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Tuesday, January 06, 2009

Standard deviation is a measure of Deviation from Mean Value

Title : RxPG TargetPG AIPG 2008 Book

Author : Dr.J.Mariano Anto Bruno Mascarenhas

Biostatistics 1 Question ( 57)

References
Park (obviously!!)
Methods in Biostatistics for Medical Students and Research Workers - 6th Edition - B.K.Mahajan - Jaypee Publishers
Methods of Biostatistics - Bhaskar Rao - PARAS Publishers
High Yield Biostatistics
The Basic Concepts in Biostatistics (given in all books)
Disease Status
Disease Status
Test Results
Diseased
Not Diseased
Total
Positive
a = true positive
b = false positive
a + b
Negative
c = false negative
d = true negative
c + d
Total
a + c
b + d
a + b + c + d
Formulae
Sensitivity = a/(a+c) x 100
Specificity = d/(b+d) x 100
Predictive Value of Positive Test = a/(a+b) x 100
Predictive Value of Negative Test = d/(c+d) x 100
Percentage of false positive = b/(b+d) x 100
Percentage of false negative = c/(a+c) x 100
Question 57
Standard deviation is a measure of
a.              Chance
b.              Deviation from mean value
c.              Central Tendency
d.              None of the above
Answer
b. Deviation from Mean Value
Reference
Park 18th edition Page 646
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Discussion
Ä     In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. It is usually denoted with the letter σ (lower case sigma). It is defined as the square root of the variance.
Ä     The standard deviation is the most common measure of statistical dispersion, measuring how widely spread the values in a data set are. If many data points are close to the mean, then the standard deviation is small; if many data points are far from the mean, then the standard deviation is large. If all the data values are equal, then the standard deviation is zero.
Ä     For a population, the standard deviation can be estimated by a modified standard deviation (s) of a sample.
Explanation
Self Explanatory. Standard deviation is a measure of dispersion
Comments
The measures of Dispersion are
Ä     Range
o       The simplest measure of dispersion
o       The difference between the highest and lowest value
Ä     Mean Deviation
o       It is the average of deviations from the arithmetic mean. The formula is
§        Mean Deviation = [  (x - x)]
§                                           
Ä     Standard Deviation
o       The most frequently used
o       Defined as the Root Mean Square Deviation
o       In case the same size is more than 30, then the formula is modified in such as way that  - 1 replaces 
Tips
The Measures of Central Tendency are
Ä     Mean
o       This is the Average
Ä     Median
o       This is the “Central Point” of the data
Ä     Mode
o       This is the most frequent value in the data

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