INTRODUCTION TO STATISTICS

Anthony J Greene2 Lecture Outline I.The Idea of Science II.Experimental Designs A.Variables 1.Independent Variables 2.Dependent Variables 3.Confounding Variables B.True Experiments: Cause & Effect 1.Between Groups Designs 2.Repeated Measures Designs C. Designs With No Independent Variable 1.Correlational Designs 2.Existing Groups D.Design Considerations 1.Sampling 2.Errors a)Sampling Error b)Sensitivity & Power c)Reliability & Validity

Anthony J Greene3 The Advancement of Theory

Anthony J Greene4 Science Fact & Theory Statistics are used to analyze data and make inferences useful for theory In general, math is the language of science

Anthony J Greene5 Fact & Theory Facts must be observable (data) Theory = understanding Theory is not hypothetical Theory is broad, fact and hypothesis are narrow Theories must be consistent with all available (relevant) facts Theory guides the search for fact Facts are only important if they inform theory Theory is more important than fact The progress of theory is the purpose of science

Anthony J Greene6 Descriptive statistics consists of methods for organizing and summarizing information. Inferential statistics consists of methods for drawing and measuring the reliability of conclusions about a population based on information obtained from a sample of the population. Two Classes of Statistics

Anthony J Greene7 The role of inferential statistics in research

Anthony J Greene8

9 The role of statistics in experimental research.

Anthony J Greene10 The role of statistics in experimental research.

Anthony J Greene11 The role of statistics in experimental research.

Anthony J Greene12 Cause & Effect: Inferential Designs Control Group Vs. Experimental Group Apply an experimental manipulation to the experimental group Compare Control and Experimental Groups If the differences between Control and Experimental Groups is unlikely to be due to chance, the manipulation must be the cause

Anthony J Greene13 An example of a Between Groups Design

Anthony J Greene14 And Example of a Repeated Measures Design

Anthony J Greene15 Independent Variable or Treatment: Each experimental condition. For one-factor experiments, the treatments are the levels of the single factor. For multi-factor experiments, each treatment is a combination of levels of the factors. –Factor: A variable whose effect on the response variable is of interest in the experiment. –Levels: The possible values of a factor. Dependent Variable or Response or outcome: The characteristic of the experimental outcome that is to be measured or observed. Cause & Effect

Anthony J Greene16 The Basic Idea of Experimental Designs Using careful controls, introduce an experimenter controlled manipulation – an I.V. (e.g., a medication, a memory task, a frightening experience, a clinical treatment plan) to one group and do nothing to another group Differences between the control and the experimental group indicate that your manipulation exerted a change (cause-effect) – measured as a D.V.

Anthony J Greene17 Basic Experimental Design: Independent & Dependent Variables

Anthony J Greene18 Confounding Variables

Anthony J Greene19 Sampling From a Population Population: The collection of all individuals or items under consideration in a statistical study. E.g., American College Students; French speaking comedians. Sample: That part of the population from which information is collected. Random Sample: A sample where each member of a population has an equal probability of inclusion in the sample. Alternatively put, all possible samples of a given size have an equal opportunity for selection.

Anthony J Greene20 In a designed experiment, the individuals or items on which the experiment is performed are called experimental units. When the experimental units are humans, the term subject or participant is used. Subjects or Participants

Anthony J Greene21 Sampling From a Population

Anthony J Greene22 The relationship between a population and a sample.

Anthony J Greene23 Sampling Error 1.Notice that the sample statistics are different from one sample to another.

Anthony J Greene24 Sampling Error 2.Three samples are selected from the same population.

Anthony J Greene25 Sampling Error 3.All of the sample statistics are different from the corresponding population parameters.

Anthony J Greene26 Sampling Error 4.The natural differences that exist, by chance, between a sample statistic and a population parameter are called sampling error.

Anthony J Greene27 Sensitivity & Power Control: Some method should be used to control for effects due to factors other than the ones of primary interest. Randomization: Subjects should be randomly divided into groups to avoid unintentional selection bias in constituting the groups, that is, to make the groups as similar as possible.

Anthony J Greene28 Types of Errors

Anthony J Greene29 Reliability Sampling Size:A sufficient number of subjects should be used to ensure that randomization creates groups that resemble each other closely and to increase the chances of detecting differences among the treatments when such differences actually exist. Replication: If an experiment cannot be replicated, its reliability becomes seriously questionable. Inability to replicate may be due to chance factors or to fraud.

Anthony J Greene30 Validity Is the thing you hoping to measure really the thing you are measuring. A classic example is I.Q. Does it measure intelligence? Maybe so, maybe not

Anthony J Greene31 Designs With No Independent Variable Not cause and effect. Existing distinctions are observed The experimenter has no control of either variable Used when experimental designs are unethical, impractical or impossible

Anthony J Greene32 Correlational Designs

Anthony J Greene33 Correlation Between Aggression and TV Violence The data show a tendency for higher levels of TV violence to be associated with higher levels of aggressive behavior.

Anthony J Greene34 Correlation Between Aggression and TV Violence Note that we have measured two different variables, obtaining two different scores, for each child.

Anthony J Greene35 Why Correlations Cannot Determine Causality e.g., relationship between introversion and overeating. It could be that overeating causes weight gain which in turn causes introversion. Or it could be that introversion causes overeating because of time spent alone. Or some third factor like depression could cause both One could not do an experiment where overeating was induced to look for an effect.

Anthony J Greene36 Existing Groups Designs