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Measures of central tendency

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  • #40130

    Finkelstein
    Participant

    I have a skewed distibution so am using Q1 as my measure of central tendency.  Is there a hypothesis test I can use to check whether there is a true difference between two values for Q1?

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    #123632

    Robert Butler
    Participant

     Q1 is a measure of non central location which is not the same thing as a measure of central tendency.  The three measures of central tendency are mean, median, and mode.  There are variations on the theme with respect to the mean – geometric and harmonic mean – but those are the biggies.  For a skewed distribution the median is probably your best bet and there are tests for differences in median values. One of the favorites – and one which may be of value to you – would be the Mood’s median test.  It is robust against outliers and it does assume the two distributions have the same shape.

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    #123633

    Ellis
    Participant

    somebody told me that mean is always lower than median, median is always lower than mode. is it true.
    Ellis

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    #123634

    Jaybee
    Participant

    Hi Ellis,
    sorry to disappoint that ‘somebody’ but they are clearly wrong…..in a man sized way.
    Think about it.
    eg. a set of random (but ascending)data (for ease of example);
    5,9,9,9,12,13,13,17,19,19,21,24,26
    Median = 13
    Mean = 15 (.076)
    Mode = 9
    my 2 penneth
    Jaybee

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    #123645

    Robert Butler
    Participant

    Jaybee is correct – somebody is wrong big time. 
    If you think of a distribution as a physical object then the mean would be the point at which you could just balance the distribution on your finger like at see-saw. For median – think grassy strip between the lanes of a 4 lane highway – that is the 50% point the point at which exactly half of the data is below and half is above – half the traffic in one direction – half the other (rush hour excepted  :-)  ) and mode is the most frequent term and it can be just about anywhere. 
      If the distribution is symmetric then all three measurements will be quite close to and may be in fact equal to one another.  If the distribution is asymmetric then all bets are off.

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    #124306

    spampurge
    Member

    A simple rule of thumb is this: If your distribution is negatively skewed, then the mean will “typically” be “pulled” down towards the “clump” of negative scores and if your distribution is positively skewed, then the mean is “typically” “pulled” up, towards the clump of positive scores. The median however, will always be the “middle most” score, where 50% of the scores in your distribution lie below and the other 50% lie above. As you can probably see, the mean in some cases will actually be higher or lower, or in the case of a normal distribution, “almost” equal to the median.This is one main reason the median is often referred to as a “more robust” measure of central tendency.

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