rstatisticscorrelationpsych

`psych::alpha`- detailed interpretation of the output


I am aware that Cronbach's alpha has been extensively discussed here and elsewhere, but I cannot find a detailed interpretation of the output table.

psych::alpha(questionaire)

Reliability analysis   
Call: psych::alpha(x = diagnostic_test)

  raw_alpha std.alpha G6(smc) average_r S/N   ase mean   sd median_r
      0.69      0.73       1      0.14 2.7 0.026  0.6 0.18     0.12

 lower alpha upper     95% confidence boundaries
0.64 0.69 0.74 

 Reliability if an item is dropped:
        raw_alpha std.alpha G6(smc) average_r S/N alpha se  var.r med.r
Score1       0.69      0.73    0.86      0.14 2.7    0.027 0.0136  0.12
Score2       0.68      0.73    0.87      0.14 2.7    0.027 0.0136  0.12
Score3       0.69      0.73    0.87      0.14 2.7    0.027 0.0136  0.12
Score4       0.67      0.72    0.86      0.14 2.5    0.028 0.0136  0.11
Score5       0.68      0.73    0.87      0.14 2.7    0.027 0.0134  0.12
Score6       0.69      0.73    0.91      0.15 2.7    0.027 0.0138  0.12
Score7       0.69      0.73    0.85      0.15 2.7    0.027 0.0135  0.12
Score8       0.68      0.72    0.86      0.14 2.6    0.028 0.0138  0.12
Score9       0.68      0.73    0.92      0.14 2.7    0.027 0.0141  0.12
Score10      0.68      0.72    0.90      0.14 2.6    0.027 0.0137  0.12
Score11      0.67      0.72    0.86      0.14 2.5    0.028 0.0134  0.11
Score12      0.67      0.71    0.87      0.13 2.5    0.029 0.0135  0.11
Score13      0.67      0.72    0.86      0.14 2.6    0.028 0.0138  0.11
Score14      0.68      0.72    0.86      0.14 2.6    0.028 0.0138  0.11
Score15      0.67      0.72    0.86      0.14 2.5    0.028 0.0134  0.11
Score16      0.68      0.72    0.88      0.14 2.6    0.028 0.0135  0.12
score        0.65      0.65    0.66      0.10 1.8    0.030 0.0041  0.11

 Item statistics 
          n raw.r std.r r.cor r.drop mean   sd
Score1  286  0.36  0.35  0.35   0.21 0.43 0.50
Score2  286  0.37  0.36  0.36   0.23 0.71 0.45
Score3  286  0.34  0.34  0.34   0.20 0.73 0.44
Score4  286  0.46  0.46  0.46   0.33 0.35 0.48
Score5  286  0.36  0.36  0.36   0.23 0.73 0.44
Score6  286  0.29  0.32  0.32   0.18 0.87 0.34
Score7  286  0.33  0.32  0.32   0.18 0.52 0.50
Score8  286  0.42  0.41  0.41   0.28 0.36 0.48
Score9  286  0.32  0.36  0.36   0.22 0.90 0.31
Score10 286  0.37  0.40  0.40   0.26 0.83 0.37
Score11 286  0.48  0.47  0.47   0.34 0.65 0.48
Score12 286  0.49  0.49  0.49   0.37 0.71 0.46
Score13 286  0.46  0.44  0.44   0.31 0.44 0.50
Score14 286  0.44  0.43  0.43   0.30 0.43 0.50
Score15 286  0.48  0.47  0.47   0.35 0.61 0.49
Score16 286  0.39  0.39  0.39   0.26 0.25 0.43
score   286  1.00  1.00  1.00   1.00 0.60 0.18
Warning messages:
1: In cor.smooth(r) : Matrix was not positive definite, smoothing was done
2: In cor.smooth(R) : Matrix was not positive definite, smoothing was done
3: In cor.smooth(R) : Matrix was not positive definite, smoothing was done

as far as I know, r.cor stand for the total-item correlation, or biserial correlation. I have seen that this is usually interpreted together with the corresponding p-value.

1. What is the exact interpretation of r.cor and r.drop?

2. How can the p-value be calculated ?


Solution

  • 1. Although this is more of a question for Crossvalidated, here is the detailed explanation of ‘Item statistics’ section:

    raw.r: correlation between the item and the total score from the scale (i.e., item-total correlations); there is a problem with raw.r, that is, the item itself is included in the total—this means we’re correlating the item with itself, so of course it will correlate (r.cor and r.drop solve this problem; see ?alpha for details)

    r.drop: item-total correlation without that item itself (i.e., item-rest correlation or corrected item-total correlation); low item-total correlations indicate that that item doesn’t correlate well with the scale overall

    r.cor: item-total correlation corrected for item overlap and scale reliability mean and sd: mean and sd of the scale if that item is dropped

    2. You should not use the p-values corresponding to these correlation coefficient to guide your decisions. I would suggest not to bother calculating them.