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The major tools of statistical data analysis were descriptive statistics; correlation statistics; reliability analysis using Cronbach’s co-efficient alpha; measures of validity, including factor analysis; multiple analyses of variance (MANVOA); and linear regression.

3.6.1. Descriptive Statistics

Descriptive statistics were used to describe the sample characteristics. Descriptive statistics provide a description of the data through percentages, modes, means, frequency distribution, kurtosis, standard error of the mean and standard deviations (Bohrnstedt & Knoke, 1988, p. 492). Descriptive statistics entail the use of tables, graphs and numerical techniques to condense and summarise data (Burns, 2000, p. 43).

3.6.2. Correlation

The most common correlation coefficient is Pearson product-moment correlation coefficient, commonly symbolized as r. The Pearson correlation can range from -1.00 to +1.00. A score closer to negative or positive 1.00 is an indication of stronger relationship and the positive and negative signs provide information about the direction of the relationship. Correlation was used to assess the association and the strength of the relationship between the dimensions of relationship quality (paternal contact, connection and communication).

3.6.3. Reliability

Assuming that what is being measured does not change, a measure is considered reliable if it repeatedly and consistently produces the same results. One of the specific methods involved in the assessment of reliability is internal consistency reliability (Burns, 2000, p. 341; Cozby, 2001, p. 94). Internal consistency estimates the reliability of an instrument administered to a group of people on one occasion.

Two indicators of internal consistency are split–half reliability and Cronbach’s α (Cronbach, 1951). Cronbach’s α is a more efficient mathematical equivalent of the average of all possible split-half estimates (Burns, 2000, p.343). Cronbach’s α was chosen to measure the internal consistency for the study instruments due to the limited access to learners and the efficacy of using it as a method of reliability. For internal consistency, an α of 0.70 and above is desirable (Santos, 1999) and the item- total correlation should be between 0.20–0.80, as higher than 0.80 is an indication of a redundant item (de Wit, Pouwer, Gemke, Delemarre-van der Waal & Snoek, 2007).

The internal consistency of each measure used in this study is presented in, the following chapter, Chapter Four.

3.6.4. Validity

The validity of an instrument is established when the instrument is shown to measure what it intended to measure (Cozby, 2001, p. 96). Validity may be measured through a variety of methods with the simplest method being that of face validity. Face validity is the principle that the measure appears to reflect the construct being measured. However, this is not sufficient to conclude that a measure is valid as appearance is not a good indicator of accuracy. Foxcroft and Roodt (2005) assert that a more stringent way of measuring validity would be to use the methodology of construct validity. Another type of validity is nomological validity, which is defined as ‘the degree to which predictions from a theoretical network containing the concept under scrutiny are confirmed’ (Netemeyer, Bearden & Sharma, 2003, p. 13). It uses correlation to evaluate the degree to which measures that are theoretically related are also empirically related.

3.6.5. Factor Analysis

Factor analysis was used for assessing the validity of the Paternal Quality Contact Time Scale. It is a ‘statistical technique for analysing the interrelationships of variables’ (Foxcroft & Roodt, 2005, p. 35). The objective is to determine the dimensions of a set of variables. By doing so the common variance between the dimensions are identified and variables that are moderately to highly correlated with each other are grouped together to form a factor (Burns, 2000, p. 272).

3.6.6. Multivariate Analysis of Variance

Multivariate Analysis of Variance (MANOVA) is an extension of the Analysis of Variance (ANOVA). ANOVA also called the F-test, is a statistical method for comparing two or more groups in terms of another variable and testing the significance of the observed differences (Pretorius, 2007, p. 214). A MANOVA is applicable when there is ‘one independent variable with more than two levels and several dependant variables’ (Pretorius, 2007, p. 299). An important aspect of a measuring instrument is that of its variance (Huysamen, 1980). If each person obtained the same score on a test, this would yield zero variance, and the test would be of no use as it would not be able to discriminate between individuals who have varying amounts of the attributes being measured. The effect of father residential status on the dimensions of contact, communication and connection were evaluated using a MANOVA.

3.6.7. Post Hoc Tests

Because of the number of analyses that typically occur in an MANOVA, post hoc tests were used to expose Type I and Type II errors that may have occurred during the analyses. Type I error is the mistake of falsely rejecting the null hypothesis when it is true (Burns, 2000, p. 117). However, sometimes the significance level has been set too high and the risk of falsely accepting the null hypothesis is more than probable. In this instance, there would be a risk of possibly committing a Type II error (Burns, 2000, p. 116).

A number of post hoc tests have been developed that attempt to minimize Type I error and the statistical power of multivariate analyses. The most commonly used post hoc tests include the Bonferonni Correction, the Scheffé test, and the Tukey honestly significant difference (HSD) test (Meyers, Gamst & Guarino, 2006, p. 427).

The Bonferonni Correction is a multiple-comparison correction, used when several dependent or independent statistical analyses are being performed simultaneously. To reduce the possibility of a lot of spurious positives the alpha level is lowered to account for the number of comparisons being performed. The adjustment entails dividing the alpha level (usually .05) by the number of dependent variables (Meyers et al., 2006, p. 373). The Scheffé test is a conservative procedure which conducts ‘a simultaneous pairwise comparison of all means using the F distribution’ (Meyers, et al., 2006, p. 427). Similarly, the Tukey HSD considers all pairwise comparisons but uses the standard error of the mean and the range distribution (Meyers et al., 2006).

3.6.8. Multiple Linear Regression

The data presented contains multiple continuous independent variables (namely, father–son contact, father–son communication apprehension and father–son connection) and multiple continuous dependant variables (all sub-categories measured on the POSIT). Multiple regression involves several variables on one side of the equation, which combine to form one single predictor variable and a single variable on the other side. The highest correlation is sought between the predictor variable and the single variable (Tabachnick & Fidell, 1996, p.195). It is therefore a method of investigating the individual and collective contributions of several

independent variables on the dependant variable (Pretorius, 2007, p. 253). Multiple regressions were used to investigate the effect of father-son relationship quality and father residential status on adolescent risk outcomes.