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Length (in minutes) of a country song

Continuous

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Temperature on a randomly selected day in Memphis, TN

Continuous

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Temperature on a randomly selected day in Memphis, TN

Continuous

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Points scored in an NCAA basketball game

Discrete

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How varying the amount of an explanatory variable affect the value of response variable

Explanation

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Observational study

Measures the value of the response variable without attempting to influence the value of either the response or explanatory variables. That is, in an observational study, the researcher observes the behavior of the individuals without trying to influence the outcome of the study. 

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Designed Experiment

if researcher assigns the individuals in a study to a certain group, intentionally changes the value of an explanatory variable, and then records the value of the response variable for each group

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Confounding

occurs in a study when the effects of two or more explanatory variable are not separated. Any relation that may exist between an explanatary variable and the response variable may be due to some othervariable or variables not accounted for in the study.

Ex: Desire for a type of food and how hungry the  subject is at the time of the study

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Lurking variable

is an explanatory variable that was not considered in a study, but that affects the value of the response variable in the study. Lurking variables are typically related to explanatory variables considered in the study. 

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3 major categories of observational studies:

1) Cross-sectional studies

2) Case-control studies

3) Cohort studies

1) collect information about individuals at a specific point in time or over a very short period of time

2) retrospective they require individuals to look back in time or require the researcher to look at existing records. In case control studies individuals who have a certain characteristics may be matched with those who do not. 

3)  identifies a group of individuals to participate in the study(cohort). Observed over a long period of time. Characteristics about individuals are recorded and come individuals will be exposed to certain factors and others will not. Downside since longer study  people drop out leading to scewed results. 

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Census

list of individuals in a population along with certain characteristics of each individual.

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Random Sampling

Subjects are selected using a chance method or a random number.

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Systematic Sampling 

Subjects are selected using a system of every  kth number after the beginning number is selected randomly.

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Stratified Sampling 

Subjects are selected by first dividing up the population into groups (called strata) and subjects within each group are selected randomly.

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Cluster Sampling 

Subjects are selected by using "intact" groups that are representative of the population.   Used

when the population is large  OR  population resides over a large geographic area.

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Statistics

is science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions.
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Data 

numeric values that are gathered through measurements and/or observations.

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Data Set

a collection of data values

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Data Value (datum)

an individual value  in a data set

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Population

Entire group to be studied

Ex: people, animals, foods, 

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Individual

person or object that is a member of the population being studied

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Sample

is a subset of the population that is being studied

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Statistic

numerical summary of a sample

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Descriptive statistics

consist of organizing and summarizing data. Described data through numerical summaries, tables, and graphes.

Examples include:  the U.S. Census, Special Interest, Group Studies, Marketing Studies, Consumer

                                             Habits, etc

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Inferential Statisitics

uses methods that take a result from a sample, extend it to the population, and measure the reliability of the result. 

Ex: Games of chance,  insurance industry, simulations, consumer taste, 

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Parameter

numerical summary of population

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Process of Statistics

1. Identify the research objective: A researcher must determine the questions he or she wants answered. The questions must be detailed so that it identifies the population that is to be studied. 

2. Collect the data needed to answer the questions posed in #1

3. Describe the data

4. Perform Inference: Apply appropriate techniques to extend the results obtained from the sample to the population and report a level of reliability of the results

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Variables

are the characteristics of the individuals within the population

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Qualitative, or categorical, variables

allow for classification of individuals based on some attribute or characteristic

Examples are: gender,  geographic area, religious affiliation, membership in a group, etc

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Quantitative variables

provide numerical measures of individuals. The values of a quantitative variable can be added or subtracted and provide meaningful results. 

Examples : age,  weight,  height,  GPA, IQ,  distance, payments,  tax  owed, etc.