## 例2.6 Cronbachのアルファ係数の計算

```*------------------- Fish Measurement Data ----------------------*
| The data set contains 35 fish from the species Bream caught in |
| Finland's lake Laengelmavesi with the following measurements:  |
| Weight   (in grams)                                            |
| Length3  (length from the nose to the end of its tail, in cm)  |
| HtPct    (max height, as percentage of Length3)                |
| WidthPct (max width,  as percentage of Length3)                |
*----------------------------------------------------------------*;
data Fish1 (drop=HtPct WidthPct);
title 'Fish Measurement Data';
input Weight Length3 HtPct WidthPct @@;
Weight3= Weight**(1/3);
Height=HtPct*Length3/100;
Width=WidthPct*Length3/100;
datalines;
242.0 30.0 38.4 13.4     290.0 31.2 40.0 13.8
340.0 31.1 39.8 15.1     363.0 33.5 38.0 13.3
430.0 34.0 36.6 15.1     450.0 34.7 39.2 14.2
500.0 34.5 41.1 15.3     390.0 35.0 36.2 13.4
450.0 35.1 39.9 13.8     500.0 36.2 39.3 13.7
475.0 36.2 39.4 14.1     500.0 36.2 39.7 13.3
500.0 36.4 37.8 12.0        .  37.3 37.3 13.6
600.0 37.2 40.2 13.9     600.0 37.2 41.5 15.0
700.0 38.3 38.8 13.8     700.0 38.5 38.8 13.5
610.0 38.6 40.5 13.3     650.0 38.7 37.4 14.8
575.0 39.5 38.3 14.1     685.0 39.2 40.8 13.7
620.0 39.7 39.1 13.3     680.0 40.6 38.1 15.1
700.0 40.5 40.1 13.8     725.0 40.9 40.0 14.8
720.0 40.6 40.3 15.0     714.0 41.5 39.8 14.1
850.0 41.6 40.6 14.9    1000.0 42.6 44.5 15.5
920.0 44.1 40.9 14.3     955.0 44.0 41.1 14.3
925.0 45.3 41.4 14.9     975.0 45.9 40.6 14.7
950.0 46.5 37.9 13.7
;
```

```ods graphics on;
title 'Fish Measurement Data';
proc corr data=fish1 nomiss alpha plots=matrix;
var Weight3 Length3 Height Width;
run;
ods graphics off;
```

ALPHAオプションを指定すると、指定の分析変数を使ってCronbachのアルファ係数が計算されます。

 Fish Measurement Data

The CORR Procedure

4 Variables: Weight3 Length3 Height Width

Simple Statistics
variable N Mean Std Dev Sum Minimum Maximum
Weight3 34 8.44751 0.97574 287.21524 6.23168 10.00000
Length3 34 38.38529 4.21628 1305 30.00000 46.50000
Height 34 15.22057 1.98159 517.49950 11.52000 18.95700
Width 34 5.43805 0.72967 184.89370 4.02000 6.74970

Pearson Correlation Coefficients, N = 34
Prob > |r| under H0: Rho=0
Weight3 Length3 Height Width
Weight3
 1.00000
 0.96523 <.0001
 0.96261 <.0001
 0.92789 <.0001
Length3
 0.96523 <.0001
 1.00000
 0.95492 <.0001
 0.92171 <.0001
Height
 0.96261 <.0001
 0.95492 <.0001
 1.00000
 0.92632 <.0001
Width
 0.92789 <.0001
 0.92171 <.0001
 0.92632 <.0001
 1.00000

このデータセットには1種類の魚の情報のみが含まれているため、すべての変数には高い相関があります。ALPHAオプションを指定すると、CORRプロシジャは、出力2.6.3に示すようなCronbachのアルファ係数を計算します。Cronbachのアルファ係数は、未加工の変数と標準化変数に関する信頼係数の下限を表します。変数は共通のエンティティを測定するため、アルファ係数では正の相関が必要となります。

Cronbach Coefficient Alpha
Variables Alpha
Raw 0.822134
Standardized 0.985145

Cronbach Coefficient Alpha with Deleted Variable
Deleted
Variable
Raw Variables Standardized Variables
Correlation
with Total
Alpha Correlation
with Total
Alpha
Weight3 0.975379 0.783365 0.973464 0.977103
Length3 0.967602 0.881987 0.967177 0.978783
Height 0.964715 0.655098 0.968079 0.978542
Width 0.934635 0.824069 0.937599 0.986626