The internal consistency of each multi-item measure was assessed using Cronbach’s Alpha Reliability Coefficient. These alpha reliability coefficients are computed from the mean score of correlations between the multiple items within a measure (Coakes & Steed, 1997). They provide an indication of the extent to which scores are consistent and reproducible. They also indicate how much variation in a score is ‘real or truth’ as opposed to chance or random error (Ware, et al. 1994). The recommended alpha reliability estimate for the inclusion of a measure in group-level analyses is .70 (Nunnally & Bernstein, 1994). The reliability coefficients, which were calculated separately for males and females, are presented in Table 10. Reliability coefficients from normative samples are also included for comparative purposes.
Table 10. Reliability Coefficients of Participants and Normative Samples. Cronbach’s Alpha Coefficients
Participants Normative
Multi-Item Measures Males Females Total Sample
α (n) α (n) SF-36 Summary Measures
• Physical Health .92 (34) .89 (116) .93
• Mental Health .82 (34) .83 (116) .88
Severity of Physical Symptoms .91 (34) .98 (120) †
SIPI Daydreaming Measures
• Positive Constructive .86 (34) .80 (117) .80
• Guilt & Fear of Failure .76 (34) .80 (119) .80
• Poor Attentional Control .72 (34) .76 (119) .81
Social Desirability Scale .66 (26) .76 ( 57) .54
Normative: Available only for total sample: SF-36 n = 18468; SIPI n = 1196; SSDS n = 49. † Alpha coefficient not available for severity of physical symptoms.
As shown in Table 10, reliability coefficients recorded by samples of males and females on the measures ranged from .72 to .98. The exception was social desirability. The male sample recorded a reliability coefficient (α = .66) that was marginally lower than the recommended figure of .70. This reliability coefficient is, nevertheless, higher than that recorded by college students (α = .54) during the development of the measure (Greenwald & Satow, 1970). The remaining reliability coefficients recorded by the samples of males and females were similar to those of normative samples.
Statistical Assumptions of Multivariate Analysis
Each measure was assessed for statistical assumptions underlying multivariate analysis prior to statistical analyses. This assessment was performed separately for males and females. It included the detection of univariate outliers and the evaluation of score normality. A summarised description of the results of data screening is presented here. A complete output table of these results is available in Appendix B.
Identification of Univariate Outliers: Univariate outliers were identified for each measure using case-wise plots of cases outside + 3.0 standard deviations. There were small numbers of univariate outliers on most measures: no more than four percent of scores were outliers for males and four percent for females on any one
measure. No participant recorded more than two univariate outliers on the combination of measures. The pattern of univariate outliers appeared random for males and females. There were measures with no univariate outliers (65%). The majority of measures (86%) contained no more than one univariate outlier.
Modification of Univariate Outliers: There are no standard guidelines as to the number of univariate outliers acceptable per measure for a sample of the present size. This is despite the growing acceptance that small numbers of extreme scores occur in most research populations under investigation (Tabachnick & Fidell, 2001). The small percentages of outliers identified per measure in the present study are much lower than the 10 percent critical value suggested recently by Tabachnick and Fidell (2001).
The inclusion of identified univariate outliers was considered important to the present study. These outliers, although different from most sample participants, were drawn directly from the intended research population. They represent legitimate observations, as it is not uncommon for patients in general practice to report a wide spectrum of health states (for example, very poor health through to excellent health; Britt et al. 2001; Sayer et al. 2000). The identified outliers were, therefore, retained in the data set. They were re-scored, however, to reduce their distributional influence by being assigned a score that was one unit larger (or smaller) than the next most extreme score in the distribution (Hair, Anderson, Tatham, & Black, 1995). There were no ‘second order’ outliers following re-scoring of initial outliers.
Normality of Score Distribution: The assumption of normality for each measure was assessed using Kolmogorov-Smirnov Statistic for females (sample size > 50) and Shapiro-Wilks Statistic for males (sample size < 50). These statistics identified three measures that were significantly skewed for males and females: severity of symptoms, frequency of daydreaming, and social desirability. The physical health of males, but not females, was also significantly skewed. A description of the direction of skewness is presented below for each non-normal distribution.
Severity of Physical Symptoms: Direction of skewness indicated that most males and
females reported physical symptoms of ‘minor severity’. Almost all males (91%) and females (94%) reported physical symptoms that were ‘not at all’ or ‘only a little’ severe. No participant reported physical symptoms with ‘a great deal’ of severity.
Frequency of Daydreaming: The distribution of scores were skewed towards less
frequent daydreaming. Most males (70%) and females (55%) reported daydreaming ‘no more than once’ in the previous one-week. A minority of males (11%) and females (6%) reported daydreaming ‘many times each day’.
Social Desirability: Direction of skewness indicated that most males and females
provided socially acceptable responses. Most males (54%) and females (72%) recorded the three highest possible scores (that is, scores ≥ 4). Only a minority of males (4%) and females (5%) did not provide a socially desirable response.
Physical Health: The distribution of scores for male physical health was skewed
towards more favourable states of health. A cluster of scores was located at the positive tail of the distribution representing greater freedom from physical limitations. This cluster accounted for near 45 percent of all scores.
Management of ‘Non-Normal’ Score Distributions: Measures that were significantly skewed were not transformed. This decision was formed for three reasons. The first reason was that multivariate statistics to be performed on the research data report findings on the basis of the F-statistic. The F-statistic is said to be
robust to violations of normality provided that measures are unaffected by the presence of outliers (Thorne & Slane, 1997). It has been argued more recently that even large deviations from normality do not significantly alter the conclusions derived from the ‘F-statistic’ (Tabachnick & Fidell, 2001). The present study assumed in light
of these reports that the validity of statistical findings would not be compromised by the inclusion of non-normal distributions.
The second reason for non-transformation was that researchers have expressed reluctance in transforming scores of standardised measures (Tabachnick & Fidell, 2001). The meaning attached to the scores of measures in the study would have been distorted had they been transformed. This distortion would have hindered the interpretation of comparisons between groups of participants on the measures, particularly if different transformations were performed for males and females. The transformation of scores would have also compromised the interpretation of comparisons between the present sample and normative samples on the measures.
The third reason for non-transformation was that most measures in the present study are non-normal distributions in the general population (Stevenson, 1996; Ware
et al. 1994). These measures have not been transformed prior to statistical analysis in previous studies (McHorney et al. 1994; McHorney & Ware, 1995; Shadbolt 1996; Walker et al. 1996). It has further been observed that most measures, of health in particular, remain significantly skewed even after transformation (Stevenson, 1996).