Biostatistics Handout

Biostatistics Handout - Biostatistics BIOSTATISTICS...

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1 BIOSTATISTICS BME 140 Lecture Prof. Frank Yin November 29, 2010 Biostatistics Rationale Unavoidable biological variability Can’t measure every individual Provides quantification Descriptive information Ability to test hypotheses Describing Data Mean vs. median Mean is simple arithmetic average th N X Median is the mid-point, i.e. 50 percentile Variance A descriptor of the variability of a population Standard deviation Square root of the variance N X 2 2 ) ( Gaussian (normal) distribution Completely described by and   and N) 2 2 1 2 1 ) ( X e X f Describing Data Mean = 40 SD = 5 30 35 40 45 50 Examples from: S. Glantz, Primer of Biostatistics, 1 st Ed., McGraw-Hil , 1981. Absolute value of SD does not inform about variability Coefficient of variation, , does: Describing Data CV Mean = 40 SD = 5 CV = 0.125 Mean = 15 SD = 2.5 CV = 0.147 Describing Data Median Non-Gaussian Distributions Mean and SD may be misleading Should use median and percentiles The 25 th percentile is closer to the median than the 75 th , this indicates the distribution is skewed toward higher values Mean = 37.6 SD = 4.5
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2 Describing Data n X X A sample vs. the entire population Since we usually cannot sample the entire population, we rely on a random sample(s) of that population to represent it. Sample mean is: Sample variance like the variance of the population Sample variance – like the variance of the population -- describes the variability of a sample of that population Note the population mean is replaced by our estimate of that mean and the denominator is n-1 rather than n. This compensates for the fact that the sample mean will never have as much variability as the entire population. 1 ) ( 2 2 n X X s Describing Data For all possible random subsamples of size n of a population: The distribution will be approximately Gaussian, regardless of the distribution of the population. Mean value of all subsamples, i.e. the mean of the means, equals the mean of the original population Standard deviation of the means of those random samples n X n s s X Smaller than the population standard deviation Call this the standard error of the mean (SEM). The true SEM from a population with SD equal to is: Unlike the SD, this measure tells you, not about the dispersion of the population, but how close a sample mean estimates the true population mean The best estimate of for a single sample, i.e. (SEM) is X Describing Data Important distinction: 1) The sample standard deviation informs about the variability of a sample 2) The SEM informs about how close the mean of a sample is to the mean of the population. 3)
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This note was uploaded on 02/14/2012 for the course NUBITRY 3304 taught by Professor Various during the Spring '01 term at Albertus Magnus.

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Biostatistics Handout - Biostatistics BIOSTATISTICS...

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