醫學統計與R語言:Cronbach's α Coefficient

 

微信公眾號：醫學統計與R語言

簡介

Cronbach's alpha  is a function of the number of items in a test, the average covariance between item-pairs, and the variance of the total score.It was first named alpha by Lee Cronbach in 1951, as he had intended to continue with further coefficients. The measure can be viewed as an extension of the Kuder–Richardson Formula 20 (KR-20), which is an equivalent measure for dichotomous items. Alpha is not robust against missing data. Several other Greek letters have been used by later researchers to designate other measures used in a similar context. Somewhat related is the average variance extracted (AVE).
克龍巴赫α係數主要用於評價量表內部條目間一致性信度的指標，適用於觀測分數為定距變量的情形。如果採用二值記分(1 , 0), 則可使用α係數公式的簡化形式—KR20公式進行信度估計(當條目記分為二分類時，α係數與KR20值一致)。若採用多列等級記分則可以採用肯德爾和諧係數(Kendall coefficient of co nco rdance , W 係數)作為信度的估計指標（W係數為評分者信度，有學者認為此兩者係數並不等價，詳見文獻：「等級評價的信度係數及其與和藹係數的關係」。然而，量表評分通常為定距變量，實際評價中仍多採用α係數）。

Example

10名醫生對8個條目（a、b、c、d、e、f、g）的評分

Syntax

- 輸入：

item <- read.csv("item.csv",header=T)
item

- 結果：

  a b c d e f g h
1  4 6 5 5 5 3 5 4
2  2 5 4 5 5 3 4 2
3  3 5 3 6 4 1 3 1
4  5 6 4 7 5 5 6 2
5  3 6 5 6 4 4 6 3
6  3 3 3 2 1 1 2 1
7  4 6 6 6 5 6 5 1
8  7 6 2 6 4 5 6 4
9  2 3 2 2 7 4 7 2
10 2 3 4 4 5 6 3 1

- 方法一：輸入1

install.packages("psych")
library(psych)
alpha(item)

- 結果1：

Reliability analysis   
Call: alpha(x = item)

  raw_alpha std.alpha G6(smc) average_r S/N ase mean   sd median_r
      0.79      0.79    0.96      0.32 3.8 0.1    4 0.98     0.31

 lower alpha upper     95% confidence boundaries
0.59 0.79 0.99 

 Reliability if an item is dropped:
  raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
a      0.77      0.77    0.92      0.33 3.4    0.110 0.060  0.31
b      0.73      0.72    0.87      0.27 2.6    0.129 0.060  0.27
c      0.80      0.81    0.92      0.37 4.2    0.099 0.061  0.37
d      0.74      0.74    0.91      0.29 2.9    0.123 0.069  0.31
e      0.79      0.80    0.96      0.36 3.9    0.100 0.061  0.37
f      0.77      0.77    0.92      0.32 3.3    0.113 0.085  0.37
g      0.74      0.74    0.94      0.29 2.9    0.122 0.073  0.27
h      0.77      0.77    0.96      0.32 3.3    0.112 0.072  0.31

 Item statistics 
   n raw.r std.r r.cor r.drop mean  sd
a 10  0.61  0.61  0.61   0.46  3.5 1.6
b 10  0.82  0.84  0.86   0.75  4.9 1.4
c 10  0.39  0.41  0.40   0.24  3.8 1.3
d 10  0.75  0.75  0.76   0.63  4.9 1.7
e 10  0.49  0.47  0.43   0.32  4.5 1.5
f 10  0.67  0.64  0.63   0.51  3.8 1.8
g 10  0.75  0.74  0.73   0.63  4.7 1.6
h 10  0.59  0.62  0.58   0.48  2.1 1.2

Non missing response frequency for each item
    1   2   3   4   5   6   7 miss
a 0.0 0.3 0.3 0.2 0.1 0.0 0.1    0
b 0.0 0.0 0.3 0.0 0.2 0.5 0.0    0
c 0.0 0.2 0.2 0.3 0.2 0.1 0.0    0
d 0.0 0.2 0.0 0.1 0.2 0.4 0.1    0
e 0.1 0.0 0.0 0.3 0.5 0.0 0.1    0
f 0.2 0.0 0.2 0.2 0.2 0.2 0.0    0
g 0.0 0.1 0.2 0.1 0.2 0.3 0.1    0
h 0.4 0.3 0.1 0.2 0.0 0.0 0.0    0

-方法二： 輸入2：

install.packages("ltm") 
library(ltm)
cronbach.alpha(item,CI=T, probs = c(0.025, 0.975))

- 結果2：

Cronbach's alpha for the 'item' data-set

Items: 8
Sample units: 10
alpha: 0.79

Bootstrap 95% CI based on 1000 samples
 2.5% 97.5% 
0.389 0.922 

-方法三： 輸入3：

install.packages("DescTools")
library(DescTools)
CronbachAlpha(item,conf.level = 0.95,cond=T)

- 結果3：

$unconditional
Cronbach Alpha         lwr.ci         upr.ci 
     0.7901492      0.7127220      0.8530935 

$condCronbachAlpha
  Item Cronbach Alpha    lwr.ci    upr.ci
1    1      0.7729402 0.6812784 0.8457318
2    2      0.7297053 0.6205901 0.8163573
3    3      0.8017265 0.7216854 0.8652897
4    4      0.7438579 0.6404558 0.8259727
5    5      0.7933635 0.7099464 0.8596077
6    6      0.7664862 0.6722190 0.8413468
7    7      0.7445693 0.6414545 0.8264561
8    8      0.7715340 0.6793045 0.8447763

cond:   logical. If set to TRUE, alpha is additionally calculated for the dataset with each item left out.