Area.doc 4/5/06
Use of Area Programs
To use any of these programs, open Minitab, click on any place in the ‘session’ part of the screen and,
using the ‘Editor’ pulldown menu, click on ‘Enable Commands.’ Now find (using the ‘file’ pulldown menu
and ‘Open Worksheet’) or prepare a worksheet and call the macro using a command beginning with ‘%.’
To arrange the graphs to print together, click on one of the graphs and then, using the ‘Editor’ pulldown
menu, click on ‘Layout Tool.’ Use the arrows provided to remove the graph (click on it first) in the layout
and then pick the number of rows and columns and use the arrows to put the graphs in the layout in the
order they were made.
The most recent A versions of these programs, NormArea6A, ChiArea6A, tArea6A and FArea6A are selfprompting, as are the older versions, NormArea5A, ChiArea5A, tArea5A and FArea5A. These do not
require a worksheet. I find it convenient to prepare and save a dummy worksheet and to store it in the same
file in which the Macros are kept. Then, when the macros are called, there is no problem finding them. To
download the version 6 routines, follow the instructions in Areadoc2. The version 5 routines are in
AreaRoutines.doc. Each of them can be copied using notepad and changing the suffix on the stored routines
from ‘.txt’ to ‘.mac’. The C versions of these routines (NormArea6C, ChiArea6C, etc.) require input to be
set up in advance and examples of this are shown below. The difference between the 5 versions and the 6
versions is line density in the graphs. Instructions for copying the denser, better graphs from version 6 are
given in AreaRoutines.doc.
An example of the use of NormArea5A follows. All my input was put in when the program asked for it.
————— 1/28/2005 10:08:24 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\notmuch.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\notmuch.MTW'
Worksheet was saved on Fri Jan 21 2005
Results for: notmuch.MTW (This worksheet is just a few numbers that are not used. Finding this
sheet orients Minitab so that it knows that the data and macros are in a file that I created called Minitab’)
MTB > %NormArea5A
Executing from file: NormArea5A.MAC
Graphic display of normal curve areas
Finds and displays areas to the left or right of a given value
or between two values. (This macro uses C100-C116 and K100-K116)
Enter the mean and standard deviation of the normal curve.
DATA> 883
DATA> 100
Do you want the area to the left of a value? (Y or N)
n
Do you want the area to the right of a value? (Y or N)
y
Enter the value for which you want the area to the right.
DATA> 700
...working...
Normal Curve Area
1
Area.doc 4/5/06
Normal Curve with Mean 883 and Standard Deviation 100
The Area to the Right of 700 is 0.9664
0.004
Density
0.003
0.002
0.001
0.000
400
500
600
700
800
900
Data Axis
1000
1100
1200
1300
Documentation for NormArea5c
Input for NormArea5c – Material is in worksheet 252PrA1d-f, which generates the solution to Problem
A1, parts d-f.
#C1 contains means, C2 contains standard deviations
#C3 contains lower limits of intervals, C4 contains upper limits of intervals
#C5 contains 0 if Area is between points in C3 and C4
#C5 contains 1 if Area is to the left of point in c4
#C6 contains 2 if Area is to the right of point in C3
So the first row below asks for a Normal curve with mean 5 and Standard deviation 6. It wants the
probability between 8 and 9.
Row
1
2
3
4
5
6
C1
5
0
5
0
5
0
C2
6
1
6
1
6
1
C3
8.00
0.50
2.00
-0.50
3.00
-0.33
C4
9.00
9.00
9.00
9.00
6.00
0.17
C5
2
2
2
2
0
0
Computer Output for this Worksheet follows.
————— 1/28/2005 10:44:37 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252PrA1df.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252PrA1d-f.MTW'
Worksheet was saved on Thu Jan 20 2005
Results for: 252PrA1d-f.MTW
MTB > %NormArea5C
Executing from file: NormArea5C.MAC
2
Area.doc 4/5/06
Executing from file: NormArea5.MAC
...working...
Normal Curve Area
...working...
Normal Curve Area
...working...
Normal Curve Area
...working...
Normal Curve Area
...working...
Normal Curve Area
...working...
Normal Curve Area
Graphs Follow.
Normal Curve with Mean 5 and Standard Deviation 6
The Area to the Right of 8 is 0.3085
Normal Curve with Mean 0 and Standard Deviation 1
The Area to the Right of 0.5 is 0.3085
0.4
Density
Density
0.050
0.025
0.000
-20
0
0.2
0.0
20
-5.0
-2.5
Data Axis
Normal Curve with Mean 5 and Standard Deviation 6
The Area to the Right of 2 is 0.6915
0.0
Data Axis
2.5
5.0
Normal Curve with Mean 0 and Standard Deviation 1
The Area to the Right of -0.5 is 0.6915
0.4
Density
Density
0.050
0.025
0.000
-20
0
0.2
0.0
20
-5.0
-2.5
Data Axis
Normal Curve with Mean 5 and Standard Deviation 6
The Area Between 3 and 6 is 0.1967
0.0
Data Axis
2.5
5.0
Normal Curve with Mean 0 and Standard Deviation 1
The Area Between -0.33 and 0.17 is 0.1968
0.4
Density
Density
0.050
0.025
0.000
-20
0
20
Data Axis
0.2
0.0
-5.0
-2.5
0.0
Data Axis
2.5
5.0
3
Area.doc 4/5/06
Documentation for ChiAreaC and ChiAreaA
Input for ChiAreaC – Material in worksheet ChiEx1
#C1 contains degrees of freedom, C2 contains zero
#C3 contains lower limits of intervals, C4 contains upper limits of intervals
#C5 contains 0 if Area is between points in C3 and C4
#C5 contains 1 if Area is to the left of point in c4
#C6 contains 2 if Area is to the right of point in C3
So the first row below asks for a ChiSquare curve with 4 degrees of freedom and the area between -4 and
+4. The second line asks for the area to the left of 20.4832 when there are 10 DF.
Row
1
2
3
4
5
C1
4
10
10
10
50
C2
0
0
0
0
0
C3
-4.0000
3.2470
3.2470
3.2470
27.9907
C4
4.0000
20.4832
20.4832
20.4832
79.4896
C5
0
1
2
0
0
Graphs Follow.
ChiSquared Curve with 4 Degrees of Freedom and Standard Deviation 2.82843
The Area Between -4 and 4 is 0.5940
ChiSquare Curve with 10 Degrees of Freedom and Standard Deviation 4.47214
The Area to the Left of 20.4832 is 0.9750
0.10
Density
Density
0.2
0.1
0.0
0
6
12
Data Axis
18
0.00
24
ChiSquare Curve with 10 Degrees of Freedom and Standard Deviation 4.47214
The Area to the Right of 3.247 is 0.9750
10
20
Data Axis
30
40
0.10
Density
Density
0
ChiSquared Curve with 10 Degrees of Freedom and Standard Deviation 4.47214
The Area Between 3.247 and 20.4832 is 0.9500
0.10
0.05
0.00
0.05
0
10
20
Data Axis
30
40
0.05
0.00
0
10
20
Data Axis
30
40
ChiSquared Curve with 50 Degrees of Freedom and Standard Deviation 10
The Area Between 27.9907 and 79.4896 is 0.9900
Density
0.04
0.02
0.00
20
40
60
Data Axis
80
100
Computer Output for this Worksheet follows.
————— 1/28/2005 7:22:02 PM ————————————————————
Welcome to Minitab, press F1 for help.
Results for: ChiEx1.MTW
MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\ChiEx1.MTW";
SUBC>
Replace.
4
Area.doc 4/5/06
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\ChiEx1.MTW'
Existing file replaced.
MTB > %ChiAreac
Executing from file: ChiAreac.MAC
Executing from file: ChiArea.MAC
...working...
Chi Squared Curve Area
Data Display
mode
median
2.00000
3.33333
...working...
Chi Squared Curve Area
Data Display
mode
median
8.00000
9.33333
...working...
ChiSquare Curve Area
Data Display
mode
median
8.00000
9.33333
...working...
Chi Squared Curve Area
Data Display
mode
median
8.00000
9.33333
...working...
Chi Squared Curve Area
Data Display
mode
median
48.0000
49.3333
MTB >
5
Area.doc 4/5/06
Input for ChiAreaA – There is no input prepared for this version because the program requests the
information from you. The nonsense worksheet ‘notmuch’ was found and used to orient Minitab as to
where the Macros were.
Output for ChiAreaA
ChiSquared Curve with 20 Degrees of Freedom and Standard Deviation 6.32456
The Area Between 10 and 15 is 0.1918
0.07
0.06
Density
0.05
0.04
0.03
0.02
0.01
0.00
0
10
20
30
Data Axis
40
50
Computer Output for this Macro follows.
————— 1/28/2005 8:23:44 PM ————————————————————
Welcome to Minitab, press F1 for help.
Results for: notmuch.MTW
MTB > %ChiAreaA
Executing from file: ChiAreaA.MAC
Graphic display of chi square curve areas
Finds and displays areas to the left or right of a given value
or between two values. (This macro uses C100-C116 and K100-K120)
Enter the degrees of freedom.
DATA> 20
Do you want the area to the left of a value? (Y or N)
n
Do you want the area to the right of a value? (Y or N)
n
6
Area.doc 4/5/06
Enter the two values for which you want the area between.
DATA> 10
DATA> 15
...working...
Chi Squared Curve Area
Data Display
mode
median
18.0000
19.3333
7
Area.doc 4/5/06
Documentation for tAreaC and tAreaA
Input for tAreaC – Material in worksheet tEx1
#C1 contains degrees of freedom, C2 contains zero
#C3 contains lower limits of intervals, C4 contains upper limits of intervals
#C5 contains 0 if Area is between points in C3 and C4
#C5 contains 1 if Area is to the left of point in c4
#C6 contains 2 if Area is to the right of point in C3
So the first row below asks for a t curve with 41 degrees of freedom and the area between -1.303 and
+1.303. The second line asks for the area to the left of 1.303 when there are 10 DF.
Row
1
2
3
4
5
C1
41
41
41
120
4
C2
0
0
0
0
0
C3
-1.303
-1.303
-1.303
-0.677
-3.747
C4
1.303
1.303
1.303
0.677
3.747
C5
0
1
2
0
0
Graphs Follow.
t Curve with 41 Degrees of Freedom and Standard Deviation 1.02532
The Area Between -1.303 and 1.303 is 0.8002
t Curve with 41 Degrees of Freedom and Standard Deviation 1.02532
The Area to the Left of 1.303 is 0.9001
0.4
Density
Density
0.4
0.2
0.0
-5.0
-2.5
0.0
Data Axis
2.5
0.2
0.0
5.0
t Curve with 41 Degrees of Freedom and Standard Deviation 1.02532
The Area to the Right of -1.303 is 0.9001
0.0
Data Axis
2.5
5.0
0.4
Density
Density
-2.5
t Curve with 120 Degrees of Freedom and Standard Deviation 1.00844
The Area Between -0.677 and 0.677 is 0.5003
0.4
0.2
0.0
-5.0
-5.0
-2.5
0.0
Data Axis
2.5
5.0
0.2
0.0
-4
-2
0
Data Axis
2
4
t Curve with 4 Degrees of Freedom and Standard Deviation 1.41421
The Area Between -3.747 and 3.747 is 0.9800
Density
0.4
0.2
0.0
-10
-5
0
Data Axis
5
10
Computer Output for this Worksheet follows.
————— 1/28/2005 9:41:47 PM ————————————————————
Welcome to Minitab, press F1 for help.
Results for: tEx1.MTW
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\tEx1.MTW".
8
Area.doc 4/5/06
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\tEx1.MTW'
Worksheet was saved on Fri Jan 28 2005
MTB > %tAreaC
Executing from file: tAreaC.MAC
Executing from file: tArea.MAC
...working...
t Area
Data Display
mode
median
0
0
...working...
t Curve Area
Data Display
mode
median
0
0
...working...
t Curve Area
Data Display
mode
median
0
0
...working...
t Area
Data Display
mode
median
0
0
...working...
t Area
Data Display
mode
median
0
0
9
Area.doc 4/5/06
Input for tAreaA – There is no input prepared for this version because the program requests the
information from you. The previous worksheet was left alone and used to orient Minitab as to where the
Macros were.
Output for tAreaA
MTB > %tAreaA
Executing from file: tAreaA.MAC
Graphic display of t curve areas
Finds and displays areas to the left or right of a given value
or between two values. (This macro uses C100-C116 and K100-K120)
Enter the degrees of freedom.
DATA> 21
Do you want the area to the left of a value? (Y or N)
n
Do you want the area to the right of a value? (Y or N)
n
Enter the two values for which you want the area between.
DATA> -2.831
DATA> -0.127
...working...
t Area
Data Display
mode
median
0
0
MTB >
10
Area.doc 4/5/06
t Curve with 21 Degrees of Freedom and Standard Deviation 1.05131
The Area Between -2.831 and -0.127 is 0.4451
0.4
Density
0.3
0.2
0.1
0.0
-5.0
-2.5
0.0
Data Axis
2.5
5.0
11
Area.doc 4/5/06
Documentation for FAreaC and FAreaA
Input for FAreaC – Material in worksheet FEx1
#C1 contains degrees of freedom for numerator
#C2 contains degrees of freedom for denominator – because of the variance formula that is used here,
degrees of freedom for the denominator must be above 4.
#C3 contains lower limits of intervals, C4 contains upper limits of intervals
#C5 contains 0 if Area is between points in C3 and C4
#C5 contains 1 if Area is to the left of point in c4
#C6 contains 2 if Area is to the right of point in C3
So the first line of input below is asking for the probability between 1.5 and 3.62 for an F distribution with
3 and 5 degrees of freedom.
Row
1
2
3
4
5
6
7
C1
3
3
4
50
50
50
50
C2
5
5
5
60
5
60
50
C3
1.50000
1.50000
3.62000
0.00000
6.14000
1.56000
0.69444
C4
3.62
3.62
5.00
1.56
6.00
6.00
1.44
C5
0
1
2
1
2
2
0
Graphs Follow
F Curve with Numerator DF of 3 Denominator DF of 5
The Area to the Left of 3.62 is 0.9000
0.50
Density
Density
F Curve with numerator DF of 3 Denominator DF of 3.33333
The Area Between 1.5 and 3.62 is 0.2222
0.25
0.00
0
20
40
Data Axis
60
0.50
0.25
0.00
80
0
20
F Curve with numerator DF of 4 and Denominator DF of 5
The Area to the Ri ght of 3.62 is 0.0954
40
Data Axis
60
80
F Curve with Numerator DF of 50 Denominator DF of 60
The Area to the Left of 1.56 is 0.9502
0.50
Density
Density
1.6
0.25
0.00
0
20
40
Data Axis
60
0.8
0.0
80
0.5
F Curve with numerator DF of 50 and Denominator DF of 5
The Area to the Ri ght of 6.14 is 0.0250
1.5
Data Axis
2.0
2.5
F Curve with numerator DF of 50 and Denominator DF of 60
The Area to the Right of 1.56 i s 0.0498
1.6
Density
0.8
Density
1.0
0.4
0.0
0
15
30
Data Axis
45
0.8
0.0
60
0.5
1.0
1.5
Data Axis
2.0
2.5
F Curve with numerator DF of 50 Denominator DF of 0.304084
The Area Between 0.69444 and 1.44 i s 0.7992
Density
1.6
0.8
0.0
0
1
2
3
Data Axis
Computer Output for this Worksheet follows.
————— 1/29/2005 1:17:58 AM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\FEx1.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\FEx1.MTW'
12
Area.doc 4/5/06
Worksheet was saved on Sat Jan 29 2005
Results for: FEx1.MTW
MTB > %FAreaC
Executing from file: FAreaC.MAC
Executing from file: FArea.MAC
...working...
F Curve Area
Data Display
mode
0.555556
Data Display
std dev
3.33333
...working...
F Curve Area
Data Display
mode
0.555556
Data Display
std dev
3.33333
...working...
F Curve Area
Data Display
mode
0.625000
Data Display
std dev
3.11805
...working...
F Curve Area
Data Display
mode
0.963934
Data Display
std dev
0.287323
...working...
F Curve Area
Data Display
mode
0.816667
Data Display
std dev
2.42670
13
Area.doc 4/5/06
...working...
F Curve Area
Data Display
mode
0.963934
Data Display
std dev
0.287323
...working...
F Curve Area
Data Display
mode
0.960784
Data Display
std dev
0.304084
14
Area.doc 4/5/06
Input for FAreaA – There is no input prepared for this version because the program requests the
information from you. The nonsense worksheet ‘notmuch’ was found and used to orient Minitab as to
where the Macros were.
Output for FAreaA
F Curve with Numerator DF of 40 Denominator DF of 22
The Area to the Left of 2.58 is 0.9899
1.2
1.0
Density
0.8
0.6
0.4
0.2
0.0
0
1
2
3
4
5
Data Axis
————— 1/29/2005 1:48:26 AM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\notmuch.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\notmuch.MTW'
Worksheet was saved on Fri Jan 21 2005
Results for: notmuch.MTW
MTB > %FAreaA
Executing from file: FAreaA.MAC
Graphic display of F curve areas
Finds and displays areas to the left or right of a given value
or between two values. (This macro uses C100-C116 and K100-K120)
Enter the degrees of freedom.DF2 must be above 4.
DATA> 40
DATA> 22
Do you want the area to the left of a value? (Y or N)
y
Enter the value for which you want the area to the left.
15
Area.doc 4/5/06
DATA> 2.58
...working...
F Curve Area
Data Display
mode
0.932609
Data Display
std dev
0.449073
Copies of the Routines
The routines and the worksheets are available in http://courses.wcupa.edu/rbove/Minitab/. They are
probably easiest to download in .txt format. Either convert them back to .mac using Notepad or change all
references to macros by adding .txt to the macro. For example, instead of using %FAreaA, use
%FAreaA.txt. There is also a printable copy at http://courses.wcupa.edu/rbove/Minitab/AreaRoutines.doc.
16