Lots of vocabulary in this chapter. Statistics is really a conceptual class, not (just) a math class.
Consider the following claim: Men are more likely than women to pass out at the dentist's office.
There are at least 2 questions that I want to ask.
Continue with this example and hit all of (or most of) the vocabulary terms below as they become relevant to the discussion.
Researchers use of statistics - refers to a set of methods and rules for organizing, summarizing, and interpreting information.
A population is the set of all individuals of interest in a particular study
A sample is a set of individuals selected from a population, ususally intended to represent the population in a study.
A prameter is a value, usually a numerical value, that describes a population. A parameter may be obtained from a single measurement, or it may be derived from a set of measurements from the population.
A statistic is a value, usually a numerical value, that describes a sample. A statistic may be obtained from a single measurement, or it may be derived from a set of measurements from the sample.
Data (this is plural, so we say "the data are", not "the data is") are measurements or observations. A data set is a collection of measurements or observations. A datum (singular) is a single measurement or observation and is commonly called a score or raw score.
Descriptive statistics are statistical procedures used to summarize, organize, and simplify data.
Inferential statistics consist of techniques that allow us to study samples and then make generalizations about the populations from which they were selected.
Sampling error is the discrepancy or amount of error, that exists between a sample statistic and the corresponding population parameter.
Random selection, or random sampling, is a process for obtaining a sample from a population that requires that every individual in the population have the same chance of being selected for the sample. A sample obtained by random selection is called a random sample.
A variable is a characteristic or condition that changes or has different values for different individuals.
A constant is a characteristic or condition that does not vary, but is the same for every individual.
With the correlational method, two variables are observed to see if there is a relationship.
In the experimental method, one variable is manipulated while changes are observed in another variable. To establish a cause-and-effect relationship between the two variables, an experiment attempts to eliminate or minimize the effect of all other variables by using random assignment and by controling or holding constant other variables that might influene the results.
The independent variable is the variable that is manipulated by the researcher. In behavioral research, the independent variable usually consists of the two (or more) treatment conditions to which subjects are exposed. The independent variable consists of the antecedent conditions that were manipulated prior to observing the dependent variable.
The dependent variable is the one that is observed for changes in order to assess the effect of the treatment.
A control group is a condition of the independent variable that does not receive the experimental treatment. Typically, a control group either receives no treatment or receives a neurtal, placebo treatment. The purpose of a control group is to provide a baseline for comparsion with the experimental group.
An experimental group does receive an experimental treatment.
A confounding variable is an uncontrolled variable that is unintentionally allowed to vary systematically with the independent variable.
The quasi-experimental method examines differences between pre-existing groups of sugjects (for example, men vs. women) or differences between groups of scores obtained at different times (for example, before treatment vs. after treatment). The variable that is used to differentiate the groups is called the quasi-independent variable, and the score obtained for each individual is the dependent variable.
A hypothesis is a prediction about the outcome of an experiment. IN experimental research, a hypothesis makes a prediction about how the manipulation of the independent variable will affect the dependent variable.
Constructs are hypothetical concepts that are used in theories to organize observations in terms of underlying mechanisms.
An operational definition defines a construct in terms of specific operations or procedures and the measurements that result from them. Thus, an operational definion consists of two components: First, it describes a set of operations or procedures for measuring a construct. Second, it defines the construct in terms of the resulting measurements.
A nominal scale consists of a set of categories that have different names. Measurements on a nomnal scale label and categorize observations, but do not make any quantitative distinctions between observations.
An ordinal scale consists of a set of categories that are organized in an ordered sequence. Measurements on an ordinal scale rank observations in terms of size or magnitude.
An interval scale consists of ordered categories where all of the categories are intervals of exactly the same size. With an interval scale, equal differences between numbers on the scale reflect equal differences in magnitude. However, ratios of magnitudes are not meaningful.
A ratio scale is an interval scale with the additional feature of an absolute zero point. With a ratio scale, ratios of numbers DO reflect ratios of magnitude.
A discrete variable consists of separate, indivisible categories. No values can exist between two neighboring categories.
For a continuous variable, there are an infinite number of possible values that fall between any two observed values. A continuous variable is divisible into an infinite number of fractional parts.
For a continuous variable, each score actually corresponds to an interval on the scale. The boundaries that separate these intervals are called real limits. The real limit separating two adjacent scores is located exactly halway between the scores. Each score has two real limits, one at the top of its interval called the upper real limit, and one at the bottom of its interval called the lower real limit. Note that the upper real limit of one interval is also the lower real limit of the next higher interval.
Some Notation