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.

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Below is the unformatted table of contents.

Table of Contents

Overview	6
Key Concepts and Terms	7
Scores	7
Number of scale items	7
Models	7
Triangulation	8
Calibration	8
Internal consistency reliability	9
Cronbach's alpha	9
Overview	9
Interpretation	9
Cut-off criteria	9
Formula	9
Number of items	10
Cronbach's alpha in SPSS	10
Example 1	10
Alpha if deleted	10
Item-total correlation	11
R-squared	11
Negative alphas	11
KR2	11
Example 2	12
Standardized item alpha	12
Cronbach's alpha in SAS	13
SAS syntax	13
SAS output	13
Other internal consistency reliability measures	14
Ordinal reliability alpha	14
Raykov's reliability rho (?)	15
Armor's reliability theta	15
Spearman's reliability rho	15
Split-half reliability	16
Split-half reliability in SPSS	16
Overview	16
SPSS menu selections	16
Spearman-Brown split-half reliability coefficient	17
Guttman split-half reliability coefficient	19
Guttman's lower bounds (lambda 1-6)	19
Split-half reliability in SAS	20
Odd-Even Reliability	20
Overview	20
Test-retest reliability	22
Overview	22
Inter-rater reliability	23
Overview	23
Cohen's kappa	23
Kappa in SPSS	23
Example	24
Interpretation	24
Weighted Kappa	25
Intraclass correlation (ICC)	25
Example	25
Sample size: ICC vs. Pearson r	26
Data setup	26
Interpretation	27
Obtaining ICC in SPSS	28
Single versus average measures	28
ICC Models	29
ICC use in other contexts	31
Assumptions	31
Additivity	31
Independence	32
Uncorrelated error	32
Consistent coding	33
Random assignment of subjects	33
Equivalency of forms	33
Equal variances	33
Similar difficulty of items	34
Same assumptions as for correlation	34
Frequently Asked Questions	34
How is reliability related to validity?	34
How is Cronbach's alpha related to factor analysis?	34
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?	36
What is the derivation of intraclass correlation coefficients?	37
What are Method 1 and Method 2 in the SPSS RELIABILITY module?	38
Bibliography	38