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Researchers must demonstrate instruments are reliable since without reliability, research results using the instrument are not replicable, and replicability is fundamental to the scientific method. Reliability is the correlation of an item, scale, or instrument with a hypothetical one which truly measures what it is supposed to. Since the true instrument is not available, reliability is estimated in one of four ways:
"	Internal consistency: Estimation based on the correlation among the variables comprising the set (typically, Cronbach's alpha)
"	Split-half reliability: Estimation based on the correlation of two equivalent forms of the scale (typically, the Spearman-Brown coefficient)
"	Test-retest reliability: Estimation based on the correlation between two (or more) administrations of the same item, scale, or instrument for different times, locations, or populations, when the two administrations do not differ on other relevant variables (typically, the Spearman Brown coefficient)
"	Inter-rater reliability: Estimation based on the correlation of scores between/among two or more raters who rate the same item, scale, or instrument (typically, intraclass correlation, of which there are six types discussed below).
These four reliability estimation methods are not necessarily mutually exclusive, nor need they lead to the same results. All reliability coefficients are forms of correlation coefficients, but there are multiple types discussed below, representing different meanings of reliability and more than one might be used in single research setting.

Overview	7
Key Concepts and Terms	8
Scores	8
Number of scale items	8
Models	8
Triangulation	9
Calibration	9
Internal consistency reliability	10
Cronbach's alpha	10
Overview	10
Interpretation	10
Cut-off criteria	10
Formula	10
Number of items	11
Cronbach's alpha in SPSS	11
Example 1	11
Alpha if deleted	11
Item-total correlation	12
R-squared	12
Negative alphas	12
KR2	12
Example 2	13
Standardized item alpha	13
Cronbach's alpha in SAS	14
SAS syntax	14
SAS output	14
Other internal consistency reliability measures	15
Ordinal reliability alpha	15
Raykov's reliability rho (?)	16
Armor's reliability theta	16
Spearman's reliability rho	16
Split-half reliability	17
Split-half reliability in SPSS	17
Overview	17
SPSS menu selections	17
Spearman-Brown split-half reliability coefficient	18
Guttman split-half reliability coefficient	20
Guttman's lower bounds (lambda 1-6)	20
Split-half reliability in SAS	21
Odd-Even Reliability	21
Overview	21
Test-retest reliability	23
Overview	23
Inter-rater reliability	24
Overview	24
Cohen's kappa	24
Kappa in SPSS	24
Example	25
Interpretation	25
Weighted Kappa	26
Intraclass correlation (ICC)	26
Example	26
Sample size: ICC vs. Pearson r	27
Data setup	27
Interpretation	28
Obtaining ICC in SPSS	29
Single versus average measures	29
ICC Models	30
ICC use in other contexts	32
Assumptions	32
Additivity	32
Independence	33
Uncorrelated error	33
Consistent coding	34
Random assignment of subjects	34
Equivalency of forms	34
Equal variances	34
Similar difficulty of items	35
Same assumptions as for correlation	35
Frequently Asked Questions	35
How is reliability related to validity?	35
How is reliability related to attenuation in correlation?	35
How should a negative reliability coefficient be interpreted?	36
What is Cochran's Q test of equality of proportions for dichotomous items?	37
What is the derivation of intraclass correlation coefficients?	37
What are Method 1 and Method 2 in the SPSS RELIABILITY module?	38
Bibliography	39