Quick Links:
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:
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:
 Set up additional binomial situations
 Customize display settings (optional)
 Run simulation
 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.
 Choose Add  Sample Grid to replace any current distributions
with a 3row, 2column grid of 6 distributions. Each distribution has editable
values for both n and p. Use the Undo button
to remove the last distributions, or select from other Add menu entries to
add to the grid of distributions.
Help Tip: Notice the sliders for n and p are
hidden because all distributions in the Sample Grid are editable. To access
the sliders, Add a distribution based on sliders, or choose Options  Show
Sliders.
 Choose Add  Binomial with Editable n to view a distribution
for which the value for n is editable (type and press Enter to change
the entry) while the value for p is based on the slider (drag it
to change).
 Choose Add  Binomial with Editable p to view a distribution
for which the value for p is editable (type and press Enter to change
the entry) while the value for n is based on the slider (drag it
to change).
 Choose Add  Binomial with Both Editable to view a distribution
for which the values for n and p are both editable (type
into their respective text boxes and press Enter after typing in each one).
 Choose Add  Binomial Based on Sliders to view a distribution
for which values for n and p are based on the values of
their respective sliders (drag them to change).
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).
 When on Automatically Do Runs is on, the number of runs specified to the
right of the Conduct button will automatically be performed as either parameter n or p is
changed. With each parameter change, the distribution is simultaneously reset
and replaced with a new binomial distribution based on the updated parameters.
Having this option checked when considering distributions based sliders is
particularly useful.
 When Show Theoretical is checked, the theoretical model will be shown as
a red histogram based on the chosen parameter
values for each distribution. Otherwise, this model is hidden.
 Choose Options  Show Sliders to show sliders
for parameter values n and p will be shown as horizontal
bars just below the toolbar. Drag a slider to change its value. Otherwise,
sliders are hidden.
 When Options  Proportion is checked, the proportion or relative
frequency of the total will be displayed above each histogram bar and the
vertical axis reflects this labeling scheme. Otherwise, the frequency or
number of items displayed will be shown.
Help Tip: If Options  Label Bars is not
checked, individual histogram bars will not be labeled yet the vertical
axis labeling will match the appropriate selection as described previously.
 Choose Options  Label Bars to display (or hide) the value for
the bar, either its frequency or relative frequency, above each histogram
bar.
Help Tip: When Label Bars is on, individual histogram
bars of the theoretical model (in red) are
not labeled but histogram bars of conducted simulations are.
 Choose Options  Grid to show (or hide) the grid. Grid display
is useful for reading values from the histogram of the distribution(s).
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.
 Conduct a Specified Number of Runs
at Once: Enter the desired number of runs in the text box to the right
of the Conduct button. Click the Conduct button to perform them at once.
Each click of the Conduct button will add the specified amount to the total
number of performed runs.
Note: The Conduct button does not have an effect on the controls
that start, stop, and determine the speed of the runs.
 Start and Stop: Use the Go and
Pause options
to start and stop the runs of the simulation at the specified speed. These
buttons do not have an effect on the Conduct button.
 Set the Speed :
To set the speed of the simulation, select Step, Slow, Medium, Fast, or Fastest
in the Simulation menu. Alternatively, the simulation will run one pace faster
with each click of the button.
Help Tip: If the speed is set at a Step pace, click
the Go button
for each new run.
 Reset :
Choose the button
to clear all performed runs and restart the simulation using the same distribution
set up.
Note: When Automatically Do Runs is on in the Options menu, drag
sliders for n and p to simultaneously reset and replace
the distribution(s) based on the updated parameter values and specified
number of runs.
Tool Menu
Choose the information button to
show the summary statistics for the simulation. Additionally, use the Tool
menu options or their corresponding toolbar.
 Clear all current distributions and start with a blank screen by choosing
Tool  New .
Then use the Add menu to consider other binomial situations and their distributions.
 Use the Tools menu to Open (),
Print (),
or Save ()
a distribution.
Note: The setup of the distribution including values for n and p will
be saved; any simulated trials will not be saved. To "Save" the distribution
as an image, capture a screen shot of the window. For Mac, press Command+Shift+3.
For Windows, press PrtScr.
See also Save & Print.

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:
 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.)
 Estimate the mean of the data set and click once to fix the hand at your
estimate.
 If you located the mean, the histogram will appear balanced (perfectly
horizontal), and the value of the mean will appear in the upperright corner
of the screen.
 Otherwise the histogram will appear tilted. To balance the histogram, drag
the hand until the histogram is balanced (it will be perfectly horizontal).
 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.
 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.
 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 "bestfit" on a scatterplot and compare to the
regression equation. 
Instructions:
 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.
 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.
 Adjust the moveable model to approximate a "bestfit" for the data.
Drag the left or rightmost 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.
 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.
 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.
 Choose Options  Excluded or the button
to exclude (or include) selected data point(s) from the regression analysis.
Points are highlighted blue when selected, colored red when
excluded, and black when included and not selected. NOTE: If the Show Equation(s)
option is on when points are excluded (or included), the regression equation(s)
will adjust accordingly, with the most recent equation in blue 
the others in red.
 Choose Options  Draw Residuals or the button
to show the residuals for each data point.
 Select Options  Draw Squares or the button
to show the squared error for each data point.
 Choose Options  Draw Means or the button
to draw vertical and horizontal lines representing the means of x and y data
values, respectively.
 When Show Equation(s) is selected from the Options menu, the equations
that correspond to drawn estimated and actual regression models will be visible.
Otherwise, equations are hidden.
 When Show Predicted Value(s) is selected from the Options menu, a table
of predicted values corresponding to all drawn regression and moveable models
will appear in a separate window. Click on a table entry and use the arrow
keys on your keyboard to move through the table of values; notice the corresponding
point and coordinates are highlighted in the scatterplot window. To close
or hide the window, choose the X button or uncheck the menu option.
Help Tip 1: A Regression Model and/or
Moveable Model must
be drawn before predicted values can be shown within the table. The table
will automatically update as you show or hide or move these models.
Help Tip 2: The Predicted Values table will automatically use
the range of x values that are shown in the scatterplot window. Type numerical
values into the Min x, Max x, and x Step boxes
and press Enter after typing in each box to change these settings.
Help Tip 3: To print the entire table of values, resize the window
to show all possible values (until there are not scroll bars on the side
or bottom); then choose Tool  Print or the button.
 Select Options  Error Thermometer to show (or hide) a depiction
of the SSE for the drawn models to the right of the scatterplot. This option
is useful when comparing the SEE of the moveable model with the SEE of the
regression model.
 Choose Options  Guess Correlation or the button
to show (or hide) the guess correlation bar to the right of the scatterplot.
Select your guess for r from one of the five options available then
click Show r to view the actual correlation value.
 Select Options  Plot Information or the button
to show (or hide) scatterplot information with customizable options. Options
include those for modifying labels for x and y, viewing basic
statistics for the plotted data, naming the plot (or title), and adjusting
window settings. Additionally, you may check options to
Show Correlation, Show SEE, and Show Confidence Bands
.
Help Tip: Press Enter on the keyboard to execute any
changes made to the name or window scale of the scatterplot.
Tool menu
Use the Tool menu options or their corresponding toolbar icon to:
 View Basic Statistics for the plotted data, which displays a summary of
statistical calculations related to the data set.
 Print or
Save the
current model as it is shown on the screen.
Note: Files are saved as images, the .gif filename extension
is appropriate. Also, the data set used to generate the scatterplot can
be saved from within Data Analysis.
See also Save & Print.