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I have a consistent data about a decision making problem where I need to decide whether I choose A or B to compete, the winner is the one with larger number per round. If I remove one point, A beats B each time. But the sample is so small that removing a data point makes the data much smaller.

The goal of this competion is to maximize the result with low standard deviation. So I have here a non-dominating situation because player B has the largest record 86 while A has the smallest SD (about 150% while B 250%).

If I make a conclusion based on smaller sample, I feel a mistake -- how can I say this statistically? How much less significant will a conclusion be if I use smaller sample?

R stands for round.

R   A   B
1   85  86
2   83  83
3   83  82
4   83  82
5   83  81
6   81  80
7   80  78

[Update]

The player I choose have to compete in the same game again against other players. I want to maximize the future rounds. Look B has a rising trend while A has historically more stable results. Will do some analysis soon.

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Much of what you say is not very clear...it seems that, whether you omit the first round or not, you should still prefer A to B. But I'll take a stab at an answer: don't omit any data, and choose A over B.

I would only omit that first round if it were clearly an error (and I'd prefer to fix it rather than omit it).

Perhaps you're thinking: go with the one with the maximum value? I would avoid the maximum as a statistic, as it's too much influenced by outlying values. So I'd suggest reformulating your statistic for comparing A and B.

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  • $\begingroup$ but B has a rising trend, it is not that easy thing to choose A over B. I want that the player will get high results in future competitions. A has more stable results but historical indicator not forward-looking indicator. Dilemma...have to investigate. $\endgroup$
    – hhh
    Sep 23, 2011 at 22:54
  • $\begingroup$ What do you mean by a "rising trend" - B's scores have been falling steadily over time. I also agree with @KarlBroman - omitting data because it doesn't give you what is, as far as I can tell, the "results you want" is a flawed way to go about any analysis. $\endgroup$
    – Fomite
    Sep 24, 2011 at 0:01

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