows dependence - I assumed A since all were declining with each other however I've been told that it is B which I can't understand. Could someone please explain it?

Description if picture is not displayed: there are 2 graphs with 3 sets of data of each. On graph A all three sets of data are declining steadily with one another. On graph B, one set of data remains consistant, one slowly declines and the other immediately drops very low and then remains consistant.

And referring to ANOVA:

- Why does a greater sample variance NOT increase the size of the F ratio?

Explanation / Answer

Since we are looking are three sets of data, in Figure (a), the other two sets are replicas of the first and hence there is no need to have the data stored exclusively. Though dependent in the mathematical sense, they can be easily reproduced without having the need to store all the values. On the other hand, in Figure (b), the other two sets can't be generated from the information on the first one, or any sort of combination of the data sets won't give reduction. Hence, the explanation.

Since the F-ratio depends on the sample variance between groups and within groups, it is possible that a greater sample variance will not increase the size of the F ratio.

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