Sample and PopulationSample and PopulationPopulation

◦ entire set of things of interest e.g., the entire piggy bank of pennies e.g., the entire population of individuals in the US

Sample◦ the part of the population about which you

actually have information e.g., a handful of pennies e.g., 100 men and women who answered an

online questionnaire about health care usage

Why Study Samples vs. Why Study Samples vs. PopulationsPopulationsIt is usually more practical to obtain

information from a sample than from the entire population.

The goal of research is to make generalizations or predictions about populations or events in general.

Much of social and behavioral research is conducted by evaluating a sample of individuals who are representative of a population of interest.

What is Sampling?What is Sampling?Population

Sample

Using data to say something (make an inference) with confidence, about a whole (population) based on the study of a only a few (sample).

Sampling Frame

Sampling Process

What you want to talk

about

What you actually

observe in the data

Inference

Methods of SamplingMethods of SamplingRandom Selection method of choosing a sample in which each individual in the population has an

equal chance of being selected A sample “n” is selection from population ‘N” Selection process with no pattern; unpredictable Reduces the likelihood of researcher bias Researcher can calculate the probability of certain outcomes

Several different ways to conduct random samplingRandom numbers table, drawing out of a hat, coin flips, etc

Why Random Assignment is best? Samples that are assigned in a random fashion are most likely to be truly representative

of the population under consideration.

Haphazard Selection (Convenience Sampling) method of selecting a sample of individuals to study by taking whoever is available or happens to be first on a list

This method of selection can result in a sample that is not representative of the population.

Sample Size and Sampling Sample Size and Sampling ErrorError Sample selection is usually mentioned in the

methods section of a research article.Appropriate sampling methods must

be evaluated. All other things being equal, smaller

samples (e.g., those with fewer than 1,000 respondents) have greater sampling error than larger samples. ◦To better understand the notion of

sampling error, it is helpful to recall that data from a sample provide merely an estimate of the true proportion of the population that has a particular characteristic

Statistical Terminology for Statistical Terminology for Sample and PopulationsSample and PopulationsPopulation Parameters

◦mean, variance, and standard deviation of a population

◦are usually unknown and can be estimated from information obtained from a sample of the population

Sample Statistics◦mean, variance, and standard

deviation you figure for the sample◦calculated from known information

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ProbabilityProbabilityExpected relative frequency of a particular outcome

outcometerm used for discussing probability for the result of an

experimentexpected relative frequency

number of successful outcomes divided by the number of total outcomes you would expect to get if you repeated an experiment a large number of times

long-run relative-frequency interpretation of probability understanding of probability as the proportion of a particular outcome

that you would get if the experiment were repeated many times

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Steps for Figuring Steps for Figuring ProbabilityProbability

Determine the number of possible successful outcomes.

Determine the number of all possible outcomes.

Divide the number of possible successful outcomes by the number of all possible outcomes.

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Figuring ProbabilityFiguring ProbabilityYou have a jar that contains 100

jelly beans. 9 of the jelly beans are green.

The probability of picking a green jelly bean would be 9 (# of successful outcomes) or 9%100 (# of possible outcomes)

Copyright © 2011 by Pearson Education, Inc. All rights reserved

Range of ProbabilitiesRange of ProbabilitiesProbability cannot be less than 0

or greater than 1.◦Something with a probability of 0 has

no chance of happening.◦Something with a probability of 1 has

a 100% chance of happening.

Copyright © 2011 by Pearson Education, Inc. All rights reserved

ppp is a symbol for probability.

Probability is usually written as a decimal, but can also be written as a fraction or percentage.

p < .05Threshold for significance in research

the probability is less than .05So, you are saying that there is less than a 5% chance

of the differences you see in your research results being from something other than random chance variation

Probability is discussed in the context of reporting statistical significance of study results. The p-value is the probability of the findings being by something other than chance occurrence.

Researcher will set the threshold prior to doing the research; Threshold p-value is usually p< .05 or p< .01

Probability, Z Scores, and the Probability, Z Scores, and the Normal DistributionNormal Distribution

The normal distribution can also be thought of as a probability distribution.◦The percentage of scores between two

Z scores is the same as the probability of selecting a score between those two Z scores.