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1.1 Collecting and Describing Data
Walla Walla Tiffin
36
Mathematics
Undergraduate 2
01/24/2013

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Term
Data
Definition

Any collection of measurements or values 

 

Term
Variable
Definition
Single characteristic being mesured or changed
Term
univariate
Definition
data contingin measurements from a single variable
Term
bivariate/paired
Definition
contains mesurements from two variables
Term
multivariate
Definition
contains data measured from three or more variables
Term
qualitative variable
Definition

one that takes on values representing categoreis or descriptions as opposed to numerical values.

 

ie. zip codes

Term
quantitative variable 
Definition
one that takes on numerical values. the values can be used in computations.
Term
discrete variable
Definition

quantitative (one with numerical value) variable in which there are gaps between the possible values of the variable

 

ie. number of residents in a household (a calcuable value ie. 300 jelly beans in a bag of jelly belly's)

Term
continuous variable 
Definition

quantitative variable for which ther is an infinite number of possible values with no gaps between the values. 

 

Ie. length of residence. Ie. Time. Ie. Number/time line...the distance between two points in infinate and continuous. you could divide forever and still have there be space inbetween. SO the amount of time that a resident lives in the home. 

Term
population
Definition
collection of ALL subjects to be studied.
Term
Sample
Definition
The sub-collection of subjects drawn from WITHIN a given population
Term
Census
Definition
Data being collected from every single member of the population bieng studied.
Term
Simple random sample
Definition
a sample is drawn from a populaiton in such a way that every group of n subjects is the population is equally likely to be choosen.
Term
systematic sample
Definition

a random sample collected from an oredered population by randomly choosing one of the first K subjects and selecting every Kth subject thereafter. 

 

ie. on an assembly line she inspects the fith object and then every fifth object there aftere. 

Term
Stratified Sample
Definition

A population is broken into several groups and then a simple random sample is collected from with in each group. 

 

 

I.e Doing a political pole we select 300 democrats, independents and republicans. we then do a simple random sample from within each strata and perform the evaluation. 

Term
Cluster sample. 
Definition

Taken by dividing the population into several groups and then picking a simple random sample of the group and then sample each of the individual in the selected group. 

 

IE Thirty flights are going out. Five flights are randomly  choosen, each person on those five flights are evaluated. 

Term
Cluster Sample: Story problem
Definition
The pastor of a large church wishes to know what proportion of his congregation would be interested in a new outreach opportunity. Since the church is so large, he decides to collect a sample by randomly selecting 25 of the 100 active small group classes and asking all members of those 25 classes if they would support the new outreach program.
Term
Simple Random: Story Problem
Definition
A county judge wishes to determine how many of the defendants that she sees have a high-school diploma. In order to collect a sample from her docket, she has her clerk use the computer to randomly select 40 case numbers and then checks the educational background of those defendants.
Term
Systematic Sample: Story Problem
Definition
Workers for a consumer survey corporation collect data at a local mall by selecting a strategic location and then randomly selecting one of the first 50 people who walk by to ask to take the survey. They then ask every 50th person who walks by to complete the survey.
Term
Stratified Sample: Story Problem
Definition
A golf pro shop wants to determine the average amount of money spent by the average customer. They suspect that men spend more in the shop than women. They therefore divide their customers into two groups: men and women. They then randomly select 40 of the male and 35 of the female customers and examine their most recent purchase.
Term
Observational Study
Definition
Specific characteristecs are seen and measured but NO ATTEMPT TO CHANGE THESE CHARACTERISTICS IS MADE
Term
Expirament
Definition
treatment is applied and effects ont eh subjects is observed.
Term
Factor
Definition
Independent varibel, the value of which is verified by the experimenter
Term
Treatment
Definition
Specific Combination of factor values
Term
Observational study:Story problem
Definition
Sam wishes to determine the length of time that it takes a radish seed to germinate. He plants radishes in his garden, and continues his normal watering and weeding process. When the first radish sprouts emerge, Sam records the length of time that has elapsed. Is Sam conducting an observational study or an experiment?
Term
Expiriment: Story Problem
Definition
Nancy is more ambitions than Sam. She wants to know if radish seeds can be made to germinate faster by altering the conditions in which they grow. To test this theory, Nancy decides that she will plant four groups of radish seeds. The first group will be watered and weeded as normal. The second group will be watered and weeded as well, but will in addition receive fertilizer every other day. The third group will be weeded as normal, but will receive twice as much water. Finally, the fourth group of radish seeds will be weeded as normal, receive fertilizer every other day, and get twice as much water. Nancy will record how long it takes each group of radish seeds to sprout. Is this an observational study or an experiment?
Term
Convenience Sample
Definition
Sampel collected by simply selecting the most easily available members of society
Term
Biased
Definition
Over-representation of one portion of a populaiton, or/and the under-representation of another. 
Term
Leading Quesiton
Definition
A quesiton phrased in such a way as to elicit a specific response. 
Term
Voluntary Response Sample
Definition
A sample in which people choose themselves whether or not to respond to a general request to participate. 
Term
Correlation
Definition

the link between to or more variables if certain ones frequently appear together with certian values of the other. 

 

ie. correlation between heigth and weight? does being taller cuase you to weigh more? or do they just happen to go together?

Term
Causation
Definition

when, between two variables, the value of one of the variables causes the value of the otehr to change. 

 

ie. measuring average driving speed and number of speeding tickets...it would be reasonable to say that there is a _________ between these to variable. Driving faster causes one to get more speeding tickets. 

Term
Lurking variables
Definition
Unmeasured variable that has an improtatn effect on the realtionship between variables in a study. 
Term
Lurking Variable: Story Problem
Definition

In a study of fuel efficiency and its relationship to weight the Buick Estate Wagon appeared to be an anomaly. Although weighing much more than most cars in its class, the Buick Estate Wagon had a better fuel economy than it should have had in relation to these other cars. Further research indicated that Buick's recommended a higher tire inflation pressure than did the other car manufacturers. Identify the lurking variable in this study.

 

Tire pressure is the lurking variable. While it has an effect on gas mileage (higher pressure = better mileage) it was not included in the original study.

Term
Causation and correlation: Story Problem
Definition

A study of nutrition and TV ownership in Africa found that there was a high correlation between a family suffering from malnutrition and not owing a television set. A statistics student concludes that there is causation as well. That is, owning a television set leads to better nutrition. Critique this conclusion.

Solution


The student is confusing causation and correlation. While there may be correlation between owning a television and having good nutrition, it is not logical to conclude that having a TV improves nutrition. It is much more reasonable to conclude that there is a lurking variable in this study. Perhaps the economic status of the families studied is causing both the differences in nutrition and television ownership.

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