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Mean and median
Given a data series (2, 5, 9), the mean (average) is
(2 + 5 + 9)/3 = 5.3, and the median is the 5.
Correlation
Correlation is a measure of the relation between two or more variables.
The value ranges from -1 to +1. Negative values
represent "negative correlation", positive values represent "positive correlation", and 0 represents a "lack of correlation".
The most commonly used correlation measure is the Pearson correlation:
r12 = [S(Yi1 - <Y>1)*(Yi2 - <Y>2)] / [S(Yi1 - <Y>1)2 * S(Yi2 - <Y>2)2]1/2
where
<Y> = SYi/n and n is the sample size.
Correlation value is frequently given with a confidence interval.
Sample and population
Population is the collection of objects of a study. Sample is a subset
of the population used to estimate the statistics of the population. For example,
the population of an opinion poll could be the whole population on the earth.
The poll can only "sample" a limited number of individuals.
Variance
Variance of a population:
s2 = S(xi-m)2/N
where m is the population mean and N is the population size.
Variance of a sample (for estimating the population variance):
s2 = S(xi-<x>)2/ (n-1)
where <x> is the sample mean and n is the sample size.
Standard deviation
Standard deviation (s or s) is the square root of the variance.
Confidence interval
The confidence intervals for specific statistics (e.g., means, or correlation)
is a range of values around the statistic where the "true" (population) statistic
can be expected to be located (with a given level of certainty).
The 95%-confidence level of the correlation is (0.78, 0.95) means that the true (population)
correlation has a 95% probability to be within the interval (0.78, 0.95).
p-value
The p-value represents the probability of error that is involved in
accepting the observed result as valid rather than a fluctuation in
the population.
The p-value of .05 is usually treated as an acceptable error level.
For more information, please visit
the Electronic Statistics Textbook.
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