Creating Graphs for Mathematical Notation

Making a Normal Distribution Graph

Basic standard normal graph This section will give you the basics needed to create a Standard Normal curve. You'll use this part to create the basic graph in each case and then make modifications listed in the other sections.

When you are done with this section, the graph will look like the graph to the right.

Label two columns of the worksheet as z and p
Choose Calc / Make Patterned Data / Simple Set of Numbers
1. Store the patterned data in z
2. Start at -3.5
3. Go to 3.5
4. Use a step size of 0.05 (you can get a smoother curve by using a smaller step size of 0.02 or 0.01)
Choose Calc / Probability Distributions / Normal
1. Choose Probability Density
2. The input column is z
3. The storage is p
Choose Graph / Scatterplot / With Connect Line
1. The y variable is p and the x variable is z
2. Choose Scale
  1. Under Axes and Ticks, uncheck all boxes for the high y-scale and the high x-scale. Check all boxes for the low x-scale. The only box that should be checked under the low y-scale is the axis line.
3. Choose Data View
  1. Under Data Display, turn off the Symbols
4. Click OK to generate the graph
Now comes the fun part, we get to clean up the graph and annotate it! Make sure your graph is essentially correct before continuing. If you have to go back and re-generate the graph using a scatterplot, you will lose all annotations.
Most of these involve editing a piece of the graph. There are a few ways to do this. You can 1) double left click the item, 2) position your mouse over the item, click the right mouse button, and choose Edit, or 3) left click on the item and then press Control-T on the keyboard (or choose the right mouse button and pick edit). The instructions below will just say "edit this part of the graph" and you can use any of the methods to perform the edit.
1. To clean up the labels we don't want, click on the "p" on the left side of the graph and delete it. Do the same thing for the "z" at the bottom of the graph.
2. Edit the normal curve
  1. Change the line type to custom with a size of 3
3. Edit the y axis scale on the left side of the graph (there are no numbers, just click on the axis line at the left)
  1. Under Scale, change the minimum scale range to 0 and the maximum scale range to 0.6. This part isn't crucial, but it helps flatten out the curve some.
  2. Under Show, uncheck all boxes, we don't want a vertical axes at all
4. Edit the x axis scale at the bottom of the graph
  1. Under Scale, change the minimum scale range to -3.5 and the maximum scale range to 3.5
  2. Under Attributes, change the line size to 2
  3. Under Font, change the font to Arial and the font size to 14
5. Edit the title and change the font to Arial and the font size to 20 points. An appropriate title for the basic graph might be "Standard Normal Distribution" but use something appropriate for the graph you're making.
6. Edit the box outside the graph region. By default it is grey, but we would like it to be transparent.
  1. Change the fill pattern to custom and set the type to none. To get to the no fill, you'll actually have to scroll up the pull down list to the box with the N in the middle.
  2. Change the borders and fill lines to custom and then change the type to none.

Customizing the Graph

At this point, we are ready to start adding things to the graph, rather than just changing what is there. There is a graph annotation toolbar that is active while you're editing a graph. If the toolbar does not appear on your screen, then go to Tools / Toolbars / Graph Annotation Tools and turn it on. Until this point, we have been using the Select Mode (the arrow), but now we're going into insert Text (the T) or a Lines (the line). Click on the appropriate mode to insert the right object. Here are generic instructions for each type of object.

Inserting Text
1. Click the T from the graph annotation toolbar
2. Click on the graph where you would like the upper left corner of the text to be (this can be changed later)
3. Type the text
4. Click OK
5. After the text is on the screen, you can edit it, change the font (to Arial), color, or size. You can also drag it to a new location on the screen since it is very unlikely that you will get it where you want it the first time
6. Fine control over the position of the text can be obtained by using the arrow keys or shift arrow (for medium control).
Inserting Lines
1. Click on the Line on the graph annotation toolbar
2. Click (and hold) the left mouse button where you would like the line to start
3. Drag the mouse to where you would like the line to end. You can force a horizontal, vertical, or diagonal (45 degree) line by holding the shift key down while dragging. Let up on the mouse button when you reach the destination.
4. If you don't get the line exactly where you want it, you can drag the line once it's on the screen. You can lengthen the lines by draging the ends, but be careful because the shift key doesn't keep it horizontal or vertical when at this point.
5. You can then edit the line to change the type, color, or size, or add arrows
6. Fine control over the position of the line can be obtained by using the arrow keys or shift arrow (for medium control)
Shading a region
- Click on the Polygon on the graph annotation toolbar (on the far right)
- Click at certain key points along the graph
- When you are done, position the cursor above (or below) the initial point, then double click to close the polygon
- You can then edit the graph and make it look like you want it to

Empirical Rule Graph (Chapters 5 - 6)

Empirical Rule Begin by creating the Standard Normal Distribution as described at the top of this document. Then we'll edit it to make it look like the graph to the right.

Edit the title.
Right click somewhere on the graph and choose Add / Reference Lines
1. The reference lines for the X positions are -3 -2 -1 0 1 2 3 (separate them with spaces)
Edit any of the reference lines
1. Change the line type to custom.
2. Make it a dashed line
3. Check the box that says Apply same attributes to all reference lines
4. Click on the Show tab
5. Tell it None for Show Label
6. Apply same label option to all reference lines
Use the instructions above from the Customizing the Graph to draw the green horizontal lines and label them with the percents.

Copying the Graph into Word

This is similar to what you do when you do the technology projects.

Right click the mouse and choose Copy Graph
Switch to your Microsoft Word document
Paste the graph into Word. It will take up most of the page, but we'll resize it.
Right click the mouse on the graph and choose Format Picture
1. Choose Size and set the width to 2"
2. Choose Layout and choose Square and then set the horizontal alignment to Right
3. Click OK
Drag the picture to where you want it to be.

Hypothesis Test Graph (Chapters 7 - 8)

Two tail hypothesis test Begin by creating the Standard Normal Distribution as described at the top of this document. Then we'll edit it to make it look like the graph to the right.

Add reference lines to the graph for the critical values

Right click somewhere on the graph and choose Add / Reference Lines
1. The reference lines for the X positions are -1.96 1.96 (separate them with spaces). Note that the critical values are not always 1.96 and -1.96, they depend on the distribution being used and whether it is a one tail or two tail test.
Edit the reference line at 1.96.
1. Under Attributes, select a Custom line type of dashed lines with a thickness of 2. Check the box that says to apply attributes to all reference lines to save having to do this to the other line at -1.96
Edit the text that says 1.96.
1. Change the text from 1.96 to "Critical Value z=1.96"

Under font, change the font to Arial, the color to red and the font size to 12. Check the box to apply font changes to all reference lines
Under alignment, set the text angle to 90 degrees, choose a custom position and make it "Below, to the left"

Edit the text for the reference line at -1.96 (NOTE: You will not have a second reference line for a one tail test).
1. Change the text to "Critical Value z=-1.96"
2. Under alignment, set the text angle to 90 degrees, choose a custom position and make it "Below, to the right
Edit the title.
Use the instructions above under "Customizing the Graph" to follow the rest of these instructions. Insert the horizontal lines for the areas. You will need three of them, one for the left portion, one for the middle, and one for the right. For each line, do the following.
1. Change the style to small dashes, the color to dark green, the thickness to 2 and add arrows where appropriate.
2. Use the mouse or arrow keys to carefully align the lines with each other
Insert the labels for "Critical Region", "Non-Critical Region", "Retain Ho", and "Reject Ho". There is not an easy way to put in an H₀, so just use a lowercase O so it is close.
1. Change the font to Arial
2. Change the font size to 14.
The labels for the areas require changing fonts and your output won't look exactly like mine because I made it much harder than it needs to be.
1. Insert text that says "1-a=0.95" and "a/2=0.025". That is, use the a instead of an alpha (α). We'll change the font in the next step so it shows up as an alpha.
2. Then edit the text and set the font to Symbol and make the size 12. That will change the a into an alpha.
To shade the critical region, use the closed polygon tool (last one on right) and click along the shaded part. You may need to practice a couple of times to get it looking right. See the "shading a region" part above.
Don't close your graph out. Make sure you save it as part of your project. But when you're all done, copy and paste it into Word. See "Copying the Graph into Word" under the Empirical Rule section.