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 ?
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.