11.3 Internal Consistency Reliability

The internal consistency is about the coherency of a set of items with respect to their intercorrelations. Cronbach’s alpha is a measure of internal consistency. Alpha consistency is the level the item correlate with the test as a whole. Usually alpha value should be at least 0.7 to be considered acceptable.

alpha(irisN,check.keys = TRUE)
## 
## Reliability analysis   
## Call: alpha(x = irisN, check.keys = TRUE)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N    ase mean   sd median_r
##       0.81      0.85    0.94      0.59 5.9 0.0084  3.9 0.86     0.62
## 
##     95% confidence boundaries 
##          lower alpha upper
## Feldt     0.76  0.81  0.86
## Duhachek  0.80  0.81  0.83
## 
##  Reliability if an item is dropped:
##              raw_alpha std.alpha G6(smc) average_r  S/N alpha se  var.r med.r
## Sepal.Length      0.71      0.81    0.86      0.59  4.2   0.0163 0.1076  0.43
## Sepal.Width-      0.88      0.96    0.96      0.88 22.9   0.0067 0.0054  0.87
## Petal.Length      0.72      0.70    0.77      0.43  2.3   0.0316 0.1261  0.37
## Petal.Width       0.68      0.73    0.86      0.47  2.7   0.0162 0.1437  0.43
## 
##  Item statistics 
##                n raw.r std.r r.cor r.drop mean   sd
## Sepal.Length 150  0.89  0.84  0.83   0.81  5.8 0.83
## Sepal.Width- 150  0.46  0.57  0.44   0.35  4.9 0.44
## Petal.Length 150  0.99  0.98  1.00   0.98  3.8 1.77
## Petal.Width  150  0.96  0.94  0.96   0.94  1.2 0.76

The check.keys=True allows us to examine if a measurement correlates negatively with the overall score, which needs to be inverted before i can contribute to the overall scores if so. In this case, alpha() inverts the sign of Sepal.Width and then calculates the alpha value. The overall alpha is 0.81 and it increases if Sepal.Width is dropped.

Neither the principal() procedure nor the alpha() procedure is an inferential statistical method (although principal() did have a goodness- of-fit test). Both of these methods are exploratory and descriptive.