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Showing posts from July, 2010

He wishes for the cloths of heaven

Had I the heavens' embroidered cloths,
Enwrought with golden and silver light,
The blue and the dim and the dark cloths
Of night and light and the half-light,
I would spread the cloths under your feet:
But I, being poor, have only my dreams;
I have spread my dreams under your feet;
Tread softly, because you tread on my dreams.                                       -- William Butler Yeats

Revisiting basic statistics

A friend of mine works for a physical therapy clinic and she needed to decide if a certain patient's physical ability -- in this case, his hand grip strength -- is good enough. She let the patient use a strength measuring device and did 3 trial measurements. The device comes with a table of typical strengths (giving the average strength, μ, and the standard deviation, σ) for different age groups and gender.

From the 3 measurements, she calculated the average measured strength of the patient's hand grip. My friend's problem starts because the average measured strength is lower than the patient's age group's lower limit, μ-σ. Her question is: how can she trust the average of her 3 measurements, and thus conclude safely that the patient really has a weak hand grip?

To answer this question, we have to make an assumption that if the patient would have to make a large number (n) of trials, the measured grip strengths would vary or fluctuate around the average measurement…