Class: Math_Stats
Source Location: /Math_Stats-0.9.1/Math/Stats.php
A class to calculate descriptive statistics from a data set.
Author(s):
Version:
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Inherited Variables
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Inherited Methods
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Class Details
[line 119]
A class to calculate descriptive statistics from a data set. Data sets can be simple arrays of data, or a cummulative hash. The second form is useful when passing large data set, for example the data set: $data1 = array (1,2,1,1,1,1,3,3,4.1,3,2,2,4.1,1,1,2,3,3,2,2,1,1,2,2); can be epxressed more compactly as: $data2 = array('1'=>9, '2'=>8, '3'=>5, '4.1'=>2);Example of use: include_once 'Math/Stats.php';
$s = new Math_Stats();
$s->setData($data1);
// or
// $s->setData($data2, STATS_DATA_CUMMULATIVE);
$stats = $s->calcBasic();
echo 'Mean: '.$stats['mean'].' StDev: '.$stats['stdev'].'
\n';
// using data with nulls
// first ignoring them:
$data3 = array(1.2, 'foo', 2.4, 3.1, 4.2, 3.2, null, 5.1, 6.2);
$s->setNullOption(STATS_IGNORE_NULL);
$s->setData($data3);
$stats3 = $s->calcFull();
// and then assuming nulls == 0
$s->setNullOption(STATS_USE_NULL_AS_ZERO);
$s->setData($data3);
$stats3 = $s->calcFull(); Originally this class was part of NumPHP (Numeric PHP package)
Method Detail
Math_Stats (Constructor) [line 176]
Constructor for the class
Parameters:
absDev [line 777]
Calculates the absolute deviation of the data points in the set Handles cummulative data sets correctly
absDevWithMean [line 800]
mixed absDevWithMean(
numeric
$mean)
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Calculates the absolute deviation of the data points in the set given a fixed mean (average) value. Not used in calcBasic(), calcFull() or calc(). Handles cummulative data sets correctly
Parameters:
calc [line 326]
mixed calc(
int
$mode, [boolean
$returnErrorObject = true])
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Calculates the basic or full statistics for the data set
Parameters:
calcBasic [line 349]
mixed calcBasic(
[boolean
$returnErrorObject = true])
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Calculates a basic set of statistics
Parameters:
calcFull [line 373]
mixed calcFull(
[boolean
$returnErrorObject = true])
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Calculates a full set of statistics
Parameters:
center [line 295]
Transforms the data by substracting each entry from the mean. This will reset all pre-calculated values to their original (unset) defaults.
coeffOfVariation [line 1144]
mixed coeffOfVariation(
)
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Calculates the coefficient of variation of a data set. The coefficient of variation measures the spread of a set of data as a proportion of its mean. It is often expressed as a percentage. Handles cummulative data sets correctly
count [line 626]
Calculates the number of data points in the set Handles cummulative data sets correctly
frequency [line 1206]
Calculates the value frequency table of a data set. Handles cummulative data sets correctly
geometricMean [line 992]
Calculates the geometrical mean of the data points in the set Handles cummulative data sets correctly
getData [line 217]
mixed getData(
[boolean
$expanded = false])
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Returns the data which might have been modified according to the current null handling options.
Parameters:
harmonicMean [line 1030]
Calculates the harmonic mean of the data points in the set Handles cummulative data sets correctly
interquartileMean [line 1273]
mixed interquartileMean(
)
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The interquartile mean is defined as the mean of the values left after discarding the lower 25% and top 25% ranked values, i.e.: interquart mean = mean(<P(25),P(75)>) where: P = percentile
interquartileRange [line 1311]
mixed interquartileRange(
)
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The interquartile range is the distance between the 75th and 25th percentiles. Basically the range of the middle 50% of the data set, and thus is not affected by outliers or extreme values. interquart range = P(75) - P(25) where: P = percentile
kurtosis [line 859]
Calculates the kurtosis of the data distribution in the set The kurtosis measures the degrees of peakedness of a distribution. It is also called the "excess" or "excess coefficient", and is a normalized form of the fourth central moment of a distribution. A normal distributions has kurtosis = 0 A narrow and peaked (leptokurtic) distribution has a kurtosis > 0 A flat and wide (platykurtic) distribution has a kurtosis < 0 Handles cummulative data sets correctly
max [line 451]
Calculates the maximum of a data set. Handles cummulative data sets correctly
mean [line 651]
Calculates the mean (average) of the data points in the set Handles cummulative data sets correctly
median [line 891]
Calculates the median of a data set. The median is the value such that half of the points are below it in a sorted data set. If the number of values is odd, it is the middle item. If the number of values is even, is the average of the two middle items. Handles cummulative data sets correctly
midrange [line 967]
Calculates the midrange of a data set. The midrange is the average of the minimum and maximum of the data set. Handles cummulative data sets correctly
min [line 427]
Calculates the minimum of a data set. Handles cummulative data sets correctly$this->_data[0]
mode [line 927]
Calculates the mode of a data set. The mode is the value with the highest frequency in the data set. There can be more than one mode. Handles cummulative data sets correctly
percentile [line 1427]
mixed percentile(
numeric
$p)
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The pth percentile is the value such that p% of the a sorted data set is smaller than it, and (100 - p)% of the data is larger. A quick algorithm to pick the appropriate value from a sorted data set is as follows: - Count the number of values: n
- Calculate the position of the value in the data list: i = p * (n + 1)
- if i is an integer, return the data at that position
- if i < 1, return the minimum of the data set
- if i > n, return the maximum of the data set
- otherwise, average the entries at adjacent positions to i
The median is the 50th percentile value.
Parameters:
product [line 548]
numeric|array|PEAR_Error product(
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Calculates PROD { (xi) }, (the product of all observations) Handles cummulative data sets correctly
productN [line 571]
numeric|array|PEAR_Error productN(
numeric
$n)
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Calculates PROD { (xi)^n }, which is the product of all observations Handles cummulative data sets correctly
Parameters:
quartileDeviation [line 1336]
mixed quartileDeviation(
)
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The quartile deviation is half of the interquartile range value quart dev = (P(75) - P(25)) / 2 where: P = percentile
quartiles [line 1237]
The quartiles are defined as the values that divide a sorted data set into four equal-sized subsets, and correspond to the 25th, 50th, and 75th percentiles.
quartileSkewnessCoefficient [line 1387]
mixed quartileSkewnessCoefficient(
)
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The quartile skewness coefficient (also known as Bowley Skewness), is defined as follows: quart skewness coeff = (P(25) - 2*P(50) + P(75)) / (P(75) - P(25)) where: P = percentile
quartileVariationCoefficient [line 1359]
mixed quartileVariationCoefficient(
)
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The quartile variation coefficient is defined as follows: quart var coeff = 100 * (P(75) - P(25)) / (P(75) + P(25)) where: P = percentile
range [line 672]
Calculates the range of the data set = max - min
sampleCentralMoment [line 1075]
mixed sampleCentralMoment(
integer
$n)
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Calculates the nth central moment (m{n}) of a data set. The definition of a sample central moment is: m{n} = 1/N * SUM { (xi - avg)^n } where: N = sample size, avg = sample mean.
Parameters:
sampleRawMoment [line 1111]
mixed sampleRawMoment(
integer
$n)
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Calculates the nth raw moment (m{n}) of a data set. The definition of a sample central moment is: m{n} = 1/N * SUM { xi^n } where: N = sample size, avg = sample mean.
Parameters:
setData [line 189]
mixed setData(
array
$arr, [optional
$opt = STATS_DATA_SIMPLE])
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Sets and verifies the data, checking for nulls and using the current null handling option
Parameters:
setNullOption [line 236]
mixed setNullOption(
$nullOption)
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Sets the null handling option. Must be called before assigning a new data set containing null values
Parameters:
skewness [line 822]
Calculates the skewness of the data distribution in the set The skewness measures the degree of asymmetry of a distribution, and is related to the third central moment of a distribution. A normal distribution has a skewness = 0 A distribution with a tail off towards the high end of the scale (positive skew) has a skewness > 0 A distribution with a tail off towards the low end of the scale (negative skew) has a skewness < 0 Handles cummulative data sets correctly
stdErrorOfMean [line 1181]
Calculates the standard error of the mean. It is the standard deviation of the sampling distribution of the mean. The formula is: S.E. Mean = SD / (N)^(1/2) This formula does not assume a normal distribution, and shows that the size of the standard error of the mean is inversely proportional to the square root of the sample size.
stDev [line 718]
Calculates the standard deviation (unbiased) of the data points in the set Handles cummulative data sets correctly
stDevWithMean [line 758]
mixed stDevWithMean(
numeric
$mean)
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Calculates the standard deviation (unbiased) of the data points in the set given a fixed mean (average) value. Not used in calcBasic(), calcFull() or calc(). Handles cummulative data sets correctly
Parameters:
studentize [line 259]
Transforms the data by substracting each entry from the mean and dividing by its standard deviation. This will reset all pre-calculated values to their original (unset) defaults.
sum [line 476]
Calculates SUM { xi } Handles cummulative data sets correctly
sum2 [line 498]
Calculates SUM { (xi)^2 } Handles cummulative data sets correctly
sumN [line 521]
Calculates SUM { (xi)^n } Handles cummulative data sets correctly
Parameters:
variance [line 698]
Calculates the variance (unbiased) of the data points in the set Handles cummulative data sets correctly
varianceWithMean [line 742]
mixed varianceWithMean(
numeric
$mean)
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Calculates the variance (unbiased) of the data points in the set given a fixed mean (average) value. Not used in calcBasic(), calcFull() or calc(). Handles cummulative data sets correctly
Parameters:
Documentation generated on Mon, 11 Mar 2019 15:39:18 -0400 by phpDocumentor 1.4.4. PEAR Logo Copyright © PHP Group 2004.
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