chapter 1 getting started what is statistics?. individuals vs. variables individuals people or...
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Chapter 1 Getting Started
What is Statistics?
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Individuals vs. Variables
Individuals• People or objects included
in the study
Variables• Characteristic of the
individual to be measured or observed
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Quantitative vs. Qualitative
Quantitative Variables• Have value or numerical
measurement for which operations such as addition or averaging make sense
Qualitative Variables• Describes an individual by
placing the individual into a category or group, such as male or female
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Population vs. Sample
Population Data• Data is from every
individual of interest• Population Parameters are
numerical measures that describe an aspect of a population
Sample Data• The data are from only
some of the individuals of interest
• Sample Statistics are numerical measures that describe an aspect of a sample
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Levels of Measurement
• Nominal – Names, Labels, Categories• Ordinal – Arranged in meaningful
mathematical order• Interval – Differences are meaningful• Ratio – Division or percentage comparisons
make sense; zero point
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Chapter 1 Getting Started
1.2 Random Samples
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Simple Random Sample (SRS)
• A simple random sample of n measurements from a population is a subset of the population selected in such a manner that every sample of size n from the population has an equal chance of being selected.
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Random Number Tables (RNT)
• Used to help secure a SRS• Steps:– Number all members of the population
sequentially.– Drop a pin on the RNT to pick a starting point– Pull digits n at a time, discarding non-used
numbers– Repetition?
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Do Now
• With a partner, discuss how a Random Number Table or Random Number Generator could be used to generate the answer key for a multiple choice test (assume 10 questions on quiz and 5 choices per question).– Rephrased: How can a RNT or RNG be used to
determine next to which letter the correct answer to each question should be placed?
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Other Methods to Secure a Sample
• Systematic• Stratified• Cluster• Multistage• Convenience
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Systematic Sampling
• Population is numbered• Select a starting point at random and pick
every kth member
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Convenience Sampling
• Create sample by selecting population members which are easily available
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Stratified Sampling
• Divide population into distinct subgroups based on specific characteristics
• Draw random samples from each strata
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Cluster Sampling
• Divide population into pre-existing segments or clusters (often geographic).
• Make a random selection of clusters.• All members of cluster are chosen.
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Multistage Sampling
• Use a variety of sampling methods to create successively smaller groups at each stage.
• Final sample is made of clusters.
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Do Now
• Copy the Blue Box from page 21 into your notebooks. This is the beginning of Section 1.3 “Introduction to Experimental Design”
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Census vs. Sample
• Census – measurements from observations from the entire population are used.
• Sample – measurements from observations from part of the population are used
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Observational Study vs. Experiment
• Observational Study – observations and measurements of individuals are conducted in a way that doesn’t change the response or the variable being measured
• Experiment – a treatment is deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured
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Within Experiments:
• Placebo Effect – occurs when a subject receives no treatment but (incorrectly) believes he or she is in fact receiving treatment and responds favorably
• Control Group – those who receive the placebo treatment
• Treatment Group – those who receive the actual treatment
• Completely Randomized Experiment – one in which a random process is used to assign each individual to one of the treatments
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Completely Randomized Experiment
• C.R.E. – is one in which a random process is used to assign each individual to one of the treatments
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Characteristics of a Well-Designed Experiment
• Block – a group of individuals sharing some common features that might affect the treatment
• Randomized Block Experiment – individuals are first sorted into blocks, and then a random process is used to assign each individual in the block to one of the treatments
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Characteristics of a Well-Designed Experiment
• Control Groups – used to account for the influence of other known or unknown variables that might be an underlying cause of change in response in the experimental group.
• Lurking or Confounding Variables – such variables
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Characteristics of a Well-Designed Experiment
• Randomization – used to assign individuals to the two treatment groups. Helps to prevent bias in selecting members to the groups
• Replication – on many patients reduces the possibility that the differences in occurred by chance alone.
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Potential Pitfalls of Surveys
• Nonresponse• Truthfulness of Response• Faulty Recall• Hidden Bias• Vague Wording• Interview Influence• Voluntary Response
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Data Collection Techniques (Summary)
• Census• Samples• Experiments• Observational Studies• Experiments• Surveys• Simulations (previously)