INTRODUCTION TO STATISTICS

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Lecture OutlineI. The Idea of ScienceII. Experimental Designs

A. Variables1. Independent Variables2. Dependent Variables3. Confounding Variables

B. True Experiments: Cause & Effect1. Between Groups Designs2. Repeated Measures Designs

C. Designs With No Independent Variable1. Correlational Designs2. Existing Groups

D. Design Considerations1. Sampling2. Errors

a) Sampling Errorb) Sensitivity & Powerc) Reliability & Validity

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The Advancement

of Theory

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Science

Fact & Theory

Statistics are used to analyze data and make inferences useful for theory

In general, math is the language of science

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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

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• 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

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The role of inferential statistics in research

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The role of statistics in experimental research.

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The role of statistics in experimental research.

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The role of statistics in experimental research.

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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

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An example of a Between Groups Design

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And Example of a Repeated Measures Design

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• 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

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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.

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Basic Experimental Design:Independent & Dependent Variables

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Confounding Variables

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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.

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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

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Sampling From a Population

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The relationship between a population and a sample.

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Sampling Error

1. Notice that the sample statistics are different from one sample to

another.

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Sampling Error

2. Three samples are selected from the same population.

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Sampling Error

3. All of the sample statistics are different from the corresponding population parameters.

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Sampling Error

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

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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.

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Types of Errors

Unknown Truth

Effect No Effect

Effect ☺ Type I: Statistical Decision No Effect Type II: ☻

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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.

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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

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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

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Correlational Designs

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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.

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Correlation Between Aggression and TV Violence

Note that we have measured two different variables, obtaining two different scores, for each child.

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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.

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Existing Groups Designs