Chapter 1 Review of Concepts

The Two Branches of Statistics

Statistics is divided into two branches: descriptive statistics and inferential statistics. Descriptive statistics organize, summarize, and communicate large amounts of numerical information. Inferential statistics draw conclusions about larger populations based on smaller samples of that population. Samples are intended to be representative of the larger population.

How to Transform Observations into Variables

Observations may be described as either discrete or continuous. Discrete observations are those that can take on only certain numbers (e.g., whole numbers, such as 1), and continuous observations are those that can take on all possible numbers in a range (e.g., 1.68792). Two types of variables, nominal and ordinal, can only be discrete. Nominal variables use numbers simply to give names to scores. Ordinal variables are rank-ordered. Two types of variables can be continuous (although both can also be discrete in some cases): interval and ratio. Interval variables are those in which the distances between numerical values are assumed to be equal. Ratio variables are those that meet the criteria for interval variables but also have a meaningful zero point. Scale variable is a term used for both interval and ratio variables, particularly in statistical computer programs.

Variables and Research

Independent variables can be manipulated or observed by the experimenter, and they have at least two levels, or conditions. Dependent variables are outcomes in response to changes or differences in the independent variable. Confounding variables systematically vary with the independent variable, so we cannot logically determine which variable may have influenced the dependent variable. The independent and dependent variables allow researchers to test and explore the relations between variables. A measure is useful only if it is both reliable and valid. A reliable measure is one that is consistent, and a valid measure is one that assesses what it is intended to assess.

Introduction to Hypothesis Testing

Hypothesis testing is the process of drawing conclusions about whether a particular relation between variables is supported by the evidence. Operational definitions of the independent and dependent variables are necessary to test a hypothesis. Experiments attempt to identify a cause–effect relation between an independent variable and a dependent variable. Random assignment to groups, to control for confounding variables, is the hallmark of an experiment. Most studies have either a between-groups design or a within-groups design. Correlational studies can be used when it is not possible to conduct an experiment; they allow us to determine whether there is a predictable relation between two variables. Outliers are extreme scores that are either very high or very low compared with the rest of the observed data. Outlier analysis studies outliers to understand how the independent variable affects the dependent variable.