ʶԵԷ㹡

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           ʶԵԷ㹡 
  
ѵػʧ
       1. ͡ʶԵԷ㹡͸Ժµ
       2. ͡ʶԵԷ㹡÷ͺص԰ҹ
       3. ö͡Ըա÷ҧʶԵ㹡šԨҧ óա͸Ժµ С÷ͺᵡҧ
   

          ʶԵԷ㹡

1. ʶԵԷ㹡͸Ժµ (Descriptive Statistics) 觻Сͺ
       1.1 ᨡᨧ
       1.2 Ѵǹҧ
       1.3 ѴáШ
       1.4 Ѵѹ

2. ʶԵԷ㹡÷ͺص԰ҹ (Inferential Statistics)
       2.1 ÷ͺص԰ҹóաҧ
       2.2 ÷ͺص԰ҹóաҧ 2
       2.3 ÷ͺص԰ҹóաҧҡ 2

       㹡÷͡ʶԵԻ㴨繵ͧҺҢŷǺҹҵҡѴдѺ 仹
       1. ҵҹѭѵ (Nominal Scale)
       2. ҵ§ѹѺ (Ordinal Scale)
       3. ҵѹҤ (Interval Scale)
       4. ҵѵǹ (Ratio Scale)
       ҵҡѴ͸Ժ㹺 6

         
           ʶԵԷ㹡͸Ժµ (Descriptive Statistics)   

     1. ᨡᨧ (Frequency Distribution) СѺŷҵ
ѭѵ ҵͧ÷ҺǡѺ ˹觷ҧԪҡ ҨҡǺȪ-˭ԧ褹 Դ ͵˹觷ҧԪҡе˹ҡ§ 觨 (Percentage) ʶԵԺ ´㹺 8 ǢʶԵԾ鹰ҹ㹡Ԩ˹ 103
     2. Ѵٹҧ (Central Tendency) 繡Ҥҡҧ
᷹ͧŷǺ ŢԵ Ѹ°ҹ аҹ ѧ´㹺 8 ʶԵԾ鹰ҹ㹡Ԩ˹ 107

     3. ѴáШ (Variation) 繤ҷ͡ҺҢŷǺ
ᵡҧѹҡ§ ʶԵԷѴáШ Ҿ §ູҵðҹ ФҤûǹ´㹺 8 ǢʶԵԾ鹰ҹ㹡Ԩ˹ 118
     4. Ѵѹ ҧ㹡÷Ԩѧͧ÷͸Ժ¶֧ѹҧô ÷͡ ֡ҹդѹѹ 㹷ȷҧ ԸաäӹdzҤѹҧ 2 ԷѹѹѺ ԷѹẺѹԷѹẺѹǶ֧㹺 8 ǢʶԵԾ鹰ҹ㹡Ԩ˹ 126 㹷СǶ֧੾Է ѹѹѺԷѹç (Spearman rank Correlation Coefficent)
       Էѹç 繴Ѫշ繤ѹҧ
ͧش ͵÷ͧش繢ŪԴҵ§ѹѺ (Ordinal Scale)

       ӹdzҡЪҡ

       ӹdzҡҧ

      Էѹç
       D ᵡҧҧӴѺͧͧش
       N , n ӹǹͧЪҡ͡ҧӴѺ


ҧ 1 ԷѹҧṹԪҡԨ¡֡ͧ ѺԪ
Ѵš֡ҢͧԵ ӹǹ 10 觼ͺҡѧ

Ե
Ԩ¡֡ͧ(x)
Ѵš֡ (y)
˹觢ͧ y
˹觢ͧ x
D
1
2
3
4
5
6
7
8
9
10
20
14
18
10
15
16
12
11
17
9
19
18
17
10
10
14
16
17
15
13
1
6
2
9
5
4
7
8
3
10
1
2
3.5
9.5
9.5
7
5
3.5
6
8
0
4
-1.5
-0.5
-4.5
-3
2
4.5
-3
2
0
16
2.25
0.25
20.25
9
4
20.25
9
4
           


Ըշ n = 10
                ҡٵ
                             

                                = 1-0.52

                                = 0.48


        ѧѹѺԪԨ¡֡ͧդѹѺѹѺԪҡѴš֡Ҥ͹ҧ¤ 0.48
= = 0.23 蹤 ҷҺѹѺͺԪԪ˹ö͸Ժ ûǹͧѹѺͧաԪ˹ 23 %


ҧ 2 ӹdzҤѹҧšõѴԹ觢ѹͧ 2 ҹ
觻ҡŴѧ

觢ѹ
šõѴԹͧ
D
1
2
1
2
3
4
5
6
7
8
9
10
5
4
8
7
6
3
1
2
10
9
5
4
8
6
7
2
1
3
9
10
0
0
0
1
-1
1
0
-1
1
-1
0
0
0
1
1
1
0
1
1
1
       

Ըշ ҡٵ
                         =
                         =    1 - 0.04

                         =    0.96

        ʴҼšõѴԹͧͧҹդʹͧѹ = = 0.92 蹤 ҷҺšõѴԹͧ ÷ҹ㴷ҹ˹ ö͸Ժ¤ûǹ õѴԹͧաҹ˹ 92

         
           ʶԵԷ㹡÷ͺص԰ҹ (Inferential Statistics)   

      óǡѺ¢ͧЪҡ
       1. ÷ͺ㹡óշաҧ (One Sample test) 繡÷ͺ ᵡҧҧ¢ͧҧ ( )Ѻ¢ͧЪҡ ( ) ͤҤ 㴤˹
       ԰ҹ
             

           1.1 óշҺûǹͧЪҡ ()
           ٵ   ˜ N (0,1)

͵ŧͧ
       1. ҧ繡ҧẺѺҨҡЪҡ÷ա
ᨡᨧ駻
       2. Ңͧõ˹¹е͡ѹ
       3. ҺҤûǹͧЪҡ
           1.2 óҺûǹͧЪҡ
           1.2.1 ҡҧբҴ˭ Z testApproximation test
                      ٵ Z =    ˜ N (0,1)
͵ŧͧ
       1. ҧ繡ҧẺѺҨҡЪҡ÷ա ᨡᨧ駻
       2. Ңͧõ˹е͡ѹ
       3. ҺҤûǹͧЪҡ
       4. ҧբҴ 100
˵
ԨѡɳйöǺԹҧ ҨжҶҡҧբҴ 30 仡繡ҧբҴ˭ Ԩ㹷ҧѧʵ ͷҧ֡ҹ äǺԹҧ 鹤͹ҧӺҡ ੾СԨ·ǢͧѺѧͧԨ·ҧ֡ͷҧѧʵ鹶ҡҧ բҴ˭鹤 ҧբҴ 100
            1.2.2 ҡҧբҴ (n < 100) t-test
                      ٵ     t =     ˜

        ͵ŧͧ
       1. ҧ繡ҧẺѺҨҡЪҡ÷աᨡᨧ駻
       2. Ңͧõ˹е͡ѹ
       3. ҺҤûǹͧЪҡ
       4. ҧբҴ¡ 100

        2. ÷ͺҧͧ (Two Sample Test)
           2.1 ÷ͺҧͧе͡ѹ (Two independent Sample test)
                 ԰ҹ
                              
                  2.1.1 óշҺҤûǹͧЪҡ÷ͧ Z-test Exact test

                         ٵ Z =     ˜ N(0,1)

͵ŧͧ
        1. ҧ繡ҧẺѺҨҡЪҡ÷ա ᨡᨧ駻
        2. Ңͧõ˹¹е͡ѹ
        3. ҺҤûǹͧЪҡ÷ͧ
             2.1.2 óҺҤûǹͧЪҡá㴡˹ ͧеͧԨóҶ֧ Ҵͧҧ

                      2.1.2.1 ҢҴͧҧСբҴ˭ Z-test Approximation test
                                ٵ Z =     ˜ N(0,1)

                       2.1.2.2 ҢҴͧҧ㴡˹ͷͧբҴ (n1 / n2 < 100) ͧԨóҶ֧ҡѹͧҴͧҧ
                      (1) ҡҧͧբҴҡѹ t-test Pooled Variance t-test
                          ٵ  Z =    ˜
                                   S =
͵ŧͧ
       1. ҧ繡ҧẺѺҨҡЪҡ÷ա
ᨡᨧ駻
       2. Ңͧõ˹¹е͡ѹ
       3. ҺҤûǹͧЪҡ÷ͧ
       4. ûǹͧЪҡ÷ͧդҡѹ
˵
         ٵ Pooled Variance t-test ͵ŧͧ鹷ӤѭС˹觡 ûǹͧЪҡ÷ͧդҡѹ 㹷ҧԺѵԼԨҺ ҢҴͧҧͧͧҡѹ (n1 = n2) ÷ͺդ (Test is Robust) 蹤 ֧ ҷԴҡ÷ͺص԰ҹ Pooled variance t-test ѧ§ѺҷԴҡ÷ͺص԰ҹ ѡɳ仵͵ŧͧ鹷 ҨСҼŷҡ÷ͺ§ѹ
            (2) ҡҧͧբҴᵡҧѹèзͺص԰ҹ͹
F-test ˜ Ҽš÷ͺҡ 㹡÷ͺ¢ͧЪҡͧ Pooled Variance t-test Ҽš÷ͺҡ ͧ Separate Variance t-test ѧٵõ仹
                          t =   ˜

                      V =

           2.2 ÷ͺҧͧǢͧѹ (Two dependent Sample test) 繡÷ͺᵡҧҧ¢ͧҧͧе͡ѹ ͧѹѹ ѡɳТͧе͡ѹդѹѹ ѡɳӤѭ
           1. ͧѴҡǡѹͧ ͺ͹¹-ͺѧ¹ (Pretest-posttest) ͺ (test -retest) ṹ͹ѧѺý֡ (before-after)
            (1) ͧѴҡͧѡɳӤѭҧС
͹ѹ繤 蹡ͧҡὴ繤 ͧҡèѺҪԡºؤź鹰ҹ IQ ҡѹ
            (2) ͧѴҡͧդԴѹҡ ôҡѺ
ص ԴҡѺص
            ԰ҹ
                         

             ٵ     t =   ˜

    d = ᵡҧͧҢͧõФ
        n = ӹǹ
         = ¢ͧ d
         = §ູҵðҹͧ d
          = ٹ

              

             

͵ŧͧ
       1. ҪԡФͧҧѺ͡Ẻ
       2. ᵡҧҧҵõͧФաᨡᨧ駻
       3. ҵõҧе͡ѹ

3. ÷ͺ㹡óշաҧҡͧ
        1.1 óյ§ ä 3 Ң ѧ鹨֧դ¢ͧ
õ 3 Ը͹ 3 Ըշռŵͼķҧ¹Ԫҿԡ .5

Ը͹
Ըշ 1
Ըշ 2
Ըշ 3
n = 100
n = 100
n = 100

       ҡѧʴ֧ººԸ͹ԸԸչѡ¹ 100
㹡÷ͺص԰ҹûǹẺҧ (One-way
Analysis of Variance : One-Way Anova)

       ԰ҹ
                   :  դ¢ͧЪҡҧ˹觤դᵡҧѹ

       ٵ      F =    ˜

          k = ӹǹ
             N = ӹǹЪҡ÷


       ҼšûǹẺҧ դᵡҧѹҧ¢ͧеͧͺᵡҧʹ ¤㴺ҧᵡҧѹ ҼšûǹẺҧǾդᵡҧѹҧ¢ͧ
ͧͺ ʴդ¤㴷ᵡҧѹ
       Ըա÷ҧʶԵԷ鷴ͺᵡҧҧѧûǹ (Post-hoc tests) ÷ͺ ººԧ͹ (Multiple Comparison tests) 仹 Ըբͧ Tukey, Scheffe, Newman-Keuls, LSD, Dancan 繵
1.2 óյͧ ä 2 Ң ºº
ķҧ¹Ԫҿԡ .5 ҡԸ͹ ѧ鹨֧դҧ 4

Ը͹
n1
n2
˭ԧ
n3
n4

ҡѧʴ֧ººķҧ¹ҡԸ͹ 2 Ը Ȫ¡Ѻ
˭ԧ Сչѡ¹ 20

        㹡÷ͺص԰ҹûǹẺͧҧ (Two-way
Analysis of Variance : two- way ANOVA) ͼŢͧемŢͧ
ѹҧ÷ͧյõ 繡÷ͺ
            1.ᵡҧҧ¢ͧṹõ繼Ҩҡѹҧ ͧ
            2.ᵡҧҧ¢ͧṹõ繼ҨҡеǷ 1
            3. ᵡҧҧ¢ͧṹõ繼ҨҡеǷ 2
       3.3 óյе еͧäǺúҧǷ觼ŵ͵õԸա÷ҧʶԵ ͧ֡ҼŢͧԸա͹ 3 Ը ͧ繹ѡ¹ 3 ö͡Ը ֧öǺõҧ ǡѺǹѡ¹ (ͧ 3 Ҩդѹ) 㹡÷ͧ駹ԨҨԨóҤ鹰ҹͧѡ¹ ռŵͼķҧ¹֧ͧäǺä鹰ҹ 㹡óչä鹰ҹ (ҡ÷ͺ͹÷ͧ) ֧繵÷١Ǻͷ¡ҵ (Covariate) 㹡Ź͡ҡṹ¢ͧõ (ķҧ¹) ѧͧṹ¢ͧ (鹰ҹ) ա ԸաҧʶԵԪԴ¡ ûǹ (Analysis of Covariance : ANCOVA) Ըչ繡÷ͺᵡҧҧ·Ѻ (Adjusted mean) 繡ûѺѹҧ¢ͧ Ѻ¢ͧ繤·ŷԴҡ觷Դѹ͹÷ͧ͡ ҼŢͧûǹչӤѭҧʶԵʴդᵡҧѹҧ 㹡óշդҡ 2 еͧӡ÷ͺʹդ·ѺǤ㴺ҧ ᵡҧѹ Ըա÷鷴ͺѧ(Post-hoc comparison) ͧûǹ ÷ͺººԧ͹ǡѺ÷ͺѧûǹ


        Ẻ֡Ѵ    

1. ʶԵԷ㹡͸Ժµúҧ͸Ժ

2. ʶԵԷ㹡÷ͺص԰ҹúҧ͸Ժ

3. ʶԵ Z-test Ѻ t-test ըش㹡ҧ ͹㹡
ҧѹҧ

4. ʶԵ t-test Pooled Variance Ѻ t-test Separate Variance
͹㹡ҧѹҧ

5.ʶԵ t-test ó Independent Ѻ ANOVA ͹㹡ҧѹҧ


 
 
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