SECTION CONTENTS

Depending on the complexity of the research design and the number of measurements obtained during data collection, we will have generated a set of scores called ‘raw data’. Section 5 is concerned with the principles of descriptive statistics, which include mathematical principles for organizing and summarizing the raw data.

In Chapter 13 we outline techniques used for tabulating and graphing data. These techniques enable us to visualize trends and identify differences across levels of the independent variables. When the data have been appropriately organized we may calculate statistics, such as the percentages and proportions of scores found in the groups being studied.

Another important use for descriptive statistics is to ‘crunch’ or condense data into typical values for representing scores. The statistics are discussed in Chapter 14 and include ‘measures of central tendency’ (mode, median and mean) and also measures of variability (range, semi-interquartile range and standard deviation). Using these statistics enables us to condense the raw data and to convey to the reader information about the research findings.

Statistics such as the mean and the standard deviation can also be applied to calculating standard scores. Standard scores are used to establish the position of a particular score relative to a population. In Chapter 15 we examine how the standardized normal distribution can be used to calculate the position of any specific score within a population and how to interpret the clinical implications of these scores.

In Chapter 16 we examine another important class of statistics called correlation coefficients. The correlation coefficient is used to express the degree and direction of association between two or more variables. For example, we could use correlation coefficients to demonstrate if there is an association between the variables ‘level of exercise’ and ‘body weight’. The closer the calculated correlation coefficient is to 1.0 (the maximum value), the more precisely we may predict from one variable to the other. Although correlation coefficients are extremely important for showing how different variables are associated, they do not necessarily indicate causal relationships between the variables. Showing causal effects requires appropriate research designs, as we suggested in Section 3.