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Math Help - Please help me with multiple comparisons - urgent (stats)

  1. #1
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    Please help me with multiple comparisons - urgent (stats)

    Hello, I just have a quick question understanding multiple comparisons and I'd appreciate any help because I'm on the verge of failing I'm reviewing for a test, and reading over questions and their corresponding answers in the back of the textbook. The question I'm stuck on deals with a psychologist testing the claim made by a drug company that a drug would help patients.

    To do this, they selected 20 patients from their hospital, and randomly assigned them to one of four groups - group 1 receiving the new drug, group 2 receiving a different drug, group 3 receiving a different drug, and group 4 as the control group. Here is the answer given in the textbook:



    I understand the first part, and how SSE is calculated and everything, but the second table with the contrasts totally baffles me. I have no idea how that table was filled in, or how I would be able to fill it in on a test if I had a different example. How were those 1s, -1s, and 2s determined? What do they mean and how were they calculated? In addition, once I go on to the appropriate post hoc test - in this case, Dunn - how do I utilise the table in terms of critical values?

    Please help me, I'm so very lost!
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  2. #2
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    Re: Please help me with multiple comparisons - urgent (stats)

    Hey mintsharpie.

    The Contrast table is just looking at doing two sample tests for (mean_a,mean_b), (mean_a,mean_c), and (mean_a,mean_control) where (x,y) looks at x - y and tests whether there will be some kind of statistical significant effect of the two means not being equal (or not).

    The contrast framework just looks at linear combinations of different treatment means and for this special case it is a difference of the other means with respect to the mean of group a.

    It looks like you will need to do some kind of ANOVA/T-test/Other test on the individual means if the original H0 ANOVA was rejected (i.e. all treatment means the same) to test whether you get significant differences in pair-wise comparisons.

    Also can you point out what a Dunn test is?
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  3. #3
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    Re: Please help me with multiple comparisons - urgent (stats)

    I have no idea what that means How was the table filled in? How were those 1s, -1s, and 2s determined? What do they mean and how were they calculated?
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    Re: Please help me with multiple comparisons - urgent (stats)

    Basically a 1 represents 1*ThatMean and a -1 means -1*mean.

    The row represents a 1*Mean_a - 1*OtherMean which is just a difference of two means.

    A contrast is just a linear combination of means and in this special case it is just a difference of the other means with respect to mean a.

    Recall that the difference of two means is something that tests whether the two means have some statistically significant difference of being equal or not equal (recall an ANOVA but in a 2 sample case it just compares the two means for inequality or equality).
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    Re: Please help me with multiple comparisons - urgent (stats)

    But how do I know where to put a 1 and where to put a -1? And how come sometimes there's a 2, or a 1/2? Basically what I'm asking is HOW do I fill in the chart? That's what I want to know - how, when given a chart like that to fill in, do I determine how to fill it in?
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  6. #6
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    Re: Please help me with multiple comparisons - urgent (stats)

    The C^2 is another thing altogether.

    Basically you are looking for the difference of two means.

    The first hypothesis for example tests mu_a = mu_b. The difference of means is given by mu_a - mu_b and the sample means for these are 1*sample_mean_a - 1*sample_mean_b.

    Now the contrast has the form of c1*mean1 + c2*mean2 + .. cn*mean_n. We can see that for mean_a we have 1 and for mean_b we have a -1 and that's why you have the values in the contrast output.

    Its the same deal with the other means: Just look at the hypotheses in the output and you will see why you have the other -1's in the control output.
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