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32 Cards in this Set
- Front
- Back
Define Statistics
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The science and craft of inductive reasoning from variable numerical evidence.
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What is Deductive Reasoning?
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Reasoning that applies a general fact to make a conclusion about a specific case. ie. pythagorean theorum applied to an isocoles triangle.
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What is Inductive reasoning?
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Reasoning that concludes something general after observing only a part. ie. 56% of Americans favor X (taken from a sample of 400; margin of error =3pct points)
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Deductive reasoning is _____ and the conclusions are _____.
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Mathematical reasoning
Certain |
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Inductive reasoning is _____ and the conclusions are _____.
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Statistical reasoning
Uncertain |
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What is the product of a statistical analysis?
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A conclusion
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Statistics is not equal to:
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Mathematics. It is inductive reasoning with a mathematical basis.
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What does a mathematical foundation provide?
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Principles, a common language and common tools for inductive reasoning from numerical evidence.
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What is an argument?
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A conclusion with justification.
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What is an opinion?
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A conclusion without justification.
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What does data analysis of a problem involve?
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Exploration (eg. graphical) Choice of statistical tool (eg. two-sample t-test) Communication of a statistical conclusion.
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When can you assume causation?
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When the experiment was randomized.
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Randomized experiment
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An investigator controls the assignment of experimental units to groups and uses a chance mechanism (like a coin flip) to make the assignment.
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Observational study
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The group status of the subjects is established beyond the control of the investigator. (bank sex study) the group status (sex of employee) was not decided by the investigator.
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Statistical inference of cause-and -effect relationships can be drawn from what types of studies?
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Randomized. NOT observational. Randomizing ensures that subjects with different and possibly relevant features are mixed between the two groups. There is a chance that the randomization could unintentionally turn out skewed, but it is made up for in the stats tools that express uncertainty. In an observational study you cannot rule out the possibility that confounding variables are responsible for group differences in the measured outcome.
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Confounding variable
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Is related to both group membership and to the outcome. It's presence makes it hard to establish the outcome as being a direct consequence of group membership.
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What role do observational studies have in serious scientific inquiries?
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-Establishing causation isn't always the goal (it may not matter why the link occurs)
-Establishing causation can be done in other ways -Analysis of observational data may lend evidence toward causal theories and suggest the direction of future research. |
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Inferences to Populations can be drawn from what kind of studies?
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Studies done with Random Sampling- subjects are selected from a well-defined population with each subject having an equal chance of being selected. It ensures that all subpopulations are represented in roughly the same mix as the overall population, This can be unintentionally become nonrepresentative, but stats inference procedures incorporate measures of uncertainty that describe that change.
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What is a simple random sample?
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A subset of the population consisting of members selected in such a way that every subset is afforded the same chance of being selected.
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Inference
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A conclusion that patterns in the data are present in some broader context.
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Statistical inference
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an inference justified by a probability model linking the data to the broader context.
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additive treatment effect model
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Y*=Y+σ
Where Y is a score and σ is a treatment |
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null hypothesis
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σ=0
typically representing the simpler state like the absence of an effect. |
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Alternate hypothesis
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σ does not equal 0
There is an effect |
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test statistic
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a statistic used to measure the plausibility of an alternative hypothesis relative to a null hypothesis.
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observed p-value
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the probability that randomization alone leads to a test statistic as extreme or more extreme than the one observed.
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one-sided p-value
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when only those test statistic outcomes larger or equal to the observed one are counted and used in the p-value calculation.
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Parameter
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an unknown numerical value describing a feature of a probability model. Indicated by Greek letters.
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Statistic
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Any quality that can be calculated from the observed data. Represented by Roman letter symbols.
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Estimate
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a statistic used as a guess for the value of a parameter. The notion for a parameter symbol is the symbol with a hat on it. The estimate van be calculated, but the parameter remains unknown.
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Mean
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An average calculated over an entire population. A mean is therefore a parameter. μ
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Average in a sample
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Both a statistic and an estimate of the population mean. Ybar
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