Statistical inference involves collecting and analyzing data in order to answer a meaningful question of interest. For instance, a researcher in education may want to know if using computers in an algebra classroom is effective in helping students build their mathematical skills. A researcher in psychology may want to know whether children who play violent video games tend to have more disturbing thoughts than children who do not play violent video games. In other fields, such as environmental science, researchers may want to know what factors contribute to global warming by asking questions such as which makes and models of automobiles emit larger amounts of greenhouse gas.
Once a researcher has described a problem he or she wishes to investigate, he or she will set out to collect or identify a set of data that consists of information about a variable or variables of interest. There are two basic types of data that can be collected, quantitative data and qualitative data.
Quantitative data is numeric in form. The main purpose of collecting quantitative data is to describe some phenomenon using numbers. For example, quantitative data could be collected to assess the effect of advertising on gross product sales.
On the other hand, qualitative data is categorical in nature and describes some phenomenon using words. For instance, qualitative data can be used to describe what the learning environment is like in a given mathematics classroom by using words to describe the types of interactions between the students and the teacher and how students appear to be engaged in learning.
Determining whether to collect quantitative or qualitative data is typically driven by the characteristic or relationship that is being assessed and the type of data that is available. The purpose of this book is to introduce some of the different statistical methods and techniques that can be used to analyze data in a meaningful way. The methods and techniques that we
will be considering in this book are broadly categorized as follows:
- Graphical displays of data
- Descriptive representations of data
- Basic statistical inference
- Regression analysis
- Analysis of variance