Data Analysis

Front 1

Define Statistics

Back 1

The science and craft of inductive reasoning from variable numerical evidence.

Front 2

What is Deductive Reasoning?

Back 2

Reasoning that applies a general fact to make a conclusion about a specific case. ie. pythagorean theorum applied to an isocoles triangle.

Front 3

What is Inductive reasoning?

Back 3

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)

Front 4

Deductive reasoning is _____ and the conclusions are _____.

Back 4

Mathematical reasoning

Certain

Front 5

Inductive reasoning is _____ and the conclusions are _____.

Back 5

Statistical reasoning

Uncertain

Front 6

What is the product of a statistical analysis?

Back 6

A conclusion

Front 7

Statistics is not equal to:

Back 7

Mathematics. It is inductive reasoning with a mathematical basis.

Front 8

What does a mathematical foundation provide?

Back 8

Principles, a common language and common tools for inductive reasoning from numerical evidence.

Front 9

What is an argument?

Back 9

A conclusion with justification.

Front 10

What is an opinion?

Back 10

A conclusion without justification.

Front 11

What does data analysis of a problem involve?

Back 11

Exploration (eg. graphical) Choice of statistical tool (eg. two-sample t-test) Communication of a statistical conclusion.

Front 12

When can you assume causation?

Back 12

When the experiment was randomized.

Front 13

Randomized experiment

Back 13

An investigator controls the assignment of experimental units to groups and uses a chance mechanism (like a coin flip) to make the assignment.

Front 14

Observational study

Back 14

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.

Front 15

Statistical inference of cause-and -effect relationships can be drawn from what types of studies?

Back 15

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.

Front 16

Confounding variable

Back 16

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.

Front 17

What role do observational studies have in serious scientific inquiries?

Back 17

-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.

Front 18

Inferences to Populations can be drawn from what kind of studies?

Back 18

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.

Front 19

What is a simple random sample?

Back 19

A subset of the population consisting of members selected in such a way that every subset is afforded the same chance of being selected.

Front 20

Inference

Back 20

A conclusion that patterns in the data are present in some broader context.

Front 21

Statistical inference

Back 21

an inference justified by a probability model linking the data to the broader context.

Front 22

additive treatment effect model

Back 22

Y*=Y+σ

Where Y is a score and σ is a treatment

Front 23

null hypothesis

Back 23

σ=0

typically representing the simpler state like the absence of an effect.

Front 24

Alternate hypothesis

Back 24

σ does not equal 0

There is an effect

Front 25

test statistic

Back 25

a statistic used to measure the plausibility of an alternative hypothesis relative to a null hypothesis.

Front 26

observed p-value

Back 26

the probability that randomization alone leads to a test statistic as extreme or more extreme than the one observed.

Front 27

one-sided p-value

Back 27

when only those test statistic outcomes larger or equal to the observed one are counted and used in the p-value calculation.

Front 28

Parameter

Back 28

an unknown numerical value describing a feature of a probability model. Indicated by Greek letters.

Front 29

Statistic

Back 29

Any quality that can be calculated from the observed data. Represented by Roman letter symbols.

Front 30

Estimate

Back 30

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.

Front 31

Mean

Back 31

An average calculated over an entire population. A mean is therefore a parameter. μ

Front 32

Average in a sample

Back 32

Both a statistic and an estimate of the population mean. Ybar