# Unit 1 Ap statistics vocabulary/concepts

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cluster sampling

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cluster sampling

A probability sampling technique in which clusters of participants within the population of interest are selected at random, followed by data collection from all individuals in each cluster

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cluster sampling is widely used because of its cost- effectiveness and ease of implementation. In many cases, the only representative sampling frame available to researchers is one based on clusters.

disadvantages: a primary disadvantage of cluster sampling is that the clusters often are homogeneous. the more homogeneous the cluster, the less precise the sample estimates. another concern is the appropriateness of the designated cluster factor used to identify the sampling unites within clusters.

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stratified sampling

a variation of random sampling; the population is divided into subgroups of characteristics (similar people get grouped together)

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Advantages: Sample accurately reflects the population structure; Guarantees proportional representation of groups within a population; Disadvantages: Very costly and time-consuming. Also, people must be clearly classified into distinct strata. Selection within each stratum suffers from same disadvantages as simple random sampling

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undercoverage bias

occurs when some groups in the population are left out of the process of choosing the sample

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non-response bias

Bias introduced into survey results because individuals refuse to participate or are not reachable

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What term do you have to put when using calculator to generate random numbers

"regenerate if repeated values"

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steps to SRS using random digits table

1. ASSIGN each member of the population from 01 to N.*

2. Determine the population size and sample size.

3. Select a starting point on the random number table. (randint)

4.) Select the firstÂ nÂ numbers (however many numbers are in your sample) whose last X digits are between 0 and N. For instance, if N is a 3-digit number, then X would be 3.

5. Continue this way through the table until you have selected your entire sample, whatever your n is

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systematic sampling

select some starting point and then select every kth (e.g. every 3rd) element in the population

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Advantages: Simple and quick to use, no need to label each member of the sample, suitable for large samples and large populations; Disadvantages: It can introduce bias if the sampling frame is not random (e.g. numbering off people for dodgeball and students stand in a certain position to be on the same team)

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Sample survey procedure

figure out â†’ 1.) population we want to describe 2.) what we want to measure 3.) how to sample

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Census

the entire population

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Population

everybody within the character of interest -> does not actually mean the entire population unless the character of interest is the entire population of the world

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advantages - most accurate representation of the data no need to even sample; disadvantages - near impossible to do when the population gets bigger

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What are some bad sampling methods

convenience sample, voluntary sample, etc

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they overestimate or underestimate the data that are not able to be generalized to the vast population.

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random sampling

a method of poll selection that gives each person in a group the same chance of being selected

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Simple Random Sample (SRS)

a sample in which each set of n elements in the population has an equal chance of selection

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confounding

When two or more variables are associated in such a way that their effects on a response variable cannot be distinguished from each other. (testing for two things at once, like the sitting and closing eyes heart rate test that we did during class)

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Control group

Experimental group whose primary purpose is to provide a baseline for comparing the effects of the other treatments. Depending on the purpose of the experiment, a control group may be given a placebo or an active treatment (called a double blind)

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Sampling with replacement

any number can be counted multiple times (e.g. lottery, prize selection the same person can get three pieces of candy)

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Sample without replacement

a number cannot be repeated (ignore duplicates) - the same item cannot be selected more than once

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How do both experimental and observational studies choose their study subjects

Both types of studies use random sampling to select participants

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Experimental study versus observational study

experimental studies involve actively assigning participants specific tasks/treatments - manipulating a variable; observational studies observe participantsâ€™ behaviors without directing them/observing data that already exists without changing anything

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Setting of experimental study versus observational study

Experimental studies are often conducted in structured environments like labs; observational studies are often conducted in natural environments without researcher control

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Cost and length difference between experimental study versus observational study

Experimental studies are generally more expensive when there are more controls; observational studies are usually less expensive but can go on for longer

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treatment

a specific condition that is applied to the individuals in an experiment â†’ consider the experimental group

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experimental units

smallest collection of individuals to which treatments are applied. When the units are people, they are often called â€śsubjectsâ€ť

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response variable

dependant variable â†’ measures an outcome of a study

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explanatory variable

independent variable â†’ the treatment/the condition; explains or predicts changes in a response variable

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advantages of an experiment over an observational study

causality establishment, control over variables, precision and accuracy, takes less time, replicability, manipulation of variables, experimental conditions(allow researchers to create conditions that might not naturally occur or take too long to occur)

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double blind

neither the subjects nor those who interact with them that measure the response variable know which treatment a subject received (real versus placebo)

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Inference for sampling

Drawing conclusions that go beyond the data at hand â†’ making inferences/generalizations about the entire populations which are likely based on the info that is put out

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Completely randomized design

Design in which the experimental units are assigned to the treatments completely by chance

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Block

Group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments

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Statistically significant

Observed effect so large that it would rarely occurred by chance (specified as the P value which is 5 percent)

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Placebo

A fake treatment (typically used on the control group to signify the effects of the real treatment)

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Prospective study

A prospective studyÂ watches for outcomes, such as the development of a disease, during the study period and relates this to other factors such as suspected risk or protection factor(s). The study usually involves taking a cohort of subjects and watching them over a long period.

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What are effective means to display categorical data

bar chart, pie chart

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What are effective means to display quantitative data

Histograms, percentage polygon, line graphs,Â cumulative percentage graphs

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response-bias

The response bias refers to ourÂ tendency to provide inaccurate, or even false, answers to self-report questions, such as those asked on surveys or in structured interviews; response bias is also introduced based on how the question is worded.

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population paramater

a population parameter isÂ a number that describes something about an entire group or population; e.g. the mean, median, standard deviation etc

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principles of experimental design

comparison, random assignment, control, replication

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replication (in an experiment)

replicating a treatment to numerous different experimental units

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common response variable

a type of lurking/confounding variable â†’ neither explanatory nor response, but still affects the relationship between both of these variables

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Control (in an experiment)

When conducting an experiment, a control isÂ an element that remains unchanged or unaffected by other variables

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what is always the first step of any type of sampling (cluster, stratified etc)

defining the population you would like to take your sample from

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what are the three types of experimental designs

completely randomized design, matched pairs design, and repeated measure design

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matched pair design

Pairs of people who share similar characteristics are each tested with differing treatments. Then, their results are compared to see if the treatment has an effect on what is being measured.

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repeated measure design

Repeated measures design isÂ a research design that involves multiple measures of the same variable taken on the same or matched subjects either under different conditions or over two or more time periods

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what are some examples of nonsampling error

data entry errors, biased survey questions (which might lead to response bias), biased processing/decision making, non-responses, inappropriate analysis conclusions, and false information provided by respondents.

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sampling frame

a list of the items or people forming a population from which a sample is taken.

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what is the diference between block design and stratified random sampling

block design is a specific method use for designing an experiment while stratified random sampling is a method of gathering a sample

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sampling variability

results vary from sample to sample

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margin of error

how far off our sample from the truth of the population

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factor

another word for explanatory variable

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how should you choose which variable to block for

blocks should be formed based on the most important sources of variability.

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levels

number of variations within a factor (explanatory variable)

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population of generalization

the people that you are pulling your sample from

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