ANALYSIS OF THE RESULTS

There are two primary statistical categories that are concerned with making meaning of raw data – namely descriptive and inferential statistics (Gravetter & Wallnau, 2011:10). Both descriptive and inferential statistics were used to investigate the research hypotheses. Each concept will be shortly defined where after the methods used for statistical analysis will be discussed.

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5.3.1 Descriptive and Inferential Statistics

The term descriptive statistics is a collective name for a number of statistical methods that are used to organise and summarise data in a meaningful way. This serves to enhance the understanding of the properties of the data. Descriptive statistics can be represented in graphical ways and numerical ways (Pietersen & Maree, 2007:183). Descriptive statistics calculated for the study include frequencies, means and standard deviations. Frequencies are the number of times a response has occurred. A mean is the sum of a set of scores divided by the scores and a standard deviation is a measure of the average of the deviations of each score around the mean (Jansen, 2007).

However, most researchers want to go beyond the point of summarizing and describing the gathered data. The purpose of most quantitative research is to use the findings from the sample data to generalise or draw conclusions about the population. This is called statistical inference, a field of statistics that relies heavily on probability theory. It is by means of probability statements that inferences are made and probability is the way of quantifying chance (Pietersen & Maree, 2007a:198). Inferential statistics were used to test whether the independent variable (the LLL programme) did have an effect on the dependent variables (tolerance in terms of gender, language, race, socio-economic status and nationality).

An integral part of the interpretation of inferential statistics is the concept of statistical significance. Statistical significance tests begin with the supposition that the null hypothesis (H0) is correct (Howell, 2010:93). For each belief that a researcher wants to test, two hypotheses are formulated – a null hypothesis and an alternative hypothesis (also known as an experimental hypothesis). The null hypothesis is denoted by H0 and is used to state the ‘no difference’ or ‘no correlation’ scenario (Pietersen & Maree, 2007a: 203).

The standard that the observed data must meet is known as the significance level or alpha (α). The standard that data must meet indicates the meaningfulness of the results and whether the results are merely the result of chance. By convention alpha is usually set to 0.05 (Stangor, 2011:147). In this study, the 95% level of confidence (p≤ 0.05)

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was therefore applied as the minimum to interpret significant differences among sets of data.

5.3.2 Methods of Analysis

It is important for the researcher to choose the correct methods of analysis. Statistical tests of hypothesis may be classified as belonging to one of two groups – parametric methods and non-parametric methods. The reason for this distinction lies in the fact that statistical tests rely on certain population characteristics for their outcome to be valid. In general, parametric methods are used when one has knowledge of the underlying distribution of the study variable. Non-parametric methods are used when very little is known about the variable’s distribution in the population. The sample size and the shape of the distribution of the variable of interest play a big role when the researcher has to decide which one of the two methods is more appropriate (Pietersen & Maree, 2007c: 225). Data is captured on different scales of measurement, each one based on the characteristics of the information in the data. There are nominal scales, ordinal scales, interval scales and ratio scales. In this order, the first one carries the least information, the second one slight more, the third one even more, while the last one carries the most. These four types of data can be classified into two broad classes – categorical data (nominal and ordinal) and numerical data (interval and ratio) (Maree & Pietersen, 2007:148-149). The statistical tests for the purpose of this study belong to the parametric method.

Three methods of statistical analysis were applied and will be discussed briefly. Firstly, in order to determine the internal reliability of the measurement instrument (the questionnaire) the Cronbach’s alpha coefficient was calculated. When a number of items are formulated to measure a certain construct, there should be a high degree of similarity among them since they are supposed to measure one common construct. The Cronbach’s alpha coefficient is used to measure the internal reliability of an instrument and is based on inter-item correlations. If the items are strongly correlated with each other, their internal consistency is high and the alpha coefficient will be close to one. If, on the other hand, the items are poorly formulated and do not

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correlate strongly, the alpha coefficient will be close to zero (Pietersen & Maree, 2007b: 216).

The second method utilized was to calculate the analysis of means by a dependent t- test. This technique can be used when the average scores on two quantitative variables need to be compared in a single sample, for example pre-test and post-test in the experimental group (Durrheim, 2006:211), similar to the current study. Three values are calculated and displayed with every t-test; these values are the test statistic (t- value), the degrees of freedom (n-1 in one-sample cases) and the p-value (probability value) (Pietersen & Maree, 2007c: 225).

The third method of analysis is the Pearson correlation coefficient which is a measure of strength of the linear relationship between two quantitative variables. It is therefore only appropriate if one can first establish that the relationship is linear, then perform analysis which will reveal the direction and the strength of the relationship, and also whether it is statistically significantly different from zero. For the statistical test (p- value) to be valid, it has to be assumed that the distribution of the variables in the population is normal, especially in small samples (Pietersen & Maree, 2007c: 246). A detailed description of the sample will be provided accordingly.