RESEARCH METHODOLOGY
5.11 Descriptive statistics
170 technique becomes applicable. Alternatively, when more than two variables interact, the multivariate technique becomes applicable.
Statistical techniques are divided into descriptive and inferential categories. If the scores of the entire population are available, descriptive statistics would be appropriate. However if the population numbers are very large, samples are the preferred method to make inferences about the corresponding population properties. In such cases, inferential statistics may apply (Welman & Kruger, 2004:208).
171 Histograms and bar diagrams are diagrams in which columns represent frequencies of the various ranges of scores or values of a quantity. This gives an overall picture of the description of the units of analysis as a whole group (Welman & Kruger, 2001: 208).
According to Dillon et al., (1994:406) graphs are also a good means of representing data from tables, and could be more effective than tables when presenting data.
5.11.2
Measures of central tendency
According to Thomas (2004: 208), measures of central tendency indicate the centre of a frequency distribution, with the three most commonly used being the mean, median and mode. Each of these is more or less appropriate depending on the specific features of the frequency distribution.
The mean: Thomas (2004:208) defines the mean or average as the sum total of the values recorded for all the cases divided by the number of cases. However the mean can be misleading especially when unusually high or low values are reflected in the distribution.
Harris (1995:96) argues that when values are in the extreme, either too high or too low, the mean will not be realistic as the mean considers every score in the distribution.
The median: According to Aiken (1994:430), the median of a group of scores is the middle score, the score below and above which one half (fifty percent) of the scores fall. Huysamen (1990:37) refers to the median as the 50th percentile and states that
“ if a frequency polygon was drawn, the median will be that point on the baseline which cuts the area of the histogram or frequency polygon into equal halves”.
172 The mode: is the value that occurs most frequently in the distribution. Bless &
Kathuria (1993:46) draw attention that the mode does not include all the scores of distribution and is the preferred for those scores that use nominal scales.
Taking into account the advantages and disadvantages of the measures for central tendency, Thomas (2004:208) recommends the mean as the most important measure of central tendency for statistical purposes.
5.11.3 Measures of dispersion/variability
Measures of dispersion, point out the extent to which the values of a distribution are spread out around the distribution’s mean. Measures of dispersion are also known as measures of variability. The measures of dispersion are the range, variance, and standard deviation. These measures provide a sound basis in terms of the manner in which a group of scores vary from the main score (Thomas, 2004:208).
Thomas (2004:208) further postulates that variance is one of the most important concepts in quantitative research analysis. Research often requires an explanation for the variance in dependent variables, and for variable analysis the existence of variance is very important. The variance in a set of values is summarized in a statistic called standard deviation. The standard deviation calculates the average differential value from the mean value for the distribution and the variance that exist. The standard deviation summarizes the degree to which a set of measures are held together or spread out around the mean value.
According to Sekaran (2000: 398) the range of a set of observations is the difference between the largest observation and the smallest observation and is regarded as a simple measure of dispersion.
173 Huysamen (1994:51) states that a range determination is the difference between the highest score and the lowest score. However, since the range is based on two scores and is limited in displaying the variability of a distribution, the semi- interquartile range would reflect a more representative measure.
Whilst descriptive statistics is a significant category for statistical procedures, inferential statistics is another major statistical procedure that is reported in research literature.
5.11.4 Inferential statistics
The main function of inferential statistics is to establish relationships among variables and draw conclusions thereafter. This statistical procedure could also be used to test statistical hypotheses. Researchers must differentiate between parametric tests and non-parametric tests when deciding which statistical test to implement. Parametric tests have the ability to provide fairly accurate results and are able to describe relationships between different variables in the population.
The drawback is that parametric tests are not conducive for nominal or rank order data and are more complex to manage compared to non-parametric tests (Harris, 1995:18-19).
However, parametric tests are better suited to data which is interval or ratio- scaled. A large sample size is recommended and the population from which the sample is drawn should reflect a normal or bell-shaped distribution (Zikmund, 1995:604).
Bless & Kathuria (1993:77) state that descriptive statistics are procedures that condense information about a set of measurements whereas inferential statistics constitute techniques that make statements based on partial information through a theory of probability. Therefore statistical inference is an application of
174 inductive reasoning that derives conclusions about a population drawn from evidence from a sample.
According to Thomas (2004: 213), it is unlikely that a sample will replicate the population exactly. It is therefore necessary to test whether the variation is statistically significant or insignificant. A test of statistical significance is a way to estimate the probability that results from a sample are due to chance variations (sampling errors) rather than indicating actual differences. When a test shows that the results are likely to have occurred due to chance, it is regarded as
“statistically significant”.
Kerlinger (1964:180) states that when a statistical value occurs by chance five times or less in a hundred (five percent), then the value is regarded as significant. However, if it occurs once or less in a hundred (one percent) then it is regarded as “very significant”. Inferential statistical techniques that are used to test the results of the survey and hypotheses include t-test, analysis of variance (ANOVA) and correlation.
5.11.4.1 T-test
The t-tests evaluates whether two groups have equivalent or different mean scores. Descriptive research compares the mean of one group with that of another group. A t-test determines whether an observed difference in means of two groups is sufficiently large to be attributed to a change in some variable or whether such change is attributed to chance (Welman and Kruger, 2004:213).
5.11.4.2
The analysis of variance (ANOVA)
The analysis of variance is an experimental strategy that entails quantitative analytical procedures. It applies to the analysis of group differences rather than individual differences. The measures to be compared with are the average
175 values of the dependent variable of the control groups. The aim of the analysis is to establish whether the differences between the control groups on the dependant variable is wide enough to indicate that they are unlikely to have occurred by chance (Thomas, 2004:214).
This test will be used to determine whether the different sub-groups of the demographic variables such as age, gender, length of service and managerial status differ on the variables of interest.
5.12 Presentation and analysis of data, and discussion of results
According to Welman & Kruger (2004:216), results of a research study could be presented by using tables (cross-tabulations), graphs, statistical summaries, means, standard deviations, correlation coefficient, and written statements from the responses obtained.
The research study utilized either one or a combination of the above methods in the presentation of the results of the survey.