# Q-Q Plot

The Q-Q plots procedure produces probability plots for transformed values. Available test distributions include beta, chi-square, exponential, gamma, half-normal, Laplace, Logistic, Lognormal, normal, pareto, Student's t, Weibull, and uniform. Depending on the distribution selected, you can specify degrees of freedom and other parameters.

• You obtain probability plots for transformed values. Transformation options include natural log, standardize values, difference, and seasonally difference.
• You can specify the method for calculating expected distributions and for resolving "ties" (multiple observations with the same value).
Test distribution
Specify a distribution type for your data. The drop-down list provides the following options:
Beta
Beta distribution. The shape1 and shape2 parameters a and b must be positive. If they are not specified, `DISTRIBUTION` estimates them from the sample mean and sample standard deviation. All observations must be in the range 0 - 1, inclusive.
Chi-square
Chi-square distribution. You must specify the degrees of freedom (df). Negative observations are not allowed.
Exponential
Exponential distribution. The scale parameter a must be positive. If the parameter is not specified, `DISTRIBUTION` estimates it from the sample mean. Negative observations are not allowed.
Gamma
Gamma distribution. The shape and scale parameters a and b must be positive. If they are not specified, `DISTRIBUTION` estimates them from the sample mean and sample standard deviation. Negative observations are not allowed.
Half-normal
Half-normal distribution. Data are assumed to be location-free or centralized. (Location parameter=0.) You can specify the scale parameter a or let `DISTRIBUTION` estimate it by using the maximum likelihood method.
Laplace
Laplace or double exponential distribution. `LAPLACE` takes a location and a scale parameter (a and b). The scale parameter (b) must be positive. If the parameters are not specified, `DISTRIBUTION` estimates them from the sample mean and sample standard deviation.
Logistic
Logistic distribution. `LOGISTIC` takes a location and a scale parameter (a and b). The scale parameter (b) must be positive. If the parameters are not specified, `DISTRIBUTION` estimates them from the sample mean and sample standard deviation.
Lognormal
Lognormal distribution. The scale and shape parameters a and b must be positive. If they are not specified, `DISTRIBUTION` estimates them from the mean and standard deviation of the natural logarithm of the sample data. Negative observations are not allowed.
Normal
Normal distribution. The location parameter a can be any numeric value, while the scale parameter b must be positive. If they are not specified, `DISTRIBUTION` estimates them from the sample mean and sample standard deviation.
Pareto
Pareto distribution. The threshold and shape parameters a and b must be positive. If they are not specified, `DISTRIBUTION` assumes a equals the minimum observation and estimates b by the maximum likelihood method. Negative observations are not allowed.
Student t
Student’s t distribution. You must specify the degrees of freedom (df).
Uniform
Uniform distribution. `UNIFORM` takes a minimum and a maximum parameter (a and b). Parameter a must be equal to or greater than b. If the parameters are not specified, `DISTRIBUTION` assumes them from the sample data.
Weibull
Weibull distribution. The scale and shape parameters a and b must be positive. If they are not specified, `DISTRIBUTION` estimates them using the least square method. Negative observations are not allowed.
Distribution parameters
Provides distribution strategy and parameter options.
Estimate from data
When selected, this setting estimates the distribution parameters based on the data and selected distribution type.
Specify
When selected, you can specify the distribution parameters for the selected distribution type.
Note: The available parameters will vary based on the selected distribution type.
Transform
The provided options set the transform and periodicity settings.
Natural log transform
Transforms the data by using the natural logarithm (base e) to remove varying amplitude.
Standardize values
Transforms the sequence or time series variables into a sample with a mean of 0 and a standard deviation of 1.
Difference
Specifies the degree of differencing that is used before plotting to convert a non-stationary variable into a stationary variable with a constant mean and variance. Enter an appropriate value in the field.
Seasonally difference
If the variable exhibits a seasonal or periodic pattern, you can use this setting to seasonally difference the variable before plotting.
Note: This setting is enabled only when a sequence or time series variable, with a defined periodicity, is selected as one of the quantitative variables.
Proportion estimation formula
The provided options set the formula that is used to estimate proportions.
Blom's
Creates new ranking variable based on proportion estimates that uses the formula `(r-3/8) / (w+1/4)`, where `w` is the sum of the case weights and `r` is the rank.
Rankit
Uses the formula `(r-1/2) / w`, where `w` is the number of observations and `r` is the rank, ranging from 1 to `w`.
Tukey's
Uses the formula `(r-1/3) / (w+1/3)`, where `r` is the rank and `w` is the sum of the case weights.
Van der Waerden's
Van der Waerden's transformation, defined by the formula `r/(w+1)`, where `w` is the sum of the case weights and `r` is the rank, ranging from 1 to `w`.
Rank assigned to ties
The provided options control the method for determining how to handle tie values. The following table shows how the different methods assign ranks to tied values.
Table 1. Ranking methods and results
Value Mean Low High Break ties arbitrarily
10 1 1 1 1
15 3 2 4 2
15 3 2 4 2
15 3 2 4 2
16 5 5 5 3
20 6 6 6 4

## Obtaining Q-Q probability plots

This feature requires the Statistics Base option.