Introduction to Statistics and Research Design, Study notes of Statistics

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Introduction to Statistics and

Research Design

Arlo Clark-Foos

Dr. John Snow and Cholera

1854.London

Sample vs. Population

 Sample: A set of observations drawn from the population of interest…

• Representative Sample:…that share the same characteristics as the population of interest.
• Latin characters (e.g., M, s ), called statistics  Population: Includes all possible observations about which we’d like to know something.
• Greek characters (e.g., μ, σ ), called parameters  Why use samples?

Transforming Observations Into

Numbers

 Constructs: hypothetical ideas that have been developed to

describe and explain human behavior

• Motivation, Anxiety, Happiness, Love, Anger, …
• Defining these constructs to be studied  GIGO (Garbage In, Garbage Out)
• Discrete Observations: Take on specific values; no other values exist between these numbers  Example: The number of people on a city bus.
• Continuous Observations: Can take on an infinite number of potential values  Example: Time taken to complete a math problem.

Scales of Measurement

Discrete & Ratio How many kids are riding on each school bus?

Variables

 Independent Variables (IV): Because variables vary, any

IV must have at least two values (levels) that it can take

on.

• IVs are manipulated or observed to determine the effects on the dependent variable  Examples: Gender*, Caffeine Intake

 Dependent Variable (DV): Observed or measured to

discover differences caused by changes in the IV.

 Examples: Political Views, Exam Scores

Variables

 Confounding vs. Extraneous

 Which of two school bus routes results in a more

enjoyable ride to school for the students?

• Hypothesis: Back roads are more relaxing and enjoyable.  Two routes, one uses back roads while the other uses main roads.
• Possible Confounds…?
• Extraneous Variables? Driver?

Test Your Knowledge

New Drug May Cure Hangovers

What would the IV and DV be in this study?

What are some possible confounding or extraneous variables

in the above new drug study?

Test Your Knowledge

Your New Awesome Bathroom Scale

Your doctor weighs you at 175 lbs. Every time you get on

your new scale at home, it shows 165 lbs. You try over

and over with your scale but it always says 165 lbs.

Is this scale reliable? Is this scale valid?

Intro to Hypothesis Testing

 What is a hypothesis?

• The predicted outcome of an experiment based on a belief about the relation between variables. Not a question! Should include direct reference to IV and DV (e.g., It is expected that participants who consume caffeine prior to learning a list of words will remember more of those words than participants who do not consume caffeine ).

 What is hypothesis testing?

• The process of drawing conclusions about whether a particular relation between variables is supported by the evidence.

Operationalizing Hypotheses

Test Yourself

In a study of the effects of cocaine on specific regions of the brain, microscopic amounts of the drug are delivered to specific regions of the brain, using the latest technology. The subjects are laboratory rats and they are randomly assigned to four groups, each group to receive the drug in only one region of the brain. The effects of the drug on arousal are measured by seeing how long a tired animal will remain awake after an injection of the drug.

• Independent Variable(s), Dependent Variable(s), Confounding Variable(s), Extraneous Variable(s), Operational Definition(s), Hypothesis(es)

Random Assignment

Why do we need random assignment? What does it

accomplish?

Will playing Scrabble regularly increase your vocabulary?

Why is this bad?

Types of Research Design:

Between- vs. Within-Groups

 Between-Groups: Participants experience one, and only

one, level of the independent variable.

 Within-Groups: The different levels of the independent

variable are experience by all participants in the study.

• Order Effects (Practice Effects): How a participant’s behavior changes when the DV is presented a second time.  Counterbalancing: Minimizes order effects by varying the order of presentation of different levels of the IV from one participant to the next.