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PSYC 204 (1)
Chapter 1

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PSYC 204
David Ostry

Chapter One: Introduction to Statistics Statistics, Science, and Observations Preview • all statistical procedures were developed to serve a purpose ◦ if you understand why a new procedure is needed, you will find it much easier to learn Definitions of Statistics • statistics (psychology) – a set of mathematical procedures for summarizing, organizing, and interpreting information ◦ shortened version of statistical procedures ◦ statistics serve two general purposes ▪ used to organize and summarize the information so that the researcher can see what happened in a research study and can communicate these results to others ▪ help the researcher to answer the general questions that initiated the research by determining exactly what conclusions are justified based on the results that were obtained ◦ provide researchers with a set of standardized techniques that are recognized and understood throughout the scientific community Population and Samples What Are They? • scientific research usually begins with a general question about a specific group (or groups) of individuals • population – the set of all the individuals of interest in a particular study ◦ LECTURE: population – all instances on some quantitative dimension ◦ the population being studied should always be identified by the researcher ◦ need not consist of people • sample – a set of individuals selected from a population, usually intended to represent the population in a research study ◦ intended to be representative of its population ◦ should always be identified in terms of the population from which it was selected Variables and Data • typically researchers are interested in specific characteristics of individuals in the population (or sample), or they are interested in outside factors • variable – a characteristic or condition that changes or has different values for different individuals • data – measurements or observations ◦ data set – a collection of measurements and observations ◦ datum – a single measurement or observation ▪ commonly called a score or a raw score Parameters and Statistics • parameter – a value (usually numerical) that describes a population ◦ usually derived from measurements of the individuals in the population • statistic – a value (usually numerical) that describes a sample ◦ usually derived from the measurements of the individuals in that sample • typically, every population parameter has a corresponding sample statistic Descriptive and Inferential Statistical Methods • the different statistical procedures to organize and interpret data can be classified into two general categories ◦ descriptive statistics – statistical procedures used to summarize, organize, and simplify data ▪ take raw scores and organize or summarize them in a form that is more manageable ▪ often results are organized in a table or a graph so that it is possible to see an entire set of scores ◦ inferential statistics – techniques that allow us to study samples and then make generalizations about the populations from which they were selected ▪ use sample data to make general statements about a population ▪ typically, researchers use sample statistics as the basis for drawing conclusions about population parameters • although samples are usually representative of their populations, a sample is not expected to give a perfectly accurate picture of the whole population ◦ sampling error – the discrepancy, or amount of error, that exists between a sample statistic and the corresponding population parameter ▪ also known as margin of error • there will always be a margin of error when sample statistics are used to represent population parameters • the unpredictable, unsystematic differences that exist from one sample to another are an example of sampling error Statistics in the Context of Research ◦ ex. students taught with one method of teaching earned a 5-pt higher score on testing than those taught with “method B” ▪ there are two possible interpretations of these results • there is no real difference in the teaching methods, and the 5-pt. difference between the samples is just a sampling error • the is really a difference between the two teaching methods, and the 5 pt. difference was caused by the different methods of teaching Data Structures, Research Methods, and Statistics Relationships Between Variables • most psych research is intended to examine the relationship between variables • to establish the existence of an relationship, researchers must make measurements of the two variables ◦ resulting measurements can be classified into two distinct data structures that also help to classify different research methods and different statistical techniques 1. One Group with Two Variables Measured for Each Individual • one method for examining the relationship between two variables is to observe the two variables as they exist naturally for a set of variables ◦ then, they simply measure the two variables for each individual ◦ researchers then look for consistent patterns in the data to provide evidence for a relationship between variables ◦ consistent patterns are often easier to see if the scores are presented in a graph • correlational research strategy – two different variables are observed to determine whether there is a relationship between them ◦ occasionally, the correlational method produces scores that are not numerical values ▪ this data is typically summarized in a table showing how many individuals are classified into each of the possible categories ◦ results form a correlational study do not provide an explanation for the relationship, and cannot demonstrate a cause-and-effect relationship 2. Comparing Two (or More) Groups of Scores: Experimental and Non- Experimental Methods • this method involves the comparison of two or more groups of scores • when this measurement procedure involves numericl scores, the statistical evaluation typically involves computing the average score for each group and then comparing the averages • if the measurement process simply classifies the individuals into non-numerical categories, statistical evaluation usually consists of computing proportions for each group, and then comparing proportions The Experimental Method • one specific research method that involves comparing groups of scores is claled the experimental method ◦ the goal of an experimental study is to demonstrate a cause-and-effect relationship between two variables ▪ specifically, an expriment attempts to show that changing the value of one variable causes changes to occur in the second variable ▪ to accomplish this goal, the experimental method has two characteristics that differentiate experiments from other types of research studies: • manipulation – the researcher manipulates one variable by changing its value from one level to another ◦ a second variable is observed to determine whether manipulation causes changes to occur • control – the researcher must exercise control over the research situation to ensure that other, extraneous variables do not influence the relationship being examined ◦ two general categories of variables that researchers must consider: ▪ participant variables – characteristics that vary from one individual to another • researchers must ensure that participant variables do not differ from one group to another • whenever a research study allows more than one explanation for the results, the study is said to be confounded (it is impossible to reach an unambiguous conclusion ▪ environmental variables – characteristics of the environment • ex. lighting, time of day, weather conditions • a researcher must ensure that individuals in treatmentAare tested in the same environment as the individuals in treatment B • researchers use three basic techniques to control other variables ◦ random assignment – each participant has an equal chance of being assigned to each of the treatment conditions ◦ matching – ensure equivalent groups or equivalent environments ◦ holding variables constant • experimental method – one variable is manipulated while another variable is observed and measured ◦ to establish a cause-and-effect relationship between the two variables, and experiment attempts to control all other variables to prevent them from influencing the results Terminology in the Experimental Method • independent variable – the variable that is manipulated by the experimenter ◦ in behavioral research, the independent variable usually consists of the two treatment conditions to which subjects are exposed ◦ independent variable consists of the antecedent conditions that were manipulated prior to observing the dependent variable • dependent variable – variable that is observed an measured ◦ observed to assess the effect of the treatment • an experimental study evaluates the relationship between two variables by manipulating one variable and measuring the dependent variable ◦ only one variable is measured ▪ different from a correlational study, where both variables are measured and the data consists of two separate scores for each individual ◦ often, an experiment will include a condition in
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