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Statistics Custom Apps

The Custom Apps for Statistics include those for exploring both univariate and bivariate data analysis. Click on the name of an app below for a description and help topics:

Univariate Data Analysis

Bivariate Data Analysis

Binomial Distributions
Estimate Center and Spread
Modeling
Click here for Help topics on other general purpose tools: Randomization Distribution, and Distribution of Sample....

Binomial Distributions

Vary the number of successes and the probability of a success on each trial to see how the shape, center, and spread of binomial distributions are affected. Conduct trials and compare theoretical models of distributions to simulation results.

Instructions:

Upon opening the custom app, a binomial distribution based on sliders for n (number of trials) and p (probability of success) is shown. The theoretical binomial model for the parameter values (default: n=50, p=0.5) is displayed in red. The following provide guidelines and tips on how to utilize the capabilities of this custom app:

  1. Set up additional binomial situations
  2. Customize display settings (optional)
  3. Run simulation
  4. Tool menu options

Set Up Additional Binomial Situations

Add menu

Select entries from the Add menu to consider multiple distributions at the same time. Values for n and p are recorded above each distribution as they are added.

Help Tip: Once a distribution is added, distinguish between those that are controlled by sliders and those that are editable by noting the colors of values for n and p. In particular, values in gray are controlled by the sliders and automatically update the distribution as sliders are dragged. White text boxes with black text are editable - first click on the desired one, type an appropriate value, then press Enter to change the corresponding distribution. Editable parameters are not affected by sliders and vice versa.

Customize Display Settings (optional)

The default settings for this custom app will Show Theoretical model (in red), Show Sliders for n and p (useful for distributions based on sliders), indicate the Proportion (as a label along the vertical axis for the histogram), and display a Grid (useful for reading from the distributions). It is not required to change any settings. If desired, access the entries within the Options menu.

Options menu

Select entries of the Options menu to turn them on (checked) or off (unchecked).

Run Simulation

After setting up the distribution(s), use the Simulation menu or their corresponding toolbar buttons to start, stop, reset, and determine the speed at which runs are performed. Also, use the Conduct button to do a specified number of runs at once. Notice that a tally of conducted runs is displayed at the bottom of the screen.

Tool Menu

Choose the information button to show the summary statistics for the simulation. Additionally, use the Tool menu options or their corresponding toolbar.

 

Estimate Center and Spread

Estimate the mean of a distribution by finding the balance point of the histogram and estimate the spread of the distribution.

Instructions:

  1. Using your mouse, move the cursor over the hand at the bottom of the Histogram Plot(s) window. (Notice that without clicking your mouse, the position of the hand moves with your mouse.)
  2. Estimate the mean of the data set and click once to fix the hand at your estimate.
  3. If you located the mean, the histogram will appear balanced (perfectly horizontal), and the value of the mean will appear in the upper-right corner of the screen.
  4. Otherwise the histogram will appear tilted. To balance the histogram, drag the hand until the histogram is balanced (it will be perfectly horizontal).
  5. The hand indicating the mean will remain fixed and a new hand will appear. Move the new hand by moving your cursor to the left or right of the mean.
  6. If the distribution is approximately normal, you can estimate the standard deviation. By dragging the hand, find the middle 2/3 (67%) of the data set (the yellow shaded area), and then click. The shaded area can be adjusted by moving the appropriate hand.
  7. Reopen the custom app to reset it.

See the Histogram entry in the Data Analysis help menu for further information about the Histogram Plot(s) window.

 

Modeling

Estimate a curve of "best-fit" on a scatterplot and compare to the regression equation.

Instructions:

  1. Choose an appropriate type of model for estimating regression.
    Examine the scatterplot of data to determine the best type of regression model for given data set. Click on the Models menu and select (or deselect) from Linear, Exponential, Power, Logarithmic, Quadratic, Cubic, Quartic, Polynomial, or Enter/Edit a Model.
  2. Estimate the regression model - Draw Moveable Line or Model.
    Choose Draw Moveable Line or Model in the Options menu or click the button. Based on the choice in Step 1, an adjustable model and its corresponding equation will be shown on the scatterplot in green.
  3. Adjust the moveable model to approximate a "best-fit" for the data.
    Drag the left- or right-most green squares along the moveable model to adjust the slope or curve of the model. Drag the green square in the center to move the model vertically or horizontally. Notice the equation of the line updates as the position of the line changes.
  4. Check the reliability of the estimated model.
    Before drawing the regression model, utilize entries of the Options menu to aid in checking the reliability of the drawn moveable model. For instance, choose Analysis or the X button to show a Residual Plot and Regression Analysis frame.
  5. Draw the regression model - Draw Regression Models
    With the estimated line is place, compare your estimate to the actual regression line. Choose Draw Regression Models in the Options menu or the button. Notice the regression model will be drawn according to the type of model selected from the Models menu. The line or curve and its corresponding equation will be shown on the plot in blue.
    Help Tip: To hide the equations of the moveable model and regression model, uncheck Show Equation(s) by selecting it from the Options menu.

Options menu

Customize how the scatterplot and regression model(s) are viewed in the modeling window. A checkmark next to an entry of the Options menu indicates that is is on or shown, otherwise, it is off or hidden.

Tool menu

Use the Tool menu options or their corresponding toolbar icon to: