Statistical Tests Employed Within the Current Study

4.2.2.1 Descriptive Statistics

“Descriptive statistics do what they say: they describe, so that researchers can then analyse and interpret what these descriptions mean” (Cohen, Manion and Morrison, 2011; 622). Descriptive statistics should be reported as they clearly communicate results to the reader (Wright, 2003; 133), and contribute to the exploration of experimental outcomes through their role in calculations regarding the magnitude and direction of experimental effects. The mean and standard deviations are reported for those data sets relevant to each research question, with descriptive statistics provided for each condition and the overall sample.

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4.2.2.2 Inferential Statistics

Inferential statistics differ from descriptive statistics in that they consider the ability to generalise findings from a sample to wider populations (Dancey and Reidy, 2011; 43). A study’s research design, research questions, experimental hypotheses and type of data must all be considered when deciding which statistical analyses may be most appropriate (Cohen, Manion and Morrison, 2011; 697).

The purpose of the quasi-experimental design used within Phase One was to compare the impact of the independent variable (i.e. intervention participation) on the respective dependent variables for research questions one and two; participants’ self-reported anxiety and parent-reported perceptions of student anxiety. The purpose of the statistical analysis (in answering those research questions outlined in section 2.11) was to compare group performance per condition (i.e. intervention or wait-list comparison condition) on the dependent variables measured at time 1 and time 2 (i.e. student or parent-report anxiety scores), to ascertain whether any statistically significant effects had been obtained and whether any positive outcomes may be attributableto attendance of the intervention.

A statistically significant result would be acknowledged if the probability of a ‘Type I error’ and the probability of the result being obtained by chance was less that 5% (p<0.05) (Dancey and Reidy, 2011; 141).

4.2.2.2.1 Parametric Tests

Parametric tests provide one such means of obtaining inferential statistics from which experimental conclusions may be drawn.

However, it should be noted that parametric tests make certain assumptions about the total population from which a study sample is drawn (Dancey and Reidy, 2011; 154). These assumptions relate to population characteristics or ‘parameters’, including:

136 (ii) The data should be normally distributed (section 4.2.2.3.1);

(iii) The variances of the population(s) should be relatively equal (section 4.2.2.3.2).

It was therefore important to undertake preliminary analyses to ensure that these assumptions were met by the data sets obtained in the current study (section 4.2.2.3).

Parametric tests are commonly used within psychological research because they provide a higher level of statistical power (ibid; 156) and a greater ability to identify a statistically significant relationship between variables, should one exist.

4.2.2.2.2 Non-parametric Tests

Conversely, non-parametric or ‘distribution-free’ tests do not make certain assumptions about the data collected and are therefore considered as alternative statistical analyses, which may be used when those assumptions underpinning parametric tests cannot be met (Dancey and Reidy, 2011; 528). Non-parametric tests were considered if those assumptions in section 4.2.2.3 were not met.

4.2.2.3 Preliminary analyses

It was necessary to undertake a number of preliminary analyses of the data obtained, to ascertain whether this data met those essential assumptions underpinning parametric tests. The checks undertaken are detailed below.

4.2.2.3.1 Tests of normality

Parametric tests work on the assumption that the data set is normally distributed. The Shapiro-Wilk test was used to test this assumption; a non- significant result (p>0.05) suggests that the data set is normally distributed, whilst a significant result (p<0.05) indicates that a data set is non-normally distributed (Razali and Wah, 2011; 21) and interpretations may lack reliability. If the data was non-normally distributed then non-parametric tests

137 were considered. Research demonstrates that the Shaprio-Wilk test is the most powerful normality test (ibid).

4.2.2.3.2 Tests of Equality of Variances

Parametric tests also assume that the variances of the populations of interest are approximately equal (Dancey and Reidy, 2011; 155). Levene’s test of Equality of Variances was used for each research question, to ascertain whether the variance of anxiety scores between intervention and wait-list groups were comparable, prior to intervention or wait-list participation. If the assumption of homogeneity of variance is violated but a study boasts equal numbers of participants in each condition then parametric tests may still employed, albeit with cautious interpretation and on the basis that the other assumptions listed were met (ibid; 156). If these conditions could not be met, then non-parametric tests were considered.

4.2.2.3.3 Tests of Equality of Means

In comparison studies, it is important to establish the extent to which the conditions are comparable, or homogenous with regards to the dependent variable, prior to the independent variable being manipulated.

Independent t-tests compare the mean performance of participants from differing conditions (Brace, Kemp and Snelgar, 2012; 120) and were used to test whether the intervention and wait-list conditions were comparable in terms of mean self-report and parent-report anxiety levels prior to the intervention phase commencing.

4.2.2.3.4 Test of Sphericity

Testing sphericity of data refers to the need to establish whether the correlations between all variables are approximately equal (Brace, Kemp and Snelgar, 2012). Tests of Sphericity are applicable to the use of an ANOVA or ANCOVA and if the within-subjects variable has more than two levels then a check for sphericity is required. As Phase One incorporates only two levels

138 of the within-subject variable (i.e. time of measurement; time 1 and time 2), Mauchly’s Test of Sphericity is not required.

4.2.2.3.5 Two-way Mixed Analysis of Variance (ANOVA)

Where the preliminary analyses outlined in section 4.2.2.3 have not been violated, parametric testing may be used.

An ANOVA represents one type of parametric test. ANOVAs can be used to test the differences in means between several groups. The current study required a two-way mixed ANOVA design for research questions one and two in which participants contribute to only one of several between-subjects conditions (Dancey and Reidy, 2011; 299). As per section 3.7.2, the ‘between-groups’ independent variable (i.e. treatment exposure) had two levels for both research questions:

(i) Student participation in the CBT-based intervention, or;

(ii) Student attendance of timetabled lessons (wait-list comparison).

The ‘within-groups’ independent variable (i.e. time) also had two levels: (i) Pre-test (time 1), and;

(ii) Post-test (time 2).

In addition to those significance levels stated in section 4.2.2.2, Wright (2003; 124) argues that effect sizes should also be reported, as “effect sizes tell the reader how big the effect size is” (ibid; 125). Effect sizes are therefore included for those ANOVAs conducted in the Phase One analyses.