เอกสารเผยแพรเพอการศกษารวมฉลอง 100 ป
การวเคราะหขอมลทางสถต
ดวยโปรแกรมสาเรจรป
Instat
รองศาสตราจารย ดารงค ทพยโยธา
ภาควชาคณตศาสตรและวทยาการคอมพวเตอร
คณะวทยาศาสตร จฬาลงกรณมหาวทยาลย
การคานวณคาสถตเบองตนการนาเสนอขอมลดวยตารางและกราฟการหาชวงความเชอม นของคาพารามเตอรการทดสอบสมมตฐานการหาสมประสทธการถดถอยและสหสมพนธการวเคราะหความแปรปรวน
รองศาสตรจารย ดารงค ทพยโยธาภาควชาคณตศาสตรและวทยาการคอมพวเตอร คณะวทยาศาสตร จฬาลงกรณมหาวทยาลย
Download Instat at http://www.rdg.ac.uk/ssc
Statistical Software Instat
การวเคราะหขอมลทางสถตดวยโปรแกรมสาเรจรป
Instat Functions
CALculate
CAL
CALculate LHS = RHS
CAL LHS = RHS
LHS = RHS
X1
?
+, - , *, /, ^?
, , , ,
SQR
EXP
LN
LOG
SQR(X) = X
EXP(X) = Xe
LN(X) = n X
LOG(X) = og(X)
PI
SIN
COS
TAN
PI =
ACS
ASN
ATNACS = arccos, ASN = arcsin
ATN = arctan
ABS
INT
SGN
ABS(X) = X
INT(X) = [ X ]
SGN(X) = signum(X)
RND(1)
RND(X)
RND(1) 1
RND(X) X
FAC
COM
PER
FAC(n) = n!
COM(r, n) = )!rn(!r!n
PER(r, n) = !r!n
ACC ACC 5
ACC n
n
Instathttp://www.rdg.ac.uk/ssc
Download data : http://pioneer.netserv.chula.ac.th/~tdumrong/instatdata
Instat
1 . . 2552
Instat . - - :
, 2551.
160
1. ( ) . 2. - - . I .
.
005.55
ISBN 978-974-03-2371-6
10330
. 0-2218-7000-3 0-2255-4441
. 0-2218-9881 0-2254-9495
. . . 0-5526-0162-5 0-5526-0165
. . . 0-4421-6131-4 0-4421-6135
. . . 0-3839-4855-9 0-3839-3239
. . . 0-3739-3023 0-3739-3023
(CHAMCHURI SQUARE) 4 . 0-2160-5300-1 0-2160-5304
Call Center 0-2255-4433 http://www.chulabook.com
email : [email protected]
. . . 0-5391-7020-4 0-5391-7025
. . . 0-5526-7010 0-5521-6388
. . . 0-7567-3648-51 0-7567-3652
. . 0-7521-8115 0-7521-8115
( ) . 43/1 . 0-2538-2573 0-2539-7091
14 . 0-2218-9889-90 0-2254-9495
. 0-2218-3557, 0-2218-3563
http://www.cuprint.chula.ac.th
Instat
Instat
1 2
Instat
-
-
-
-
-
-
Instat
1.
Instat
Instat
Download Website
http://www.rdg.ac.uk/ssc
http://www.rdg.ac.uk/ssc/software/instat/instat.html
Download
Website
http://pioneer.netserv.chula.ac.th/~tdumrong/instatdata
Window in Instat
Window
Window Current Worksheet
1. *.wor
2. Graphs, Statistics
3. F11
4. F2 Window
Current Worksheet Window Commands and
Output
Window Commands and Output
1.
2. Output *.out
3.
4. Copy
Word
5. Output File
Edit View/Edit Text Open
Output File *.out
6.
Window Graphs
1. *.igt
2. Load File Load graph
Graphics Load graph
3.
4. Word
Copy
Word Paste
Window Table
1. *.itb
2. Window graph
Window Current Worksheet
3. Load File Load Table
Statistics Tables Load Table
4. Save File Save
( Window Table )
1 1 - 24
1.1 Instat 1
1.2 2
1.3 2 5
1.4 Two data Columns 6
1.5 Factor 7
1.6 9
2 25 - 48
2.1 Statistics Summary Describe 26
2.2 Statistics Summary Column Statistics 32
2.3 Statistics Summary Group 34
2.4 Statistics Tables Frequency 36
2.5 Statistics Tables Summary 38
2.6 Statistics Tables General 40
2.7 Graphics 42
3 49 - 68
3.1 49
3.2 55
3.3 65
4 69 - 96
4.1 0H : = 0 69
4.2 0H : 1 = 2 2 73
4.3 0H : D = 0d 2 82
4.4 0H : 2 = 20 87
4.5 0H : 21 = 2
2 90
4.6 0H : p = 0p 93
4.7 0H : 1p - 2p = 0p ( 1p 2p ) 95
5 97 - 112
5.1 97
5.2 105
6 113 - 132
6.1 113
6.2 %100)1(
122
6.3 0H : = 0 125
6.4 0H : = 0 128
7 133 - 146
7.1
(One-Way ANOVA, Simple-Factor ANOVA) 133
7.2
(Randomized Complete Block Designs, Mutiple-Factor ANOVA) 139
1 Window Commands and Output 147 - 148
2 Instat macro programing Instat 149 - 150
3 Instat Log File 151 - 152
4 Word Excel Instat 153 - 154
1
1.1 Instat Instat
1. Icon
Start / All Programs
2. Instat Logo Instat
1 2
Instat
Instat
1. Instat+ for Windows Instat
2. Command menu bar
3. Current Worksheet Window Current Worksheet
4. UNTITLED.WOR
5. Commands and Output Window
F2 Window Current Worksheet
Window Commands and Output
6.
7. Instat X1, X2, X3, ...
8. Instat id, sex, age, ...
9. 1, 2, 3, ... 10.
1.2
1. Instat X1 x
2. 5 2, 3, 7, 5, 12
3. example001.wor
4.
1 3
1. 1 x
2.
2
2, 3, 7, 5, 12
Enter
X1 Instat
x
3. 3
File
4. Save Save Worksheet As
1. Excel
2. copy
Word Excel
4
1 4
5. 4 example001 ( wor )
5 example001.wor
6. 6 Statistics
7. 7 Summary Describe
Descriptive Statistics
1.
Instat
directory
InstatWorking
2. directory
directory
1 5
8. 8
X1
Available data
9. OK Window Commands and Output
1.3 2 1 : 12, 15, 23, 34, 42, 55 X1(sample1)
2 : 18, 29, 44, 35, 65, 72, 84, 89 X2(sample2)
2
1. X1(sample1) X2(sample2)
1.
(*.out)
2. 35
3. Copy
Word
4. DES
Window Commands and Output
1 6
X1, X2 Instat
sample1, sample2
2. X2(data) X1-F(code)
X1-F Data Factor ( Instat
Factor )
X2 Instat
code
data
1.4 Two data Columns 1. Instat
Window Current Worksheet
2. 1
sample1 sample 2
1 7
1.5 Factor 1. Instat Window Current Worksheet
2. 1 code data
code 1 1
2 2 data
2 X1 Factor
Factor -F
3. Manage Column Properties Factor
1 8
4. Factor Make or modify a factor column
1. Data column X1(code)
2. Number of levels (
1.6)
5. OK
1 X1 X1-F Factor
1. 2
2. 2 columns Two data columns
3.
Data columns and Two Factor levels
1. Number of levels Instat
2. Attach to existing lebel column
Labels
3. Attach to new lebel column
lebel
4. Generate new label column from
data lebel
5.
Factor Option Make
factor into an ordinary variable
factor
1 9
1.6
Instat
1. ........................
2.
3. ................................
4.
5.
6. ...........................................
7. ..........................
8. ............................
Instat
(file name) Instat (Instat variable name)
(User variable label) (missing value)
(value label Factor)
example4.wor
1. Instat X1
id
2. Instat X2
sex
-9
1 Male 2 Female
1 10
3. Instat X3
age
-99
4. Instat X4
educ
-9
1 Under_gr 2 Graduate 3 Post_gr 4 Doctor
5. Instat X5
status
-9
1 Single 2 Married 3 Widow 4 Divorced
6. Instat X6
income
2
-9999
7. Instat X7
grade
2
8. Instat X8
bonus
2
-999
1.
2. 1 2
-9
1 11
3.
-99
4. 1
2
3
4
-9
5. 1
2
3
4
-9
6.
-999
7.
8.
-999
1. 1
2.
3. 37
4.
5.
6. 5500
7. 3.78
8. 11000
Window Current Worksheet
1. Instat X1, X2, .... , X8 column Current WorkSheet
2. id, sex, age, educ, status, income, grade, bonus
1
2
4
1 12
3.
4. (Missing value)
5. (Value label)
1. Instat
Instat File New Worksheet ( Ctrl + N)
2. Window Current Worksheet
3. 1 id, sex, age, educ, status, income, grade, bonus
4. 50
id sex age educ status income grade bonus1 1 37 2 4 5500 3.78 110002 2 29 3 1 4100 3.89 123003 2 48 1 2 5400 3.67 216004 1 -99 1 2 -999 2.78 199985 2 33 2 -9 -999 3.00 299976 2 45 3 4 8300 3.45 166007 2 38 1 4 7700 3.89 77008 2 23 3 1 3900 3.67 117009 1 34 2 4 4500 2.56 9000
10 1 50 2 2 6700 2.69 670011 2 43 2 2 4700 3.56 1880012 2 37 3 2 3900 3.00 390013 1 24 2 1 3300 2.45 990014 1 46 2 2 4900 2.45 1470015 1 32 1 1 4000 3.87 800016 1 42 2 3 6600 3.67 1320017 1 38 4 2 8000 3.23 32000
1 13
18 2 41 2 3 7000 3.45 2100019 2 -99 1 -9 2000 3.21 200020 1 54 2 2 7400 3.00 2220021 2 32 3 -9 6200 2.56 2480022 1 43 1 2 4700 2.45 1880023 2 22 1 1 3400 3.78 340024 1 40 2 2 5900 2.67 1770025 1 37 4 -9 7500 3.45 2250026 1 28 1 1 3100 2.78 930027 1 44 3 2 6800 2.56 1360028 1 56 2 2 6400 2.78 1920029 1 35 3 1 5800 3.33 580030 2 42 1 2 3900 2.56 1170031 1 21 2 1 4700 2.67 1410032 1 39 2 2 5900 2.89 1770033 1 45 1 2 4900 2.56 490034 1 31 1 2 3100 3.23 930035 1 51 2 3 5400 3.01 540036 1 23 3 1 6300 2.77 1260037 1 40 3 2 7100 2.89 2130038 1 47 2 3 6600 2.77 1980036 1 53 2 2 7200 2.31 2160040 2 27 2 1 1700 2.67 510041 1 29 4 1 5000 2.89 1500042 1 40 3 2 6000 3.67 1800043 2 30 1 1 3000 2.56 1200044 2 53 2 2 4700 3.00 940045 1 31 1 1 2800 2.74 560046 1 45 2 2 5700 2.67 2280047 1 22 2 4 4300 3.07 430048 2 34 1 1 3900 2.56 780049 2 33 3 2 6700 2.12 2010050 1 54 2 2 4800 2.66 19200
50 data_001.wor
1 14
5. Missing value
Manage Resize Worksheet
6. Resize Worksheet Worksheet sizes
1. 1 -9
2. 2 -99
3. 3 -999
7. OK
1. Missing value -9 *
2. Missing value -99 **
3. Missing value -999 ***
1 15
Value label sex, educ, status
8. Labels ( 1)
Label
9. Label
Column L1 Male, Female
Column L2 Under_gr, Graduate, Post_gr, Doctor
Column L3
Single, Married, Widow, Divorce
1 16
Label sex
10.
Manage Column Properties Factor
11. Factor
Make or modify a factor column
12. 1.
2.
Data column
3. Instat
Option : Number of levels = 2
1. Number of levels Instat
2. Attach to existing lebel column
Labels
3. Attach to new lebel column
lebel
4. Generate new label column from
data lebel
5.
Factor Option Make
factor into an ordinary variable
factor
1 17
13. 1. Option : Attach to existing label column
2. L1 Label
3. Label Column L1 Male
Female
14. OK
1. 1 Male 2 Female
2. X2 -F Factor value label
Label educ
15. Manage Column Properties Factor
1 18
16. Factor Make or modify a factor column
1. X4(educ)
2. Instat Option : Number of levels = 4
3. Option : Attach to existing label column
4. L2 Label column L2
5. Label Column L2 Under_gr, Graduate, Post_gr, Doctor
17. OK
1. 1 Under_gr 2 Graduate
3 Post_gr 4 Doctor
2. X4 -F Factor value label
1 19
Label status
18. Manage Column Properties Factor
19. Factor Make or modify a factor column
1. X5(status)
2. Instat Option : Number of levels = 4
3. Option : Attach to existing label column
4. L3 Label column L3
5. Label Column L3 Single, Married, Widow, Divorce
1 20
20. OK
1. 1 Single 2 Married
3 Widow 4 Divorce
2. X5 -F Factor value label
1. Label
1. Manage Column Properties Factor
Make or Modify a factor column
2. Label Data column
3. Option : Make factor into an ordinary variable
2. (ordinary variable) Factor
Option : Detach label column
1 21
21. Manage Column Properties Format
22. Format Format data
X6(income) 2
1. X6
2. 0.00
3. Required format
0.00
23. OK
income 2
1 22
24. Manage Column Properties Format
Format Format data
X7(grade) X8(bonus) 2
1. X7, X8
2. 0.00
3. Required format 0.00
25. OK
grade bonus 2
Format 0.00 grade 5 3
Format 0.00 grade 5 3.00
1 23
26. Manage Worksheet Information
27. Worksheet Information
1. 2. directory
3. Label 3 4. 8
28. Option Columns
1. Column X1, X2, X3, ...
2.
Name id, sex, age, ...
3.
Vaiable Label
Factor Label
1 24
1. Window Current Worksheet File
2. Save Save as data_002
3. Save
1. File Open Worksheet
2. Open Worksheet Open file for input
3. Open
1.
Instat
directory
InstatWorking
2. directory
directory
2
1 2 Instat
1. Statistics Summary Describe
1 3
Stem and Leaf, Boxplot, Cumulative frequency
2. Statistics Summary Column Statistics
3. Statistics Summary Group
4. Statistics Tables Frequency 1 2
5. Statistics Tables Summary
6. Statistics Tables General
7. Graphics Plot
8. Graphics Boxplot Box Plot
9. Graphics Histogram Histogram
10. Graphics Frequency Chart
11. Graphics Stem and Leaf
2 26
2.1 Statistics Summary Describe Statistics Summary Describe
1. example005.wor Window Current Worksheet
2. Statistics Summary Describe
3. Describe Descriptive Statistics
1. X3
2. Instat
2 27
4. OK Window Commands and Output
1.
2. DES X3 Instat
DES X3 Window Commands and Output
3. age
4.
No. of observations 50 50
No. not missing 48 48 2
Minimum 21
Maximum 56
Range 35 = max - min
Mean 37.938
Std. deviation 9.5526
Std. deviation 1n
)xx( 2i
n
1 i
Statistics Summary Describe
(Additional statistics) 1 3
Stem and Leaf, Boxplot, Cumulative frequency
2 28
Descriptives Statistics
4. (Additional statistics)
3. Descriptive Statistics
1. Additional statistics
2. Additional statistics
Standard error, Median, Quartiles
5.
1. Percentiles
2. Percentiles
45P 90P 45 90 ( comma 45, 90)
Instat
2 29
6. 1. Proportions
2. Proportions
25 25
3. 25
4.
7.
1. 4 Precision 4
2. Kg, mm, inch Unit
3.
4. Graphics
Check box
Stem and Leaf, Boxplot
Cumulative frequency
2 30
8. OK
1. Title
2. Instat Window Commands and Output
3. Statistics Summary Describe
4. Additional statistics 1 3
5. 45 90
6. 25
7. 25
12.5% 48
8.
4
STEM & LEAF
2 31
Stem and Leaf
1. = 21 = 56 48 ( Missing data )
2. 5 : 6 6 56 1
3. 20 - 24 6 21, 22, 22, 23, 23, 24
25 - 29 10 - 6 = 4 27, 28, 29, 29
:
35 - 39 7 35, 37, 37, 37, 38, 38, 39
:
50 - 54 7 - 1 = 6 50, 51, 53, 53, 54, 54
55 - 59 1 56
Box Plot
1. = 21
2. 1. = 31
3. = 38
4. 3. = 45
5. = 56
6.
Cumulative frequency
1. Copy Word
CTRL+C
Word Paste
2.
2 32
2.2 Statistics Summary Column Statistics Statistics Summary Column Statistics
1.
example005.wor
Window
Current Worksheet
2. Statistics Summary Column Statistics
3. Column Statistics Column Statistics
1. X3
2. Count, Mean, St. dev, Median Percentiles 50
4.
OK
2 33
5. Column Statistics
1. By factor
2. X4(educ)
1.
Factor
2. For factor
4. OK
1. For factor 2. X4(educ) 3. Under_gr
OK
2 34
2.3 Statistics Summary Group Statistics Summary Group
1. example005.wor Window Current Worksheet
2. Statistics Summary Group
3. Group Grouped Frequency Distribution
1. X3
2. Display percentages
2 35
4.
OK
1. Window Commands and Output File Save Save as
Save Commands and Output As
( .out ) Save
2.
Window Current Worksheet Window Commands and Output
Edit View/Edit Text Open
Open Text File for Editing Open
2 36
2.4 Statistics Tables Frequency Statistics Tables Frequency 1 2
1.
example005.wor
Window
Current Worksheet
2. Statistics Tables Frequency
3. Frequency Frequency Tables
1. X4
4. OK
1. Window ( )
2. File Save Save as ( .itb ) Save
3.
3.1 Current Worksheet Statistics Tables Load Table
3.2 Window Table ( ) File Load Table
4. ( )
2 37
2
5. 3.
Frequency Tables
1. X2, X4 Factors
6. OK 2
2 sex, educ, status
X2, X4, X5 Factors
2 38
2.5 Statistics Tables Summary Statistics Tables Summary
1. example005.wor Window Current Worksheet
2. Statistics Tables Summary
3. Summary Summary Tables
1. X5 status
2. X3 age
3. Means, Medians, St. Deviations
2 39
4. OK
X5, X4 Factors
OK
2 40
2.6 Statistics Tables General Statistics Tables General
1.
example005.wor
Window
Current Worksheet
2. Statistics Tables General
3. General General tables
1. X2, X5
2 sex, status
2. X6 income
3. Averages
4. Add Statistic
5.
Means(4;0;;X6;)
Add Statistic
3., 4. 5.
2 41
4. OK
(Male Single) = 4375.0
(Female Single) = 3333.3
(All, Single) = 3928.6
X2, X5, X4 Factors
(Male, Single, Under_gr) = 3300
2 42
2.7 Graphics2.7.1 Graphics Plot
Graphics Plot
1.
example005.wor
Window
Current Worksheet
2. Graphics Plot
3. Plot Plot
1. X6 income Y
2. X3 age X
4. OK
2 43
2.7.2 Graphics Boxplot
5. Graphics Boxplot
6. Boxplot BoxPlot
1. X3 Data to be ploted
7. OK
1. Window Save
( )
File Save Save as
Save Graph As ( .igt ) Save
2.
2.1 Window Current Worksheet Window Commands and Output
Graphics Load Graph Open
2.2 Window ( )
File Load Graph
Graph Open
3. ( )
2 44
2.7.3 Graphics Histogram
5. Graphics Histogram
6. Histogram Histogram
1. X3 Variable to plot age
2.
3. 5
7. OK
2 45
8. Graphics Histogram Histogram Histogram
1. X3 Variable to plot age
2. 10
9. OK
1. Options
2.
2 46
2.7.4 Graphics Frequency Chart
10.
Graphics Frequency Chart
11.
Frequency Chart Frequency Chart
1. X4 Variable to plot educ
2. Bar
(Chart type) 4 (Bar) (Hbar)
(Pie) (Line)
12. OK
(Pie)
2 47
13. Graphics Frequency Chart Frequency Chart
Frequency Chart
1. X4(educ) educ
2. Option : Cluster by
3. Option : Cluster by
Factor X2(sex)
X2(sex)
14. OK
2 48
2.7.5 Graphics Stem and Leaf
15. Graphics Stem and Leaf
16. Stem and Leaf Stem and Leaf
1. X3 Data to be displayed age
17. OK
1. = 21 = 56 48 ( Missing data )
2. 5 : 6 6 56 1
3. 20 - 24 6 21, 22, 22, 23, 23, 24
25 - 29 10 - 6 = 4 27, 28, 29, 29
:
35 - 39 7 35, 37, 37, 37, 38, 38, 39
:
50 - 54 7 - 1 = 6 50, 51, 53, 53, 54, 54
55 - 59 1 56
3
3.1 %100)1(
1. 2
n x
%100)1( x - 2
zn
x + 2
zn
2. 2
n x 2s
2.1 n 30 %100)1(
x - 2
zns x +
2z
ns
2.2 n 30 %100)1(
x - 2
tns x +
2t
ns = n - 1
3. 2
n 30 x
%100)1( x - 2
zn
x + 2
zn
4. 2
n 30 x 2s
2 2s
%100)1( x - 2
zn
x + 2
zn
3 50
%100)1( 2
2
2
2s)1n( 2 2
2 1
2s)1n( = n - 1
3.1.1 2 = 1600
829.5 790.6 829.9 780.0 750.7 810.2 717.8 786.3 835.8 739.0770.1 722.8 804.4 786.9 732.5 823.7 726.6 725.6 799.8 801.4765.5 720.5 811.0 829.2 810.1
25 780
95%
2 = 1600
n = 25 x = 780
95%
x - 025.0zn
x + 025.0zn
780 - 1.9625
40 780 + 1.9625
40
764.32 795.68
95% (764.32, 795.68)
%100)1( Instat
1.
1
x 25
example6.wor
2. Statistics Simple Models Normal, One Sample
3 51
3. Normal, One Sample
Simple Models - Normal Distribution, One Sample
1. Single data column
2. 5
3. z, t F 6
- t
- z ( s )
- 2
4.
3 52
4. Simple Models - Normal Distribution, One Sample
1. Single data column
2. X1 X1(x)
3. Mean, known variance (z-interval)
4. Mean, known variance (z-interval) St. Dev Variance
5. 95%
5.
OK
95% (764.32, 795.68)
1. ZInt 'x' ; sde 40 Window Commands and Output
2. 95% = 41
ZInt 'x' ; sde 41 Window Commands and Output
3 53
4.
4. Simple Models - Normal Distribution, One Sample
1. Single data column
2. X1 X1(x)
3. Mean (t-interval)
4. 95%
5.
OK
95% (763.48, 796.51)
1. TINt 'x' Window Commands and Output
2. 8 ACC 8 Window
Commands and Output
3 54
95% (763.48, 796.51)
x - 2
tns x +
2t
ns = n - 1
= 0.05, 2 = 0.025, = 25 - 1 = 24, 24 , 0.025t = 2.064, x = 780, s = 40.002
95% x - 2
tns x +
2t
ns
780 - 2.06425002.40 780 + 2.064
25002.40
780 - 16.5128256 780 + 16.5128256
763.4871744 796.5128256
%100)1( 4.
4. Simple Models - Normal Distribution, One Sample
1. Single data column 2. X1
3. Variance (F-interval) 4. 95%
5.
OK
3 55
95% (31.234, 55.649) 95% (975.58, 3096.8)
95% (975.58, 3096.8)
2
2
2s)1n( 2 2
21
2s)1n( = n - 1
n = 25, = 0.05, 2 = 0.025, = 24, 2025.0 = 39.364, 2
975.0 = 12.401, 2s = 1600.2
95% 2 2
2
2s)1n( 2 2
21
2s)1n(
364.39)2.1600)(24( 2 401.12
)2.1600)(24( 975.6 2 3096.9
3.23.2.1 %100)1( 1 - 2
21. 1n 30 2n 30 1.1 2 2
1 22
%100)1( 1 - 2
( 1x - 2x ) - 2
z2
22
1
21
nn 1 - 2 ( 1x - 2x ) + 2
z2
22
1
21
nn
1.2. 2 21 2
2 2
1s , 22s 2
1 , 22 2
1s , 22s
%100)1( 1 - 2
( 1x - 2x ) - 2
z2
22
1
21
ns
ns 1 - 2 ( 1x - 2x ) +
2z
2
22
1
21
ns
ns
2. 1n 30 2n 30 2.1 2 2
1 22
%100)1( 1 - 2
( 1x - 2x ) - 2
z2
22
1
21
nn 1 - 2 ( 1x - 2x ) + 2
z2
22
1
21
nn
2.2 2 21 2
2 2
1s 22s
2.2.1 21 = 2
2 %100)1( 1 - 2
( 1x - 2x ) - 2t Ps
21 n1
n1 1 - 2 ( 1x - 2x ) +
2t Ps
21 n1
n1
3 56
2Ps = 2nn
s)1n(s)1n(
21
222
211 = 1n + 2n - 2
2.2.2 21 2
2 %100)1( 1 - 2
( 1x - 2x ) - 2
t2
22
1
21
ns
ns
1 - 2 ( 1x - 2x ) + 2
t2
22
1
21
ns
ns
=
)1n(1)n
s()1n(
1)ns
(
)ns
ns
(
22
2
22
12
1
21
22
22
1
21
3.2.1 2
1n = 9 1
61.36 57.76 71.94 61.77 58.66 71.61 71.52 58.67 62.77
2n = 16 2
56.92 58.30 67.48 53.96 62.00 59.61 52.02 61.6064.83 58.55 52.53 64.74 55.51 66.18 55.51 54.18
95% 1 - 2
Instat
1.
2 data1, data2
example7.wor
2. Statistics Simple Models Normal, Two Samples
3 57
3. Normal, Two Samples
Simple Models - Normal Distribution, Two Samples
1.
1.1 Two data columns 2
1.2 Data columns and two factor levels 2
1 (Factor variable)
1
3. 7
3. z, t F 6
- t
- z
- F
4.
3 58
5.
5.1 2
5.2 2
4. Simple Models - Normal Distribution, Two Samples
1. Two data columns
2. Data Column X1(data1)
2nd Data Column X2(data2)
3. Means (t-interval)
4. 95%
5. 2
3 59
5. OK
21 2
2
95% 1 - 2 (-0.02916, 10.052)
21 = 2
2
4.
1. Two data columns
2. Data Column X1(data1)
2nd Data Column X2(data2)
3. Means (t-interval)
4. 95%
5. 2
3 60
5.
OK
21 = 2
2
95% 1 - 2 (0.38758, 9.6357)
%100)1(
22
21
s
s
2f1 2
2
21 2
2
21
s
s
2 1f
1 1 = 1n - 1, 2 = 2n - 1
4. 1. Two data columns
2. Data Column X1(data1)
2nd Data Column X2(data2)
3. Variances (F-interval)
4. 95%
3 61
5. OK
95% (0.44819, 5.8796)
95% 22
21
22
21
s
s
2f1 2
2
21 2
2
21
s
s
2 1f
1
1 = 1n - 1 = 9 - 1 = 8 2 = 2n - 1 = 16 - 1 = 15
15) (8, 0.025,f = 3.2, 15) (8, 0.975,f = 8) (15, 0.025,f
1 = 10.41 2
1s = 35.853, 22s = 25.008
95% 22
21
008.25853.35
2.31 2
2
21 008.25
853.35)1.4
1(1
0.4482 22
21 5.8796
3 62
3.2.2 %100)1( D
2 ( )
%100)1(
D 2 ( )
n 1 2
1. 2.
1x 1y
2x 2y
3x 3y
: :
nx ny
1. id = ix - iy , i = 1, 2, ... , n
2. d
3. ds
1. n 30 %100)1( D
d - 2
znd D d +
2z
nd
2. n 30
%100)1( D
d - 2
tn
sd D d + 2
tn
sd = n - 1
%100)1( D
3.2.2 10
1 2 10
1 (test1) 2 (test2)1 76 812 60 523 85 874 58 705 91 866 75 777 82 908 64 639 79 85
10 88 83
3 63
id = i1test - i2test , i = 1, 2, ... , 10
98% D
Instat
1.
2 test1, test2
example9.wor
2. Statistics Simple Models Normal, Two Samples
3. Normal, Two Sample
Simple Models - Normal Distribution, Two Samples
3 64
1. Two data columns
2. Data Column X1(test1)
2nd Data Column X2(test2)
3. Means (t-interval)
4. 95%
5.
4. OK
95% D (-6.1644, 2.9644)
8
1. Window Commands and Output
2. ACC 8
ACC n n , n = 1, 2, 3, 4, ... , 10
3. ACC 5
3 65
3.33.3.1 %100)1( p
%100)1( p p - 2
z nqp p p +
2z n
qp p = nx
p = 35
example005.wor 50 95% p
1. example005.wor
2.
Statistics Simple Models Proportion, One Sample
3. Proportion, One Sample
One proportion - binomial model
1. Layout Single data column
2. X3 X3(age)
3. Option Less than 35
3 66
4. Option Simple Normal (symmetrical)
5. 95%
3. OK
1. n = 48
2. 35 x = 19
3. p = 4819 = 0.396
4. nqp = 0.071
5. 95% p (0.257, 0.534)
3.3.2 %100)1( 1p - 2p
%100)1( 1p - 2p
( 1p - 2p ) - 2
z2
22111
nqp
nqp 1p - 2p ( 1p - 2p ) +
2z
222
111
nqp
nqp
1p = 11
nx , 2p =
22
nx
1p = 35
2p = 35
example005.wor 50 95% 1p - 2p
1. example005.wor
3 67
2. Statistics Simple Models Proportions, Two Samples
3. Proportions, Two Samples
Two proportions - binomial model
1. Layout Data column and two factor levels
2. X3 X3(age)
3. X2 X2(sex)
4. 1st Factor Value Female
5. 2nd Factor Value Male
6. Option Less than 35
7. 95%
3 68
3. OK
1. 1n = 17 2n = 31
2. 35 1x = 9
35 2x = 10
3. 1p = 35 = 179 = 0.529
2p = 35 = 3110 = 0.323
4. 1p - 2p = 3110 - 17
9 = 0.207
5.2
22111
nqp
nqp = 0.147
6. 95% 1p - 2p (-0.082, 0.496)
2p 1p Instat 1p - 2p
1p 2p Instat 2p - 1p
4
4.1 0H : = 0
1. 0H : = 0
1H : 0
2.
3. n x 2s
4. Z t
5. z t 4.
6.
6.1 Z 2
z 2
z Z 2
z Z 2
z
6.2 t 2
t 2
t t 2
t t 2
t
7.
7.1 Z z 2
z z 2
z 0H
7.2 t t 2
t t 2
t 0H
4. ( )
1. 2 Z =
n
x 0
2. 2
2.1 n 30 s Z =
ns
x 0
4 70
2.2 n 30 t =
ns
x 0
3. 2
n 30 Z =
n
x 0
4. 2
n 30 s Z =
ns
x 0
Instat
1. 0H : = 0
1H : 0
2.
3. n x 2s
4. t Z
5. t =
ns
x 0 t = n - 1
z =
n
x 0 z
6. t
Sig. (2-tailed) t
Sig. (2-tailed)
= 2 t t
= 2 P( t t )
z Sig. (2-tailed) = 2 P( Z z )
7. 2
1 t 2
t
t 2
t t 2
t 0H
z 2
z
z 2
z z 2
z 0H
2 Sig. (2-tailed)
Sig. (2-tailed) 0H
4 71
1
1H : 0 1H : 0
Z z z
Z z Z z
t t t
t t t t
Sig. (2-tailed)
t 0, Sig. (2-tailed) 2
0H
z 0, Sig. (2-tailed) 2
0H
t 0, Sig. (2-tailed) 2
0H
z 0, Sig. (2-tailed) 2
0H
4.1.1 50
50 12
41, 42, 47, 41, 54, 26, 26, 65, 34, 49, 29, 50 0.05
1. 0H : = 50
1H : 50
2. = 0.05
3.
x
example10.wor
example10.wor
4. n 30 t
4.1 Statistics Simple Models Normal, One Sample
4 72
4.2 Normal, One Sample
Simple Models - Normal Distribution, One Sample
1. Single data column
2. X1 X1(x)
3. Mean (t-interval)
4. Significance Test
5. 0H : = 50 50 Value
6. 2-tailed Significant
4.3 OK
4 73
5. t = -2.33 = 116. Sig. (2-tailed) t
Instat Sig. (2-tailed) = 0.0400 7.
1. t = -2.329 110.025,t = 2.201 1H : 50 t -2.201 t 2.201 0H
2. Sig. (2-tailed) = 0.05 Sig. (2-tailed) = 0.04 0.05 = 0H
50 0.05
4.2 0H 1 = 2
1. 0H : 1 = 2 1H : 1 2
2. 3. 1n 1 1x , 2
1s 2n 2 2x , 2
2s 4. Z t 5. z t 4. 6.
6.1 Z
2z
2z Z
2z Z
2z
6.2 t
2t
2t t
2t t
2t
7. 7.1 Z z
2z z
2z 0H
7.2 t t
2t t
2t 0H
4 74
0H : 1 = 2 2
1. 1n 30 2n 30
1.1 2 21 2
2
Z =
2
22
1
21
2121
nn
)()xx(
1.2. 2 21 2
2
21s 2
1 21s
22s 2
2 22s
Z =
2
22
1
21
2121
nn
)()xx(
2. 1n 30 2n 30
2.1 2 21 2
2
Z =
2
22
1
21
2121
nn
)()xx(
2.2 2 21 2
2
21s 2
2s
2.2.1 21 = 2
2 t =
21p
2121
n1
n1s
)()xx(
2ps = 2nn
s)1n(s)1n(21
222
211 = 1n + 2n - 2
2.2.2 21 2
2 t =
2
22
1
21
2121
ns
ns
)()xx(
=
)1n(1)n
s()1n(
1)ns
(
)ns
ns
(
22
2
22
12
1
21
22
22
1
21
21 = 2
2 4.4
Instat
1. 0H : 1 = 2
1H : 1 2
2.
4 75
3. 1n 1, 2n 2
1x 2x 21s 2
2s
4. t
21 = 2
2 t =
21p
2121
n1
n1s
)()xx(
2ps =
2nns)1n(s)1n(
21
222
211 = 1n + 2n - 2
21 2
2 t =
2
22
1
21
2121
ns
ns
)()xx(
=
)1n(1)n
s()1n(
1)ns
(
)ns
ns
(
22
2
22
12
1
21
22
22
1
21
5. t t
6. Sig. (2-tailed) t
Sig. (2-tailed)
= 2 t t
= 2 P( t t )
7. 2
1 t 2
t
t 2
t t 2
t 0H
2 Sig. (2-tailed)
Sig. (2-tailed) 0H
1
1H : 1 - 2 0 1H : 1 - 2 0
Z z z
Z z Z z
t t t
t t t t
Sig. (2-tailed)
t 0, Sig. (2-tailed) 2
0H
t 0, Sig. (2-tailed) 2
0H
4 76
4.2.1 2
1 1
2 2
1 16 ( )
161 162 183 174 164 184 185 183 184 184185 174 194 175 174 198
2 18 ( )
181 184 182 183 183 184 184 185 183 183184 185 183 184 184 172 195 183
0.05
2
1. 0H : 1 = 2
1H : 1 2
2. = 0.05
3.
w1
1
w2
2
( example11.wor)
4. 2 30
t
4.1 Statistics Simple Models Normal, Two Samples
4 77
4.2 Normal, Two Samples
Simple Models - Normal Distribution, Two Samples
1. Two data columns
2. X1(w1) X2(w2)
3. Means (t-interval)
4. Significance Test
5. 2-tailed Significant
6. 0H : 1 = 2
0H : 1 - 2 = 0 0 Value
7. t 2
4.3
OK
4 78
21 2
2
5. t =
2
22
1
21
2121
ns
ns
)()xx( =
)1n(1)
ns
()1n(
1)ns
(
)ns
ns
(
2
2
2
22
1
2
1
21
2
2
22
1
21
Instat t = -2.15 = 19.4
6. Instat Sig. (2-tailed) = 0.0446
7.
1. t
19,025.0t = 2.093 20,025.0t = 2.086 19.4,025.0t = 2.1
1H : 1 2
t -2.1 t 2.1 0H
2. Sig. (2-tailed)
1H : 1 2
= 0.05 Sig. (2-tailed)
Sig. (2-tailed) = 0.0446 0.05 = 0H
0.05
t 2
4 79
4.2.2 2
1n = 9 1
61.36 57.76 71.94 61.77 58.66 71.61 71.52 58.67 62.77
2n = 16 2
56.92 58.30 67.48 53.96 62.00 59.61 52.02 61.6064.83 58.55 52.53 64.74 55.51 66.18 55.51 54.18
10 0.05
2
1. 0H : 1 - 2 = 10
1H : 1 - 2 10
2. = 0.05
3. example7.wor
Window Current Worksheet
4. 2 30
t
4.1 Statistics Simple Models Normal, Two Samples
4.2 Normal, Two Samples
Simple Models - Normal Distribution, Two Samples
4 80
1. Two data columns
2. X1(data1) X2(data2)
3. Means (t-interval)
4. Significance Test
5. 2-tailed Significant
6. 0H : 1 - 2 = 10
10 Value
7. t 2
4.3 OK
4 81
21 = 2
2
5. t =
21p
2121
n1
n1s
)()xx(
2ps = 2nn
s)1n(s)1n(21
222
211 = 1n + 2n - 2
Instat t = -2.33
= 23
6. Sig. (2-tailed) t
Instat Sig. (2-tailed) = 0.0357
7.
1. t
23,025.0t = 2.069
1H : 1 - 2 10
t -2.069 t 2.069
t = -2.33 0H
2. Sig. (2-tailed)
1H : 1 - 2 10
= 0.05 Sig. (2-tailed)
Sig. (2-tailed) = 0.0357 0.05 = 0H
10 0.05
4 82
4.3 0H : D = 0d 2 2
0H : D = 0d
1. 0H : D = 0d
1H : D 0d
2.
3. n 1 2 ( )
1. 2.
1x 1y
2x 2y
3x 3y
: :
nx ny
1. id = ix - iy , i = 1, 2, ... , n
2. d
3. ds
4. Z t
n 30 Z =
ns
ddd
0
n 30
t =
ns
ddd
0 = n - 1
5.
6.
6.1 Z 2
z 2
z Z 2
z Z 2
z
6.2 t 2
t 2
t t 2
t t 2
t
7.
7.1 Z z 2
z z 2
z 0H
7.2 t t 2
t t 2
t 0H
4 83
Instat
1. 0H : D = 0d
1H : D 0d
2.
3. n d ds
4. t Z
5. t
t =
ns
ddd
0 = n - 1 z =
ns
ddd
0
6. t Sig. (2-tailed) t
Sig. (2-tailed) = 2 t
t
= 2 P( t t )
Z Sig. (2-tailed) = 2 P( Z z )
7. 2
1. t z
t t 2
t t 2
t 0H
Z z 2
z z 2
z 0H
2. Sig. (2-tailed)
Sig. (2-tailed) 0H
1
1H : D 0d 1H : D 0d
Z z z
Z z Z z
t t t
t t t t
Sig. (2-tailed)
t 0, Sig. (2-tailed) 2
0H
z 0, Sig. (2-tailed) 2
0H
t 0, Sig. (2-tailed) 2
0H
z 0, Sig. (2-tailed) 2
0H
4 84
4.3.1 5
2 2
1 2 3 4 5
2.0 2.0 2.3 2.1 2.4
2.2 1.9 2.5 2.3 2.4
0.05
Instat
1. 0H : D = 0
1H : D 0
2. = 0.05
3.
Window Current Worksheet
xray
chem
Save example12.wor
4. 30 t
4.1 Statistics Simple Models Normal, Two Samples
4.2 Normal, Two Samples
Simple Models - Normal Distribution, Two Samples
4 85
1. Two data columns
2. X1(xray) X2(chem)
3. Means (t-interval)
4. Significance Test
5.
6.
0H : D = 0 0 Value
7. 2-tailed Significant
4.3 OK
4 86
5. t = 1.581139 = 4
6. Sig. (2-tailed) t Sig. (2-tailed) = 0.1890
7.
1. 4,025.0t = 2.776 t -2.776 t 2.776
t = 1.581 0H
2. Sig. (2-tailed)
Sig. (2-tailed) = 0.1890 0.05 = 0H
0.05
0H : D = 0.1
1H : D 0.1
Value 0.1
7.
1. 4,025.0t = 2.776 t -2.776 t 2.776
t = -3.16 0H
2. Sig. (2-tailed)
Sig. (2-tailed) = 0.0341 0.05 = 0H
0.01 0.05
4 87
4.4 0H : 2 = 20
1. 0H : 2 = 20
1H : 2 20
2.
3. n 2s
4.
5. 2 = 20
2s)1n(
Sig. (1-tailed) Sig. (2-tailed)
Instat
1. 20 2s Sig. (1-tailed) = P( 2 2 )
Sig. (2-tailed) = 2 P( 2 2 )
2. 2s 20 Sig. (1-tailed) = 2 P( 2 2 )
Sig. (2-tailed) = 2 P( 2 2 )
6. 2
21 2
2
= n - 1
2 2
21 2 2
2
7. 1. 2
2 2
21 2 2
2 0H
2. Sig. (2-tailed)
Sig. (2-tailed) 0H
1
1H : 2 20 1H : 2 2
0
21
2
2 21
2 2
Sig. (1-tailed)
20 2s Sig. (1-tailed)
0H
20 2s Sig. (1-tailed)
0H
4 88
4.4.1
0.81
10
5.25 3.76 5.36 3.67 6.05 3.89 3.39 6.12 6.49 6.03
2 = 0.81 2 0.81
0.05
1.
0H : 2 = 0.81
1H : 2 0.81
2. = 0.05
3.
Window Current Worksheet
x
Save example60.wor
4.
4.1
Statistics Simple Models
Normal, One Samples
4.2 Normal, One Samples
Simple Models - Normal Distribution, One Sample
4 89
1. Single data column
2. X1(x)
3. Variance (F-interval)
4. Significance Test
5. 0H : 2 = 0.81
0H : = 0.9
0.9 Value
6. 2-tailed Significant
4.3 OK
5. 2 = 20
2s)1n( 2 = 16.001
6. 29,025.0 = 19.023, 2
9,975.0 = 2.7 = 10 - 1 = 9
2 2.7 2 19.023
Sig. (2-tailed) Instat
20 = 0.81 1.4401 = 2s
Sig. (2-tailed) = 2 P( 2 16.001) = 2(0.066860708097003) = 0.1337
7. 1.
2 0H
2. Sig. (2-tailed)
Sig. (2-tailed) = 0.1337 0.05 = 0H
0.81 0.05
4 90
4.5 0H : 21 = 2
2
Instat
1 2
( 21s 2
2s )
1. 0H : 21 = 2
2
1H : 21 2
2
2.
3. 21s , 2
2s
4. F
5. f = 22
21
s
s ( 2
1s 22s )
21s 2
2s f 1
Sig. (2-tailed) = 2 P(F f )
Sig. (1-tailed) = P(F f )
6.
1 = 1n - 1 2 = 2n - 1
21
f 2
f
F 21
f F 2
f
7. 1.
f 21
f f 2
f 0H
2. Sig. (2-tailed)
Sig. (2-tailed) 0H
1 ( 21s 2
2s )
1H : 21 2
2
f
F f
Sig. (1-tailed) Sig. (1-tailed) 0H
4 91
4.5.1 5 1
1.024 0.972 1.004 0.986 1.015
6 2
1.017 0.991 1.018 0.975 0.983 1.018
0H : 21 = 2
2 1H : 21 2
2 0.1
1. 0H : 21 = 2
2
1H : 21 2
2
2. = 0.1
3.
Window Current Worksheet
x Save
example61.wor
4. F
4.1 Statistics Simple Models Normal, Two Samples
4.2 Normal, Two Samples
Simple Models - Normal Distribution, Two Samples
4 92
1. Two data columns
2. X1(data1) X2(data2)
3. Variances (F-interval)
4. Significance Test
5. 0H : 21 = 2
2
22
21 = 1 ( testing variance ratio)
1 Value
6. 2-tailed Significant
4.3 OK
5. f = 22
21
s
s = 1.1629
6. 1 = 1n - 1 = 4 2 = 2n - 1 = 5
5),(4,0.05f = 5.199 5),(4,0.95f = 4),(5,0.05f
1 = 26.61 = 0.1597444
F 0.1597444 F 5.199
7. 1. f
f 0H
2. Sig. (2-tailed)
Sig. (2-tailed) = 0.8518 0.1 0H
2 0.1
4 93
4.6 0H : p = 0p
1. 0H : p = 0p
1H : p 0p
2.
3. n n 30 p
4. Z
5. z
Sig. (2-tailed) = 2 P( Z z )
6. 2
z 2
z Z 2
z Z 2
z
7. 2
1 z 2
z z 2
z 0H
2 Sig. (2-tailed)
Sig. (2-tailed) 0H
1
1H : p 0p 1H : p 0p
Z z z
Z z Z z
Sig. (2-tailed)
z 0, Sig. (2-tailed) 2
0H
z 0, Sig. (2-tailed) 2
0H
4.6.1 p = 35
example005.wor 50 p = 0.5 0.05
1. 0H : p = 0.5
1H : p 0.5
2. = 0.05
3.
4. Z Instat
4.1 example005.wor
4.2 Statistics Simple Models Proportion, One Sample
4.3 Proportion, One Sample One proportion - binomial model
4 94
1. Layout
Single data column
2. X3
X3(age)
3. Option Less than
35
4. Option Simple
Normal (symmetrical)
5.
Significance Test
6. 0H : p = 0.5 0.5 Value
7. 2-tailed Significant
4.4 OK
5. Instat 1. 1 66
2. z = -1.44
3. Sig. (2-tailed) = 0.1489
6. 025.0z = -1.96 025.0z = 1.96 Z -1.96 Z 1.96
7. 1 z = -1.44 0H
2 Sig. (2-tailed) = 0.1489 0.05 = 0H
p = 0.5 = 0.05
4 95
4.7 0H : 1p - 2p = 0p ( 1p 2p )
1. 0H : 1p - 2p = 0p ( 1p 2p )
1H : 1p - 2p 0p
2.
3. 1n 1 1p
2n 2 2p
4. Z
5. z Sig. (2-tailed) = 2 P( Z z )
6. 2
z 2
z Z 2
z Z 2
z
7. 1 z 2
z z 2
z 0H
2 Sig. (2-tailed)
Sig. (2-tailed) 0H
1
1H : 1p - 2p 0p 1H : 1p - 2p 0p
Z z z
Z z Z z
Sig. (2-tailed)
z 0, Sig. (2-tailed) 2
0H
z 0, Sig. (2-tailed) 2
0H
1p = 35
2p = 35
example005.wor 50 1p - 2p = 0
1p - 2p 0 0.05
1. 0H : 1p - 2p = 0
1H : 1p - 2p 0
2. = 0.05
3. ( example005.wor)
4. Z Instat
4.1 example005.wor
4.2 Statistics Simple Models Proportions, Two Samples
4.3 Proportions, Two Samples
Two proportions - binomial model
4 96
1. Layout
Data column and
two factor levels
2. X3
3. X2
4. 1st Factor Value
Female
5. 2nd Factor Value
Male
6. Option Less than
35
7.
Significance Test
8. 0H : 1p - 2p = 0
0 Value
9.
2-tailed Significant
4.4 OK
5.
1.
1 68
2. z = 1.40
3. Sig. (2-tailed) = 0.1603
6. 025.0z = -1.96 025.0z = 1.96 Z -1.96 Z 1.96
7. 1 z = 1.40 0H
2 Sig. (2-tailed) = 0.1603 0.05 = 0H
1p - 2p = 0 = 0.05
5
5.1
1. 0H :
1H :
2.
3. io , i = 1, 2, 3, ... , k
4.
5. ie
2 = k
1i i
2ii
e)eo(
6. 2
= k - - 1
2 2
7.
2 2 0H
5 98
5.1.1 3 240
x 3
example14.wor
0.05
1. 0H :
1H :
2. = 0.05
3. io
example14.wor 1o = 24, 2o = 98, 3o = 95, 4o = 23
4.
5. ie
x = 0, 1, 2, 3 ie
X io X P(X = x) ie
0 24 081
81 (240) = 30
1 98 183
83 (240) = 90
2 95 283
83 (240) = 90
3 23 381
81 (240) = 30
240 240
2 = 4
1i i
2ii
e)eo( = 30
)3024( 2 + 90
)9098( 2 + 90
)9095( 2 + 30
)3023( 2
= 1.2 + 0.7111 + 0.2778 + 1.6333 = 3.8222
6. = 3
205.0 = 7.815 2 7.815
7.
2 7.815 2
0H
Instat
1. 0H :
1H :
5 99
2.
3. io
4.
5. ie
2 = k
1i i
2ii
e)eo(
Sig. (1-tailed) = P( 2 2 )
6. 2
= k - - 1
2 2
7. 2 1. 2 2 0H
2. Sig. (1-tailed) 0H
5.1.1 3 240
x 3
example14.wor
0.05
Instat
1. 0H :
1H :
2. = 0.05
3. io
1 2
2 3
:
240 3 example14.wor
4.
5. 5.1 ie
0, 1, 2, 3 81 , 8
3 , 83 , 8
1 240
0 1e = 81 (240) = 30
1 2e = 83 (240) = 90
2 3e = 83 (240) = 90
3 4e = 81 (240) = 30
5 100
5.2 example14.wor
( )
example14.wor
Statistics Summary Group
5.3 io , i = 1, 2 , 3, 4
Statistics Summary Group
5.4 Group
1. X1
5.5 OK
io , i = 1, 2 , 3, 4
1o = 24, 2o = 98, 3o = 95, 4o = 23
5 101
5.6 ( X2(o))
( X3(e))
1.
2. X2(o), X3(e)
5.7 2 Sig. (1-tailed) 2
Statistics Simple Models Goodness of Fit
5.8 Goodness of Fit Googness of Fit
1. X2(o)
2. X3(e)
3.
ie
Number of estimated parameters 0
0 Number of estimated parameters
5 102
5.9
OK
Instat
io ie
1 24 30
2 98 90
3 95 90
4 23 30
240 240
1. 2 = k
1i i
2ii
e)eo( = 3.8 = 3
2. Sig. (1-tailed) = 0.2813
6. = 3
205.0 = 7.815 2 7.815
7. 1. 2 7.815 0H
2. Sig. (1-tailed) = 0.281312 0.05 0H
0.05
5 103
o e
5.1.2 2 X, Y
4
1 : 2 : 3 : 4 = 1 : 3 : 3 : 1
800
1 77 2 338 3 262 4 123
0.05
1. 0H :
1H :
2. = 0.05
3. 1o = 77, 2o = 338, 3o = 262, 4o = 123
1 : 2 : 3 : 4 = 1 : 3 : 3 : 1 N = 800
1e = 81 (800) = 100, 2e = 8
3 (800) = 300, 3e = 83 (800) = 300, 4e = 8
1 (800) = 100
3.1 o
e
3.2 Statistics Simple Models Goodness of Fit
5 104
3.3 Goodness of Fit Goodness of Fit
1. X2(o)
2. X3(e)
3.
ie
Number of estimated parameters 0
3.4
OK
Instat
io ie
1 77 100
2 338 300
3 262 300
4 123 100
800 800
1. 2 = 4
1i i
2ii
e)eo( = 20.2 = 3
2. Sig. (1-tailed) = 0.0002
5 105
6. = 3
205.0 = 7.815 2 7.815
7.
1. 2 = 20.2 7.815 0H
2. Sig. (1-tailed) = 0.0002 0.05 0H
0.05
5.2 2
1. 0H : A B
1H : A B
2.
3. ijo
4.
5. ije
ijo ije = NCR ji i = 1, 2, 3, ... , r j = 1, 2, 3, ... , c
1A 2A 3A cA
1B
2B
:
:
rB
11o
21o
:
:
1ro
12o
22o
:
:
2ro
13o
23o
:
:
3ro
...
...
...
c1o
c2o
:
:
rco
1R
2R
:
:
rR
1C 2C 3C ... cC N
ije 5 N 50
2 = r
1i
c
1j ij
2ijij
e)eo(
= (r - 1)(c - 1)
6. 2 = (r - 1)(c - 1) 2 2
7. 2 2
2 2 0H
5 106
Instat
1. 0H : A B
1H : A B
2.
3. ijo
4.
5. ije
2 = r
1i
c
1j ij
2ijij
e)eo(
2 = Sig. (1-tailed) = P( 2 2 )
6. 2 = (r - 1)(c - 1)
2 2
7. 2 1. 2 2 0H
2. Sig. (1-tailed) 0H
5.2.1 example15.wor
3
2
0.05
Instat
1. 0H :
1H :
2. = 0.05
3. ijo
4.
5. 5.1 example15.wor
5 107
X1(ID)
X2(area) Factor
1 = (east) 2 = (west)
X3(religion) Factor
1 = (protestant), 2 = (catholic) 3 = (jewish)
5.2 area, religion Statistics Tables Frequency
5.3 Frequency Frequency Tables
1. X2, X3
2 Factor
2. Column Factor 1
5.4 OK
5 108
5.5 Window Current Worksheet
X4, X5, X6 Table 1
5.6 ije
Statistics Simple Models Chi-square Test
5.7 Chi-square Test Chi-square Test
1. Layout of data Multiple Data Columns
2.
X4, X5, X6
5 109
5.8 OK
Instat
182 215 203
201.6 210.6 187.8600
154 136 110
134.4 140.4 125.2400
336 351 313 1000
1. ( ) ije ( )
2. 2 = 8.1 = 2
3. Sig. (1-tailed) = 0.0177
6. 205.0 = 5.991 = 2
2 5.991
7. 1 2 = 8.1 5.991 0H
2 Sig. (1-tailed) = 0.0177 0.05 0H
0.05
5 110
5.2.2
3
25 45 32
175 455 168
0.05
1.
0H :
1H :
2. = 0.05
3.
X1, X2, X3
3.1 ije
Statistics Simple Models Chi-square Test
5 111
3.3 Chi-square Test Chi-square Test
1. Layout of data Multiple Data Column
2. X1, X2, X3
5.4 OK
5 112
Instat
1. ( ) ije ( )
25 45 32
22.7 56.7 22.7102
175 455 168
177.3 443.3 177.3798
200 500 200 900
2. 2 = 7.3 = 2
3. Sig. (1-tailed) = 0.0258
6. 205.0 = 5.991 = 2
2 5.991
7. 1 2 = 7.3 5.991 0H
2 Sig. (1-tailed) = 0.0258 0.05 0H
0.05
6
2
(simple linear regression) (correlation)
(simple linear regression) 1
1
y = a + bx n y = a + b n x y = a + b n x n y = a + bx
(Simple correlation)
2
y = a + bx n y = a + b n x y = a + b n x n y = a + bx
y = a 2x + bx + c
y = a + 1b 1x + 2b 2x + ... + nb nx
6.1 X Y X, Y x|Y = + x
(regression coefficients) (intercept)
x|Y = + x y = a + bx
( correlation )
r
6 114
1. -1 1
2. X Y
3. = 0 X Y
4. 0 X Y X Y
5. 0 X Y X Y
6. b r
7. b Y X
1. 2.
1x 1y
2x 2y
: :
nx ny
a b y = a + bx r
n
1iix ,
n
1iiy ,
n
1iiiyx ,
n
1i
2ix ,
n
1i
2iy
1 b = 2n
1ii
n
1i
2i
n
1ii
n
1ii
n
1iii
xxn
yxyxn
a = y - b x
r = 2n
1ii
n
1i
2i
2n
1ii
n
1i
2i
n
1ii
n
1ii
n
1iii
yynxxn
yxyxn
2 b = xxxy
SS
r = yyxx
xySS
S
xxS = n
1i
2i )xx( =
n
1i
2ix - n
x2n
1ii
, yyS = n
1i
2i )yy( =
n
1i
2iy - n
y2n
1ii
xyS = n
1iii )yy)(xx( =
n
1iiiy x - n
y xn
1ii
n
1ii
6 115
x 1.5 1.8 2.4 3.0 3.5 3.9 4.4 4.8 5.0
y 4.8 5.7 7.0 8.3 10.9 12.4 13.1 13.6 15.3
y = a + bx r
x y 2x xy 2y
1.5 4.8 2.250 7.200 23.040
1.8 5.7 3.240 10.260 32.490
2.4 7.0 5.760 16.800 49.000
3.0 8.3 9.000 24.900 68.890
3.5 10.9 12.250 38.150 118.810
3.9 12.4 15.210 48.360 153.760
4.4 13.1 19.360 57.640 171.610
4.8 13.6 23.040 65.280 184.960
5.0 15.3 25.000 76.500 234.090
i9
1ix = 30.3 i
9
1iy = 91.1 2
i9
1ix = 115.11 ii
9
1iyx = 345.09 2
i9
1iy = 1036.65
x = 93.30 = 3.366667 y = 9
1.91 = 10.122222
b = 29
1ii
9
1i
2i
9
1ii
9
1ii
9
1iii
xx(9)
yxyx)9(
= 2)3.30()11.115)(9()1.91)(3.30()09.345)(9( = 2.93028
a = 10.122222 - 2.93028(3.366667) = 0.256947
y = 0.256947 + 2.93028 x
r = 2n
1ii
n
1i
2i
2n
1ii
n
1i
2i
n
1ii
n
1ii
n
1iii
yynxxn
yxyxn
= 22 )1.91(5)(9)(1036.6)3.30()(9)(115.11
)1.91)(3.30()09.345)(9( = 0.991089
6 116
2 xxS = 9
1i
2ix - 9
x29
1ii
= 115.11 - 9)3.30( 2
= 13.1
yyS = 9
1i
2iy - 9
y29
1ii
= 1036.65 - 9)1.91( 2
= 114.515556
xyS = 9
1iii yx - 9
yx9
1ii
9
1ii
= 345.09 - 9)1.91)(3.30( = 38.386667
b = xxxy
SS
= 1.13386667.38 = 2.93028
r = yyxx
xySS
S =
515556.1141.13386667.38 = 0.991089
6 117
Instat
1. x y
Window Current Worksheet Save example16.wor
2. Graphics Plot
3. Plot
1. X2 (Y-Variable(s))
2. X1 (X-Variable)
6 118
4. OK Window
1. Graph1 Instat Save
Graphics Load Graph
2. Plot
3.
Pointer
6 119
1. X
2. ( X : Independent variable or Explanatory variable)
3. Automatic scale
4. X 1
5. X 6
6. X 0.5
7. gridlines
Y ( Y : Dependent variable or Response variable)
6 120
Instat
1. x y
Window Current Worksheet
Save example16.wor
example16.wor
2. Statistics Regression Simple
3. Simple Simple Linear Regression
1. X2 (Response variable Dependent variable)
2. X1 (Explanatory variable Independent variable)
Option Plots
6 121
4. OK
y = a + bx
y = a + bx
x|Y = + x
1. (Y-intercept) a = 0.2569
2. (slope) b = 2.93
Fitted equation y = 0.2569 + 2.93 x
3. B = b = 0.1489
= n - 2 = 9 - 2 = 7
4. 95% (2.5783, 3.2823)
5. r
r b
r = squareR = 9823.0 = 0.9446
r = 0.9446
R Square = 0.9823 y = a + bx
2R 1 y = a + bx 2R 0 y = a + bx
6 122
2R = 0.1
y = a + bx y 10 %2R = 0.98226
y = a + bx y 98.226%
r b
1. r = 0.9446 X, Y
X Y X Y
2. b = 2.93
X 1 Y 2.93
X 1 Y 2.93
6.2 %100)1(
%100)1(
b - 2
tXXSS b +
2t
XXSS = n - 2
%100)1(
a - 2
t s xx
n
1i
2i
nS
x a +
2t s
xx
n
1i
2i
nS
x = n - 2
s = 2nSSE SSE = yyS - b xyS
6.2.1 (
) ( 0.01 )
4.3 126
4.5 121
5.9 116
5.6 118
6.1 114
5.2 118
3.8 132
2.1 141
7.5 108
6 123
1. b y = a + bx
2. a ( Y) y = a + bx
3. 95%
4. 95% x|Y = + x
5. r
1. 2
rain
air
Save example17.wor
2. Statistics Regression Simple with groups
3. Simple with groups Comparison of regression
1. X2 (Response variable Dependent variable)
2. X1 (Explanatory variable Independent variable)
6 124
4. OK
6 125
Instat
1. b = -6.324
2. a = 153.18
3. 95% -7.511 -5.137
4. 95% 147 159.4
5. r = - squaredR = - 9578.0 = -0.9787
( r b )
6.3 0H : = 0 2
1. 0H : = 0
1H : 0
2.
3. n r
4. t
5. t = 2r12nr = n - 2
Sig. (2-tailed) t
Sig. (2-tailed) = 2 P(t t )
6. 2
t 2
t t 2
t t 2
t
7.
1
t 2
t t 2
t 0H
2 Sig t
t 2
t t 2
t t 2
t
P(t t ) 2
2 P(t t )
Sig. (2-tailed)
Sig. (2-tailed) 0H
= 0 t = 2r12nr t =
)SS(b
xx
6 126
1
1H : 0 1H : 0
- 2n,t 2n,t
t - 2n,t t 2n,t
Sig. (2-tailed)
t 0
Sig. (2-tailed) 2
0H
t 0
Sig. (2-tailed) 2
0H
6.2.1
0.05
1. 0H : = 0
1H : 0
2. = 0.05
3. Instat
example17.wor ( 116)
4. t
5. Instat REGRESSION COEFFICIENTS
REGRESSION COEFFICIENTS
1. t = -12.600 = n - 2 = 9 - 2 = 7
2. Sig. (2-tailed) = P(t t ) = 0.0000
Sig. (2-tailed) = 0.0000045792
6. - 7,025.0t = -2.365, 7,025.0t = 2.365 t -2.365 t 2.365
7. 1 t 0H
2 Sig. (2-tailed) = 0.0000 0.05 0H
0.05
6 127
0H : = 0 ANOVA
2
1. 0H : = 0
1H : 0
2.
3.
4.
5. ANOVA
yyS , xxS , xyS ANOVA
SST = 2i
n
1iy - n
)y( 2i
n
1i = yyS
SSR = b xyS = 2b xxS
SSE = SST - SSR
ANOVA TABLE
SOV SS DF MS F Sig
Regression SSR 1 MSR f = MSEMSR P(F f )
Residual SSE n - 2 MSE
Total SST n - 1
6. )2,1(,f 1 = 1 , 2 = n - 2
F )2,1(,f
7. 1 f )2,1(,f 0H
2 Sig. (1-tailed) 0H
6.2.1
0.05
1. 0H : = 0
1H : 0
2. = 0.05
3. Instat
6 128
example17.wor ( 116)
4. F
5. Instat ANOVA for regression of air on rain
ANOVA for regression of air
1. f = 158.77 1v = 1, 2v = 7
2. Sig. (1-tailed) = P(F f ) = 0.0000
Sig. (1-tailed) = 0.0000045792
6. )7,1(,05.0f = 5.59 F 5.59
7. 1 f = 158.768 5.59 0H
2 Sig. (1-tailed) = 0.0000 0.05 0H
0.05
6.4 0H : = 0
y = 2 + 3x x 1 y 3
= 0
0 = 0
1. 0H : = 0
1H : 0
2.
3. n b, s, xxS
4. t
5. t =
xxSsb = n - 2
Sig. (2-tailed) = 2 P(t t )
6 129
6. 2
t 2
t t 2
t t 2
t
7. 1
t 2
t t 2
t 0H
2 Sig. (2-tailed) 0H
0 = 0 = 0
0 = 0 t = 2r12nr t =
xxSSb
1
1H : 0 1H : 0
2n,t 2n,t
t 2n,t t 2n,t
Sig. (2-tailed)
t 0
Sig. (2-tailed) 2
0H
t 0
Sig. (2-tailed) 2
0H
6.2.1 (y)
(x) x|Y = + x = 0
0.05
1. 0H : = 0
1H : 0
2.
3. n b, s, xxS
4.
5. Instat REGRESSION COEFFICIENTS
6 130
REGRESSION COEFFICIENTS
1. t = 2r12nr = -12.600 = n - 2 = 9 - 2 = 7
2. Sig. (2-tailed) = P(t t ) = 0.0000
Sig. (2-tailed) = 0.0000045792
6. 7,025.0t = -2.365 7,025.0t = 2.365
t -2.365 t 2.365
7. 1 t = -12.6 0H
2 Sig. (2-tailed) = 0.0000 0.05 0H
x|Y = + x 0 0.05
0 0
1. 0H : = 0
1H : 0
2.
3. n
4.
5. t =
xx
0
Ss
b = n - 2
Sig. (2-tailed) = 2 P( t t )
6. 2
t 2
t t 2
t t 2
t
7. 1 t 2
t
t 2
t t 2
t 0H
2 Sig. (2-tailed) 0H
1
1H : 0 1H : 0
2n,t 2n,t
t 2n,t t 2n,t
Sig. (2-tailed)
t 0
Sig. (2-tailed) 2
0H
t 0
Sig. (2-tailed) 2
0H
6 131
x 1.5 1.8 2.4 3.0 3.5 3.9 4.4 4.8 5.0
y 4.8 5.7 7.0 8.3 10.9 12.4 13.1 13.6 15.3
x|Y = + x
= 2.5 2.5 0.05
1. 0H : = 2.5
1H : 2.5
2. = 0.05
3. n
4. x
y Window Current Worksheet
Save example16.wor
4.1 Statistics Regression Simple
4.2 Simple Simple Linear Regression
6 132
1. X2 (Response variable dependent variable)
2. X1 (Explanatory variable independent variable)
3. Significance Test
4. 0H : = 2.5
Value 2.5
4.3 OK
1. b = 2.93
2. Standard error xxSs = 0.1489
3. slope = 2.5 Simple Linear Regression
4. t = 2.89
5. Sig. (2-tailed) = 2 P(t t ) = 0.0233
5. t = 2.89 = 7 Sig. (2-tailed) = 0.0233
6. 7,025.0t = -2.365 7,025.0t = 2.365
t -2.365 t 2.365
7. 1 t 0H
2 Sig. (2-tailed) = 0.0233 0.05 0H
= 2.5 0.05
7
2
7.1
(One-Way ANOVA, Simple-Factor ANOVA) 1n , 2n , ... , kn 1, 2, ... , k k
(Treatments)
5
6
( %)
1 2 3 4 5
551 595 639 417 563
457 580 615 449 631
450 508 511 517 522
731 583 573 438 613
499 633 648 415 656
632 517 677 555 679
7 134
k
1 , 2 , ... , k 2
0H : 1 = 2 = ... = k
1H : 2
(Treatment)
1 2 ... j ... k
1 11x 12x ... j1x ... k1x
2 21x 22x ... j2x ... k2x
: : : : :
i 1ix 2ix ... ijx ... ikx
: : : : :
jjnx
22nx
11nx ... kknx
1n 2n jn kn
1.T 2.T j.T k.T ..T
1.x 2.x j.x k.x ..x
Treatment
N = = 1n + 2n + ... + kn ijx = i j
j.T = j
j.x = j
..T = ..x = NT.. =
3
1. (SST : TOTAL SUM OF SQUARE, Total Sum Square)
SST = k
1j
jn
1i
2ijx - N
T2..
2. Treatment (SSTR : TREATMENT SUM OF SQUARE, Between-
Groups Sum Square) SSTR = k
1j j
2j.
nT
- NT2
..
3. Treatment (SSE : ERROR SUM OF SQUARE, Within-Groups Sum Square, Residual Sum Square) SSE = SST - SSTR
SST, SSTR, SSE (ANalysis Of VAriance : ANOVA)
7 135
ANOVA
(SOV (SS) (DF) (MS)
f
(Treatment)SSTR k - 1 MSTR =
1kSSA f =
MSEMSTR
(Error)SSE N - k MSE = kN
SSE
(Total) SST N - 1
Sig. (1-tailed) f
1 = k - 1, 2 = N - k
Sig. (1-tailed) = P(F f )
1. 0H : 1 = 2 = 3 = ... = k
1H : 1 2 3 ... k ( 2 )
2.
3.
4. F
5. f ANOVA
6. f 1 = k - 1, 2 = N - k F f
7. 1 f f 0H
2 Sig. (1-tailed) 0H
7.1.1 5 ( 125)
1 , 2 , 3 , 4 , 5 1, 2, 3, 4, 5
1 , 2 , 3 , 4 , 5 0.05
1. 0H : 1 = 2 = 3 = 4 = 5
1H : 1 2 3 4 5 ( 2 )
2. = 0.05
3.
4. F
5. F ANOVA
7 136
N = 30 SST = x2ij
6
1i
5
1j - N
T2.. = 2551 + 2457 + ... + 2679 - 30
168542 = 209376.8
SSTR = 6T2
j.5
1j - N
T2.. = 6
36642791366334163320 22222 - 30
168542 = 85356.467
SSE = 209376.8 - 85356.467 = 124021.33
ANOVA
(SOV) (SS) (DF) (MS)
f
(Treatment)SSTR = 85356.467 k - 1 = 4 21339.117 4.30
(Error)SSE = 124020.33 N - k = 25 4960.8133
(Total) SST = 209376.8 N - 1 = 29
6. 05.0f = 2.76 1 = 4, 2 = 25 F 2.76
7. f = 4.30 2.76 0H
Instat
1. 0H : 1 = 2 = 3 = ... = k
1H : 1 2 3 ... k ( 2 )
2.
3.
4. F
5. F ( ANOVA )
5.1 f
5.2 Sig. (1-tailed) F
6. 6.1 f 1 = k - 1, 2 = N - k F f
6.2 Sig. (1-tailed)
7. 1 f f 0H
2 Sig. (1-tailed) 0H
Instat 7.1.1
1. 0H : 1 = 2 = 3 = 4 = 5
1H : 1 2 3 4 5 ( 2 )
2. = 0.05
7 137
3.
3.1
type trement
weight
example19.wor
trement
Factor column
1. X1 ordinary variable
2. X1-F Factor column
X1(type) Factor column
3.5
3.2
Manage Column Properties Factor
3.3 Factor
Make or modify a factor column
1. X1(type)
Factor column
2. X1(type) 5
7 138
3.4 OK
X1
Ordinary variable
Factor column X1-F
3.5
Statistics Analysis of Variance
One-way
3.6 One-way
OneWay Analysis of Variance
1. X2(weight)
2. treatment
X1(type)
3.
3.7 OK
7 139
ANOVA
SOV SS DF MS f Sig. (1-tailed)
Treatment(weight) 85356.467 4 21339.117 4.3 0.009
Error 124020.33 25 4960.8133
Total 209376.8 29
4. Sig f 5. ANOVA f = 4.3 Sig. (1-tailed) = 0.0096. 1 = 4, 2 = 25 05.0f = 2.76
F 2.76 7. 1 f = 4.3 2.76 0H
2 Sig.(1-tailed) = 0.009 0.05 0H 0.05
7.2-
Randomized Block Design
(Block) (Treatment)
4 5
7 140
1 2 3 4
1 44 38 47 36
2 46 40 52 43
3 34 36 44 32
4 43 38 46 33
5 38 42 49 39
1
2 (Factor)
1 Treatment 1 Block 1
(Treatment)
1 2 ... j ... k
1 11x 12x ... j1x ... k1x .1T .1x
2 21x 22x ... j2x ... k2x .2T .2x
3 31x 32x ... j3x ... k3x .3T .3x
: : : : : : :
i 1ix 2ix ... ijx ... ikx .iT .ix
: : : : : : :
b 1bx 2bx ... bjx ... bkx .bT .bx
1.T 2.T ... j.T ... k.T ..T
1.x 2.x ... j.x ... k.x ..x
N
ijx j i j = 1, 2, ... , k i = 1, 2, ... , b
j.x = j ( thj treatment mean)
..x = (grand mean overall mean)
.ix = i ( thi block mean)
j.T = j ( thj treatment total)
.iT = i ( thi block total)
..T = (grand total overall total)
7 141
4
1. (SST : TOTAL SUM OF SQUARE, Total Sum Square)
SST = 2..ij
b
1i
k
1j)xx( =
k
1j
b
1i
2ijx -
NT 2
..
2. Treatment (SSTR : TREATMENT SUM OF SQUARE, Between-
Treatment Sum Square) SSTR = 2..j.
k
1j)xx(b = b
Tk
1j
2j.
- N
T 2..
3. Block (SSBL : BLOCK SUM OF SQUARE, Between-Groups Sum
Square) SSBL = )xx(k 2..i.
b
1i= k
Tb
1i
2.i
- N
T 2..
4. Treatment Block
(SSE : ERROR SUM OF SQUARE, Within-Groups Sum Square, Residual Sum Square)
SSE = SST - SSTR - SSBL
ANOVA
(SOV)(SS) (DF) (MS)
f
(Treatment)SSTR k - 1 MSTR =
1kSSTR treatmentf
= MSE
MSTR
(Block)SSBL b - 1 MSBL = 1b
SSBL blockf = MSE
MSBL
(Error)SSE (b - 1)(k - 1) MSE = )1k)(1b(
SSE
(Total) SST N - 1
1. (Treatment)
0H : 1. = 2. = 3. = ... = k.
1H : 1. 2. 3. ... k. ( 2 )
(Block)
0H : .1 = .2 = .3 = ... = .b
1H : .1 .2 .3 ... .b ( 2 )
2.
7 142
3.
4. F
5. F ANOVA
Treatment Sig. (1-tailed) = P(F treatmentf )
Block Sig. (1-tailed) = P(F blockf )
6. 6.1 Treatment f
1 = k - 1, 2 = (b - 1)(k - 1) F f
6.2 Block f
1 = b - 1, 2 = (b - 1)(k - 1) F f
7. 7.1 Treatment
7.1.1 treatmentf f Treatment 0H
7.1.2 Sig. (1-tailed) treatmentf 0H
7.2 Block
7.2.1 blockf f Block 0H
7.2.2 Sig. (1-tailed) blockf 0H
7.2.1 4
5
1 2 3 4
1 44 38 47 36
2 46 40 52 43
3 34 36 44 32
4 43 38 46 33
5 38 42 49 39
0.05 4
0.05 5
1.
( Treatment)
0H : 1. = 2. = 3. = 4.
1H : 1. 2. 3. 4. ( 1 )
( Block)
0H : .1 = .2 = .3 = .4 = .5
1H : .1 .2 .3 .4 .5 ( 1 )
2. = 0.05
7 143
3. Window Current Worksheet
3.1
X1(man)
X2(machine)
X3(time)
Save example20.wor
trement Block
Factor column
1. X1 X2
ordinary variable
2. X1-F X2-F
Factor column
X1(man) X2(machine) Factor column
3.8
3.2 Manage Column Properties Factor
3.3 Factor Make or modify a factor column
1. X1(man) Factor column
2. X1(man) 5
7 144
3.4 OK X1(man)
Factor column (X1-F)
3.5 Manage Column Properties Factor
3.6 Factor
Make or modify a factor column
1. X2(machine)
Factor column
2.
X2(machine) 4
7 145
3.7 OK X2(machine)
Factor column (X2-F)
3.8
Statistics Analysis of Variance
Orthogonal
3.9 Orthogonal
Analysis of Variance for Orthogonal Designs
1. X3(time)
2. treatment block
X1, X2
3.10 OK
7 146
Instat
SSTR(machine) = 338.8 MSTR(machine) = 112.93
SSBL(man) = 161.5 MSBL(man) = 40.375
SSE = 73.7 MSE = 6.1417 SST = 574.0
4. F
5. ANOVA
ANOVA
SOV SS DF MS f Sig. (1-tailed)
machine 338.8 3 122.93 treatmentf = 18.4 0.000
man 161.5 4 40.375 blockf = 6.6 0.005
Error 73.7 12 6.1417
Total 574.0 19
6.
(machine) 12),(3,0.05f = 3.94 F 3.94
(man) 12),(4,0.05f = 3.26 F 3.26
7.
(Treatment : var name = machine)
1. treatmentf = 18.4 3.49 0H
2. Sig. (1-tailed) = P(F treatmentf ) = 0.000
Sig. (1-tailed) = 0.000 0.05 0H
4 0.05
(Block : var name = man)
1. blockf = 6.6 3.26 0H
2. Sig. (1-tailed) = P(F blockf ) = 0.005
Sig. (1-tailed) = 0.005 0.05 0H
5 0.05
1
Window Commands and Output
Instat
Window Commands and Output
1.
1.
1. X1(x) 5 2, 3, 7, 5, 12
2. DES X1 X1
3.
Statistics Summary Describe X1(x)
2.
1. X1, X2, X3
2. CHIsquare X1-X3 X1, X2, X3 2 ( 102)
2.
1. ?
2. X1, X2 Window Current Worksheet
1148
3.
1. X1, X2 ( X3, X4 )
2. calc X3 = 2*X1 X3
3. calc X4 = X1+X2 X4
4. Manage Calculations
1. 25/4 OK
2. 1.
3.
4. Option Further functions
Probability Comb com com(r, n) = )!rn(!r!n
Npr npr npr(k) P(Z k)
Summary Sum sum sum(X1) X1
Count cou cou(X1) X1
2
Instat macro programing Instat
Instat
Instat macro
1. Window macro
1.1 Window Current Worksheet
1.2 Edit View/Edit Macro New
1.3 New Window Editing Commands
2. macro
2.1 DES X1
2.2 ?SUM(X1)
3. Macro
3.1 Window Editing Commands
3.2 File Save File Save As
3.3 Save Save Text File As
3.4 macro1 ( macro file *.ins)
3.5 Save
Editing Commands
Editing macro1.ins
2150
4. Macro
4.1 X1 example001.wor
4.2 Window Commands and Output
4.3 @macro1 Enter
Window Commands and Output
1. @macro1 Enter
2. DES X1
3. ?SUM(X1)
5. Macro
Submit Run Macro
5.1 Window Current Worksheet
5.2 Submit Run Macro
5.3 Run Macro
Run Macro
5.4 macro1
5.5 OK
6. Macro
6.1 Window Current Worksheet
6.2 Edit View/Edit Macro Open
6.3 Open Edit macro
6.4 marco1
6.5 OK Window Editing Commands
macro1.ins
Save
3
Instat Log File
Instat Instat
Log File
1. Instat
1.1 Instat Window Current Worksheet
1.2 Edit Command Logging Start ( F9)
1.3 Start Start Logging Commands to a File
1.4 Log1
(
Log file Log1)
1.5 OK
1.6 OK Window Commands and Output LOG @Log1.log
Instat Log1.log
1. Window Current Worksheet
2. example001.wor
3.
Statistics Summary Describe X1(x)
Window Commands and Output
3152
2. Instat Log File
2.1 Window Current Worksheet
2.2 Edit Command Logging Stop ( Shift+F9)
2.3 Stop Window Commands and Output LOG
Log1.log
3. Log1.log
3.1 Window Current Worksheet
3.2 Edit Command Logging View Log File ( Ctrl+F9)
3.3 View Log File Open Log File
3.4 Log1 Open
3.5 Open Window Viewing log1.log
1. Log File log1.log
2. example001.wor
3. DES X1
Statistics Summary Describe X1(x)
1. Log File
2. Copy Log File macro
3. Log File
Edit View/Edit Text Open ( Shift+F8)
*.log
4
Word Excel Instat
Word Excel Instat
1. Word Instat
1.1 Word
1.2 Copy
1.3 Window Current Worksheet
1
1.4 Paste Copy Word
1. Word
2. Word Instat
1. ?SUM(X1) X1(a)
2. ?MEAN(X2) X2(b)
3. ?SDE(X3) X3(c)
4154
2. Excel Instat
2.1 Excel
2.2 Copy
2.3 Window Current Worksheet
1
2.4 Paste Copy Excel
1. test1, test2, test3
2. Excel Instat
1. ?SUM(X1) X1(test1)
2. ?MEAN(X2) X2(test2)
3. ?SDE(X3) X3(test3)
Instat Functions
MIN
MAX
SUM
MEAN
SDE
SSQ
COU
MIN(X) = X
MAX(X) = X
SUM(X) = X
MEAN(X) = X
SDE(X) =
X
SSQ(X) =
X
COU(X) = X
K1 = LHS.
K2 = LHS.
Constants
K1 - K9
X1 Current Worksheet
NPR
NDE
Normal distribution
NPR(k) = P(Z k)
NDE(p) = k
P(Z k) = p
TPR
TDE
Student's t distribution
TPR(k, v) = P(t k) df = v
TDE(p, v) = k
P(t k) = p df = v
CPR
CDE
Chi-square distribution
CPR(k, v) = P( 2 k) df = v
CDE(p, v) = k
P( 2 k) = p df = v
FPR
FDE
F distribution
FPR(k, v1, v2) = P(F k)
FDE(p) = k P(F k) = p
df = (v1, v2)
โปรแกรม Instat สามารถ Download ไดจาก Website http://www.rdg.ac.uk/ssc
ตามเง�อนไขท�ไดรบอนญาต เชนใชงานสวนตว หนงสอเลมน�ทาใหผอานสามารถ
ใชโปรแกรม Instat ไดโดยงาย เพราะวาทกข �นตอนของการทางานดวยคาส �งของ
Instat จะมภาพประกอบการทางาน มการอางองทฤษฎทางสถต และ สตรท�ใช
เน�อหาภายในเลมประกอบดวย
♦ การสรางแฟมขอมล
♦ การคานวณคาสถตเบ�องตน เชน Mean, Median
♦ การแจกแจงความถ� หาคาเปอรเซนตไทล
♦ การนาเสนอขอมลในรปแบบตาราง
♦ การเขยนกราฟ เชน Stem and Leaf, Boxplot
♦ การหาชวงความเช�อม �นของคาพารามเตอร
♦ การทดสอบสมมตฐาน คาเฉล�ย ความแปรปรวน
♦ การทดสอบภาวะสารปสนทด
♦ การทดสอบความเปนอสระ
♦ การเขยนกราฟ แผนภาพการกระจาย
♦ การหาสมการเสนถดถอย (regression line)
♦ สมประสทธ� สหสมพนธ (Correlation)
♦ การวเคราะหความแปรปรวน (ANOVA)
จดจาหนายโดยศนยหนงสอแหงจฬาลงกรณมหาวทยาลย
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