Statistics, use of in Case Study

Conceptual Overview and Discussion

Statistical analysis is common in survey and experimental research designs. However, it can also be used in case study research, either by itself or in combination with qualitative analysis. There are three essential elements of statistics: (1) the population, (2) the sample, and (3) the variable. The population is a collection of units that the researcher wants to study, such as people, objects, neighborhoods, and events. A sample is a subset of units from a population. A variable is a characteristic or property of a unit from the population, for example, people's age and the number of births in a neighborhood. Performing statistical analysis is then focused on systematical classification and analysis of variables collected in a study on a number of units from the population of interest.

A huge number of statistical tests are available. In addition, the available literature on statistical analyses is abundant, ranging from introductory books to advanced mathematical texts. Although computer software for statistical analysis (e.g., R, SAS, S-PLUS, SPSS, STATA) has become increasingly available and more user friendly, performing statistical analysis is generally considered thorny. Taking into account these considerations, good practice of statistics in case studies requires well-founded choices. Some important considerations here are the type of statistics needed, the sample drawn, the goal of the analysis, the type of variables, statistical testing, and statistical significance.

With regard to the type of statistics needed, it is common to differentiate between descriptive and inferential statistics. Descriptive statistics focus on the manageable and understandable presentation of numerical information. Examples are figures of sports games (e.g., batting averages) stock markets, unemployment rates, and so on. Descriptive statistics are presented numerically (e.g., means and percentages), in tables (e.g., a frequency table), and in graphical displays (e.g., line and bar charts and scatter plots). In inferential statistics information derived from samples is used to make estimates, decisions, and predictions about the population as, for example, in a case study that bases the usage of rhetoric in editorials of a daily French newspaper, on a sample of one editorial per week during 1 year, to draw conclusions about all editorials of the newspaper, the population. In general, the greater the sample size, the more accurate the estimates from the population. Sampling is necessary when it is not possible or practically feasible to incorporate the whole population into the case study. Although the ideal of statistical theory is random sampling in order to make correct inferences, statistical analyses are also used in case studies that do not meet this requirement.

A huge amount of inferential statistical tests are available, and the choice depends on the goal of the analysis. In general, this goal is differentiated in (a) the comparison of the distribution of variables and (b) the study of relationships between variables. An example of the former is to analyze whether there are differences in birth rates between types of neighborhoods. An example of the latter is to investigate whether and how birth rates in neighborhoods are correlated with living conditions. Another important aspect for the choice between various statistical tests is the type of variables embodied in the level of measurement. The researcher should consider the values or categories that variables may have, for example grade points ranging from very poor to excellent indicated by the values 1 to 10. There are four levels of measurement, in ascending order: (1) nominal, (2) ordinal, (3) interval, and (4) ratio. A nominal measurement level means that categories of variables differ; for example, for the variable “gender” the categories are male and female. An ordinal level means that the categories differ and also have a rank order; for example, the variable “education,” with 15 levels, ranging from no education (value: 1) to university level (value: 15). Other, well-known examples of ordinal variables are attitude measures used in the social sciences, which often are measured with 5- or 7-point scales. Variables with an interval measurement level possess the features of ordinal variables and, in addition, have equal distances between the values. Examples are the variable grade points just mentioned, and temperature measured on the Fahrenheit scale. The highest level of measurement is the ratio level, which has the features of the three preceding measurement levels and, in addition, has a nonarbitrary, meaningful, value of zero; for example, length, weight, temperature measured in grades Kelvin, and the percentage of people receiving university education. The level of measurement determines which statistical tests that can be performed; for example, mean scores are allowed only for interval and ratio scales.

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