21
Inference Chapter about Variables:
Part III Review
BPS - 5th Ed.
Chapter 21
1
Data Production
Data Basics
Individuals (subjects)
Variables
o Categorical vs Quantitative
o Units of Measurement
o Explanatory vs Response
Data production basics
o Observation vs Experiment
o Simple Random Samples
o Completely Randomized Experiments
Beware
o Really bad data production can make interpretation
impossible (voluntary response, confounding)
o Weakness in data production can make generalizing
conclusions difficult (for example, sampling students at only
BPS - 5th Ed. one campus)
Chapter 21
2
Data Analysis
Plot your data
Look for overall pattern
Striking deviations
Add numerical descriptions based on what you see
One quantitative variable
Graphs: Stemplot, histogram, boxplot, probability plot
Pattern: distribution shape, center, spread. Outliers?
Density curves to describe overall pattern (like the Normal
curves)
Numerical descriptions: five-number summary or and s.
Beware
Averages and other simple descriptions can miss the real story
Lurking variables
Effects of outliers
Effects of influential observations
BPS - 5th Ed.
Chapter 21
3
The Reasoning of Inference
Inference uses sample data to infer conclusions
about the population.
Data should come from an SRSs or randomized
comparative experiments
Always examine your data before doing
inference. Inference often requires a regular
pattern, such as roughly with Normal no strong
outliers.
Key idea: What would happen if we did this
many times?
BPS - 5th Ed.
Chapter 21
4
The Reasoning of Inference (cont.)
Confidence Intervals
Estimate a population parameter
The method captures the parameter approximately
the stated percentage of the time (95% CI, If we
constructed confidence intervals over and over, about
95% would capture the true mean)
Beware
The margin of error of the confidence interval does
not include the effects of practical errors such as
undercoverage and nonresponse.
BPS - 5th Ed.
Chapter 21
5
The Reasoning of Inference (cont.)
Significance Tests: assess evidence against H0 in favor
of Ha
P-value
The probability of a Type I error based on your sample
Smaller the P-value, the stronger the evidence against the null
hypothesis (H0)
If H0 were true, how often would I get an outcome favoring the
alternative this strongly?
Statistical significance at a particular level (0.05 for
example), P-value < 0.05, means that an outcome this
extreme would occur less than 5% of the time if H0 were
true.
Beware
P<0.05 is not sacred
Statistical significance is not the same as practical significance
BPS - 5th Ed.
Chapter 21
6
The Reasoning of Inference (cont.)
Methods of Inference
Choose the right inference procedure.
Carry out the details.
State your conclusions.
BPS - 5th Ed.
Chapter 21
7
Inference About Variables
BPS - 5th Ed.
Chapter 21
8