inst/help/chi-squared.md

In Kucharssim/JASP-LearnStats: Distributions (Beta) Module for JASP

Chi-squared Distribution

Demonstration of the Chi-squared distribution.

Show Distribution

Displays theoretical Chi-squared distribution, given specified parameter values.

Parameters

• k: Shape
• λ: non-centrality parameter

Display

• Explanatory text: Displays explanatory text
• Parameters, support, and moments: Displays the definition of parameters, the support of the random variable, and the moments of the theoretical distribution
• Probability density function: Displays the probability density plot
• Cumulative distribution function: Displays the cumulative distribution plot
• Quantile function: Displays the quantile plot

Options

• Range of x from ... to ... : Defines the limits of the x-axis of the probability density plot and cumulative distribution plot, and the limits of the y-axis of the quantile plot.
• Highlight density: Highlights the probability density on the probability density plot and cumulative distribution plot at specified values of x
• Highlight probability: Highlights the probability in between the specified values of x in the density plot (area under the curve), and highlights the cumulative probability at the specified values in the cumulative distribution plot
• Interval: Select the bounds of the interval to display: Density is highlighted at the lower and upper bounds, the probability is displayed for the specified interval.

Generate and Display Data

• Variable name: Specify the name of the variable. Once filled, creates an empty column in the current data set.
• Number of samples: Specify the number of samples.

• Draw samples: Sample from the theoretical distribution.

• Get variable from data set: Select a variable to display and fit with the theoretical distribution.

Statistics

• Descriptives: Displays a descriptive table of the selected variable.
• First ... moments: Displays a table with the raw and central sample moments of the selected variable. Defaults to first 2 moments.

Plots

• Histogram with ... bins: Display a histogram of the selected variable with the number of specified bins.
• Empirical cumulative distribution: Displays an empirical cumulative distribution plot of the selected variable.

Estimate Parameters

• Maximum likelihood: Fit the theoretical distribution to the selected variable by maximizing the likelihood function. The parameter values specified in Show distribution section serve as starting points for the procedure.

Output

• Estimates: Displays a table with the parameter estimates. Changing parametrization changes which parameters are displayed.
  • Std. error: Displays the standard error of the parameter estimates
  • Confidence interval: Displays the confidence interval of the parameters at the specified confidence level.

Assess Fit

Plots

• Histogram vs. theoretical pdf: Displays a histogram of the selected variable overlayed with the probability density function of the fitted distribution
• Empirical vs. theoretical cdf: Displays an empirical cumulative distribution plot overlayed with the cumulative distribution function of the fitted distribution
• Q-Q plot: Displays the quantile-quantile plot. The x-axis shows the theoretical quantiles of the data points under the fitted distribution, the y-axis shows the empirical quantiles of the selected variable.
• P-P plot: Displays the probability-probability plot. The x-axis shows the theoretical value of the cumulative density function of the data points under the fitted distribution, the y-axis shows the empirical percentiles of the selected variable.

Statistics

• Kolmogorov-Smirnov: Displays the Kolmogorov-Smirnov test
• Cramer von Misses: Displays the Cramer von Misses test
• Anderson-Darling: Displays the Anderson-Darling test

Kucharssim/JASP-LearnStats documentation built on Jan. 23, 2020, 3:47 a.m.