# 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.

- From the menus choose:
- Select one or more numeric variables and move them onto the Variables field.
- Select a test distribution.

Optionally, you can select transformation options to obtain probability plots for transformed values and specify a method for calculating expected distributions.