Probability Distribution Calculations
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This menu provides probability calculations for a range of discrete and continuous probability distributions. This allows many of the calculations that are looked up in Statistical tables to be quickly computed.

A simple diagram is provided for each calculation type to illustrate what is being calculated. The input value is displayed in blue and the resulting calculated value in red. The curves shown for continuous distributions are the probability density function, and for discrete distributions the bars represent the individual probability values at a given deviate. The actual curve/histogram displayed is indicative only, and may not match the actual shape of the selected distribution.

These calculations can be conducted with more generality with the Calculations menu.

Distributions

Specifies the distribution to be used for the calculations. Following the usual convention, these are divided into two categories:

Continuousa range of continuous distributions
Discretea range of discrete distributions can be selected from the drop down list

The linear correlation coefficient (r) is the distribution of the correlation coefficient of X and Y under the assumption that they are independent and both normally distributed. For N observations, the linear correlation coefficient has N-2 degrees of freedom. Note a partial correlation coefficient can be tested for significance using this distribution, but with degrees of freedom N-2-V, where V is the number of variables held constant.

Further details of other distributions available on this menu are given in the printed and online documentation.

Parameters

These fields specify the parameters for the selected distribution.

Calculation Type

Lists the different types of calculation that are available for the chosen distribution. Note the term 'deviate' indicates the value on the x axis which is being calculated, as opposed to a probability value. Not all calculation types are available for all distributions.

Cumulative Lower Probabilitythe cumulative probability below the given deviate.
Cumulative Upper Probabilitythe cumulative probability above the given deviate.
Equivalent Deviatethe deviate for which the cumulative probability below it is equal to the given probability.
Deviates excluding probabilitythe pair of deviates for which the probability outside the interval is equal to the given probability. These are placed so that half the excluded probability is above and below the interval.
Deviates containing probabilitythe pair of deviates for which the probability inside the interval is equal to the given probability. These are placed so that half of the complementary probability (1-p) is above and below the interval.
Confidence Limits of Sample MeanThis gives the confidence limits for a mean so that on resampling, the true mean would be contained in this interval with a probability alpha.
Critical value (one sided)this gives the deviate for which the standardized deviate would only exceed with the given probability.
Critical value (two sided)this gives the deviates for which the absolute standardized deviate would only exceed with the given probability, or for non-symmetrical distributions, the pair of deviates defining an interval.
Probability in Intervalthe cumulative probability between the given lower and upper deviates.
Probability outside Intervalthe cumulative probability outside the given lower and upper deviates.
Probability Densitythe value of the probability density at a given deviate. This is only defined for continuous distributions.
Individual Probabilitythe individual probability at a particular deviate. This may only be calculated for a discrete distribution.

Input Value

This is the given value for the specified calculation, labelled appropriately for each calculation. Note that when providing a probability, either a proportion between 0 and 1 or a percentage between 1% and 100% can be provided. If a percentage less than 1 is provided this will be interpreted as a proportion, so you cannot use % less than 1.

When entering deviates, discrete distributions should only use 0,1,2... and some continuous distributions require only positive values.

Display in Spreadsheet

If this item is selected, the results from the calculation, along with the input to the calculation will be displayed in a new spreadsheet. Note that if you have the option selected you will be warned if you create multiple spreadsheets, without closing the previous ones.

Allow list of values or data structure names

If this option is selected, multiple numbers (a list in either space or comma delimited format, a progression (e.g. 0...5 for 0,1,2,3,4,5)) may be provided, or a variate name (e.g. X) may be typed into the input value. This is not available for all calculations.

When this option is active, the size of the input value field is extended to allow for space for typing, but all validation of the input values is suppressed.

Action Buttons

RunRun the probability calculation.
CancelClose the menu without further changes.
DefaultsSet the menu settings back to the default settings. Clicking the right mouse on this button produces a pop-up menu where you can choose to set the menu using the currently stored defaults or the GenStat default settings.

See Also