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An examination of two methods of forming confidence intervals for coefficient alpha Barchard, Kimberly Anne
Abstract
Coefficient alpha (Cronbach, 1951) is a commonly used measure of reliability. Feldt (1965) and Hakstian and Whalen (1976) developed methods of forming confidence intervals for coefficient alpha. In this thesis, three issues related to these confidence intervals were examined. First, their performance under fixed and random sampling of conditions (e.g., items, raters) was compared. When conditions were fixed, the confidence intervals were accurate for the kinds of data studied. When conditions were random, as few as 77% of the .95 confidence intervals included the parameter. Second, some researchers have recently questioned what constitute the necessary assumptions of these confidence intervals. In response, it was shown in this thesis that, contrary to what has been claimed, sphericity is not sufficient, although compound symmetry is. Compound symmetry may, in fact, be necessary, but no definitive proof of this can be offered at this time. Third, the performance of the two confidence intervals under random sampling of conditions was explored in more detail. Neither the type of confidence interval used nor heterogeneity of conditions means had any effect on the performance of the confidence intervals. However, heterogeneity of variances reduced the proportion of confidence intervals including the population value. This effect was most pronounced when the population value was high (.90) and when the number of conditions was low (5). The following conclusions were reached. Researchers conducting Monte Carlo studies of coefficient alpha should simulate the type of sampling that they are most interested in, as results depend on the type of sampling used. The Feldt (1965) and Hakstian and Whalen (1976) confidence intervals are precise when conditions are fixed; however, when conditions are random and variances heterogeneous, these intervals should be used with caution, especially if the data contain fewer than 20 conditions. The two types of confidence intervals perform very similarly, and hence the choice of method is left to the researcher. Lastly, a call is made for more robust procedures to be developed, and one possible approach to such a robust procedure has been identified.
Item Metadata
Title |
An examination of two methods of forming confidence intervals for coefficient alpha
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1995
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Description |
Coefficient alpha (Cronbach, 1951) is a commonly used measure of reliability. Feldt
(1965) and Hakstian and Whalen (1976) developed methods of forming confidence
intervals for coefficient alpha. In this thesis, three issues related to these confidence
intervals were examined. First, their performance under fixed and random sampling of
conditions (e.g., items, raters) was compared. When conditions were fixed, the
confidence intervals were accurate for the kinds of data studied. When conditions were
random, as few as 77% of the .95 confidence intervals included the parameter. Second,
some researchers have recently questioned what constitute the necessary assumptions of
these confidence intervals. In response, it was shown in this thesis that, contrary to what
has been claimed, sphericity is not sufficient, although compound symmetry is.
Compound symmetry may, in fact, be necessary, but no definitive proof of this can be
offered at this time. Third, the performance of the two confidence intervals under random
sampling of conditions was explored in more detail. Neither the type of confidence
interval used nor heterogeneity of conditions means had any effect on the performance of
the confidence intervals. However, heterogeneity of variances reduced the proportion of
confidence intervals including the population value. This effect was most pronounced
when the population value was high (.90) and when the number of conditions was low
(5).
The following conclusions were reached. Researchers conducting Monte Carlo studies of
coefficient alpha should simulate the type of sampling that they are most interested in, as
results depend on the type of sampling used. The Feldt (1965) and Hakstian and Whalen
(1976) confidence intervals are precise when conditions are fixed; however, when
conditions are random and variances heterogeneous, these intervals should be used with
caution, especially if the data contain fewer than 20 conditions. The two types of confidence intervals perform very similarly, and hence the choice of method is left to the
researcher. Lastly, a call is made for more robust procedures to be developed, and one
possible approach to such a robust procedure has been identified.
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Extent |
5765041 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-01-31
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0099003
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1995-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.