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Saturday, 4 May 2013

Elementary Statistics chapter 2


 Basic Concepts




Population
The entire collection of events that you are interested in.
Although we wish to make claims about the entire population, it is often too large to deal with.
Two ways of getting around this ...


Random Sampling

Choose a subset of the population ensuring that each member of the population has an equivelant chance of being sampled
Examine that sample and use your observations to draw inferences about the population
Example: Voting Polls, Television Ratings
Note, however, that the inferences drawn are only as good as the randomness of the sample
If the sample is not random, it may not be representative of the population. When a sample is not representative of its parent population, the external validity of any inferences is called into question.
Example: Most psychology experiments

Random Assignment

When studying the effects of some treatment variable, it is also important to randomly assign subjects to treatments
Random assignment reduces the likelihood that groups differ in some critical way other than the treatment
If random assignment is nor used then the internal validity of the experimental results may be compromised
Example: Text book manipulation across years

Variables

Assume we have a random sample of subjects that we have randomly assigned to treatment groups
Example: Stop-smoking study
Now we must select the variables we wish to study, with the term variable referring to a property of an object or event that can take on different values
Examples: # of cigs smoked, abstinance after one week
Note the distinction; # of cigarettes smoked is a continuous variable, whereas abstinance is a categorical variable
Another distinction related to variables concerns variables we measure (dependent variables) versus variables we manipulate (independent variables)
For Example: Whether or not we give a subject the stop-smoking treatment would be the independent variable, and the # of cigarettes smoked would be a dependent variable


What Do We Do With The Data?

Descriptive Statistics are used to describe the data set
Examples: graphing, calculating averages, looking for extreme scores
Inferential Statistics allow you to infer something about the the parameters of the population based on the statistics of the sample, and various tests we perform on the sample
Examples: Chi-Square, T-Tests, Correlations, ANOVA
NOTE: See section in book on measurement scales
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