Statistical MethodsIntroductory Concepts by Adam J. McKee Using F. J. Gravetter and L. B. Wallnau's Essentials of Statistics for the Behavioral Sciences (4th Ed.). Populations Scientific Research begins with a general question about specific group(s) of individuals. In statistical terminology, the entire group that a researcher wants to study is called a population. Samples Most of the time, populations are huge. All voters in the United States, all college students, etc. In practice, the researcher must settle on a much more manageable group selected from the population—a sample Sample Defined A sample is a set of individuals selected from a population, usually intended to represent the population in a research study. Parameters and Statistics When we talk about statistics, we need to know whether we’re talking about a sample or a population. A characteristic of a population is called a parameter. A characteristic of a sample is called a statistic. Parameter A value that describes a population. Parameters describe the whole population of interest. Median household income taken from the 2000 Census is an example of a parameter. Statistic A statistic is a value that describes a sample. How Research Questions are Answered Research questions are answered by gathering information. In the sciences, information is gathered by making observations and taking measurements. Clarifying Terminology The word data is plural, and must be used with a plural verb – "The Data Are" A measurement for an individual is called a Datum – the singular form of Data. A datum is more commonly called a score or raw score. A complete set of scores is called a data set or simply the data. Two Types of Statistical Procedures Descriptive Statistics – statistical procedures that are used to summarize, organize, and simplify data. E.g., mean, median, mode. Inferential statistics -- techniques that allow us to study samples and then make generalizations about the populations from which they were selected. Problems with Samples Samples provide only limited information about the population. Any given sample will be different to some degree from the population. It is important that a sample be representative of the population – That is, the characteristics of the sample should be consistent with the characteristics of the population. Such a sample is called a representative sample. Sampling Error The discrepancy, or amount of error, that exists between a sample statistic and the corresponding population parameter. At this stage it is only important to realize that a statistic obtained from a sample generally will not be identical to the corresponding population parameter. "margin of error" If you compare one sample with another, there will typically be a difference between the sample statistics even though the sample comes from the same population. The margin of error in opinion poles—say who is going to be president—is sampling error. What is Science? Science is an attempt of explain, predict, and control things—it is an attempt to discover orderliness in the universe. What is most interesting to us is generally things that change (vary) Q: What does "Vary" mean? A characteristic or condition that changes or varies is called a variable Individual v. Environmental Variables can be characteristics that differ from one individual to another—height, weight, religion, political party. Variables can also be characteristics of the environment—temperature, time of day. Variables do not always have to describe people—how much light is in a parking lot? Constant Things that do not change are called constants. We know that water freezes at 32 degrees F. What is science? Science involves the search for relationships between variables. To document relationships, we must make observations—measurements. The Correlational Method The simplest way to look for relationships between variables is to make observations of variables as they exist naturally and see whether there is a relationship. This type of relationship is often incorrectly used to say that one thing caused another. Correlation does not demonstrate causation. The Experimental Method The goal of the experimental method is to establish cause and effect relationships. That is, to show that changes in one variables cause changes in another variable. Two Characteristics of the Experimental Method The researcher manipulates one of the variables and observes the second variable to determine if the manipulation caused a change The researcher exercises control over the research situation to ensure that other, extraneous variables do not influence the relationship being examined. How are variables controlled? Two common techniques: Random assignment such that each subject has an equal change of being assigned to each treatment condition—all other extraneous factors cancel each other out Controlling or holding constant other variables—same room temp, same time of day, same type of instruments, etc. Independent and Dependent Variables Independent Variables – variables that are manipulated by the researcher; often a treatment condition. Dependent Variables – variables that are observed for change when the independent variable is manipulated. In cause and effect terminology, a change in the independent variable causes a change in the dependent variable (avoid saying this aloud) Control and Experimental Conditions Individuals in the control condition do not receive the experimental treatment. Individuals in the experimental condition do receive the experimental treatment. The control condition provides a baseline with which to compare the experimental condition. Quasi-Experimental Method Studies that are almost, but not quite, real experiments. In Quasi-experimental designs, there is no manipulation by the researcher. In this type of design, the variable that defines the groups is naturally occurring. This type of design is used when we want to examine naturally occurring differences, such as gender; or when manipulation of the IV would be impractical or unethical/illegal. E.g., the effects of heroin use on longevity. Quasi-experiments and Cause As with Correlational studies, it is inappropriate to make cause and effect conclusions based on quasi-experimental designs because all variables were not controlled. Cause and effect can only be established with a true experiment. Scales of Measurement Different types of measurements provide us with more or less information. Researchers have divided quantitative measurements into four different scales to help us determine the limitations and appropriate statistical techniques to use with our data. Nominal Scale A nominal scale is a set of categories that have different names. Measurements on the nominal scale do not make any quantitative distinction between observations. Although categories on the nominal scale are not quantitative values, they are sometimes represented by numbers, and are coded as numbers in computer programs. Ordinal Scale The categories that make up an ordinal scale have separate names but are also ranked in terms of size. Ex. Sports teams are often ranked; we know that team A is better than team B, but we don’t know how much better. Interval and Ratio Scale Both the interval and ratio scales have an ordered set of categories Both have a series of intervals that are exactly the same size The advantage to these is that they allow you to measure how much difference there is between two scores. E.g., temperature, inches, centimeters, IQ, ACT scores, etc. Ratio scales have the additional requirement of an absolute zero point. Discrete and Continuous Variables A discrete variable consists of separate, indivisible categories—no values can exist between neighboring categories. E.g., a roll of the dice A continuous variable can be divided into fractional parts. E.g., Time, distance Statistical Notation: Scores Raw scores are usually represented by the letter X. When observations are made for a second variable, the letter Y is often used. When scores for several individuals are obtained, it is customary to put the scores in columns and head them with the letters X and Y. Statistical Notation: N & n The text uses the capital letter N to represent the number of people or things in a population The lower case letter n represents the number of people or things in a sample If you have PowerPoint, click here for an animated overview of Statistical Notation.
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