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What is statistics?
A field of study that involves methods for describing and analyzing data. It reduces uncertainty and provides for better decision making.
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What is a population
Universe of cases or subjects of interest to the analyst. People, thins or concepts
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What is a sample
An observable subset of the population. It needs to mirror the population.
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What are some types of samples?
Random and Non Random
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What is a random sample
All units have an equal chance of being included in the sample.
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What are 3 ways to obtain a random sample?
- 1. Using a table of random numbers
- 2. Computer generated random samples
- 3. Software selected random sample
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Describe a simple random sample.
- -Assign all elements a number, in a class of 25 - assign 1 - 25
- -Determine the sample size example: 5
- -Use a table to assign random numbers to provide 5 random numbers between 1 and 25
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Describe systematic sample
- -Produce names of population
- -Determine sample size (5)
- -Divide the total (25) by the sample size (5) = 5
- -Take every 5th name on the list for inclusion in the sample
- -If the 5th person refuses, the analyst must begin the count to 5 again.
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Describe a stratified sample
Divide the number of STRATA (groups) that share similar characteristics. Draw random samples from each Stratum.
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Cluster Sampling is?
Sampling based on selecting clusters from a population and then sampling from those clusters. Examples: geography - rural, suburbs, city
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Describe the differences between stratified and cluster sampling
Cluster samples only include a subset of the clusters. Stratified samples include all of the strata. Stratified samples allow for more precision.
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Name some non random sampling types
- 1. Convience samples - surveying the first 10 people in a parking lot
- 2. Volunteers- American Idol
- 3. Judgemental sample- a sample based on expert judgment
- 4. Quota sample - convience sample designed to provide a certain distribution
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Define sampling error
The difference between the sample and the larger population that is due to pure random chance .
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What is true of sample error.
As sample size increases sampling error decreases .
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Define bias
The differences between a sample and the population that are not do to pure random chance.
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Describe a fact about sampling bias.
Unlike sampling error, sampling bias will not decrease as your sampling number increases .
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Describe some sources of selection bias
- -A group that is under represented in your samples.
- -A group that fails to respond to your survey non response bias
- -A group that self select so as the sample, American Idol.
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Define measurement error
Inaccuracy or miscalculation of the observation , caused by unclear questions, leading questions, questions containing social desirability componant.
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Define Validity
Does the instrument measure what it intended to measure.
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Define Reliability
Does the instrument provide constant results over repeated measurements.
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Name and describe 4 dimensions to validity
- 1. Face - does the anayst have confidence in the measuring instrument
- 2. Content- concerned with the sample population representatives-
- 3. Correlative - the results have a high correlation to other established measures of validity
- 4. Predictive- the resilts should be able to successfully predict outcomes gre = success in a graduate program
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Define external validity
Results that can be readily generalized to the larger population are said to have external validity.
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Define internal validity
Did I measure what I claimed to measure by eliminating all confounding variables
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List and describe 8 threats to internal validity
- 1. History - external events that produce an effect that can be confused with the outcome. school program success vs economic boom happening at same time
- 2. Maturation - internal factors that can be confused with outcome - treated allergies that resolve over time, due to tx or due to growth of child
- 3. Testing- measuring a person that can produce the effect confusing the outcome- Stalins arrival improves productivity
- 4. Instrumentation - changes in the measurement tool
- 5. Statistical regression to the mean - selection of a group due to their deviance from the mean - odds are that next measurement that group will regressed to
- mean.
- 6. Selection bias
- 7. Experimental mortality- subjects dropping out of study will change the composition of the sample.
- 8. Selection-Maturation Interaction -any bias in selection will interact with maturation to produce a greater effect than maturation alone
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Name 3 research design techniques
- 1. Pre-experimental - policy is changed and later a decision is made to evaluate the policy
- 2. Quasi Experimental - uses a comparison group. Ex: impact of affirmative action on female employment in shipyards.
- 3. Experimental -includes randomization componant. Participants randomly selected and randomly assigned to experimental or control group.
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Describe an example of the paradox of internal and external validity
Real world clinical trials often may have a drug that is valid in a controlled setting (high internal value) but not effective in the real world where patients don't follow direction (low external validity)
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List 4 levels of measurement
- 1. Nominal - catagorizing information. Hair Color: 1= blond 2= brunette 3= other
- 2. Ordinal - ranked in order of some rype of continuum. 1= strongly agree 2= agree 3= neutral 4= disagree 5= strongly diagree
- 3. Interval - regular numbers where distance between the numbers is the same and all numbers anchored by an arbitrary zero - IQ, Temp, Test scores
- 4. Ratio Scale distance between points is equal and anchored by a non arbitrary zero. Hourly wage, height, weight, age, miles driven in a day
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Give some examples of Nominal data
- -Gender
- -Ethnicity
- -Marital status
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Give some examples of Ordinal Data
- -Movie ratings
- -Scio economic status
- -Rating of meat in the store
- -Rank order of anything
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Name some examples of Interval Data
- -Degrees F OR C
- -Most personality measures
- -Intelligence scores
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List some examples of Ratio Data
- -Annual income in dollars
- -Distance as measured in miles, inches, centimeters etc..
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What arithmetical operation is used for Nominal Data
Counting
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What arithmetical operations can be used for Ordinal Data?
Gretaer than or less than
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What arithmetical operation is permitted with Interval Data?
Addition and subtraction of the scale values
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What arithmetical operation is permitted with Ratio Data?
Multiplication and division of scale values
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Name the measures of central tendency begining with the most commonly used.
- 1. Mean
- 2. Mode
- 3. Median
- 4. Trimmed Mean
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Define Mode
A measurement of central tendoncy that is equal to the score that occurs most often in the distribution.
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Define Median
The score that divides the distribution in half. =(n + 1) / 2 will identify the positon of the median
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Define the Mean
The arithmetic average of scores. Sum the scores and divide by the number of scores.
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Which measures of central tendoncy are not useful in statistical decsion making but may be helpful interms of describing them
Mode and Median
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