Download population parameters - Penn State Department of Statistics

Doing the Right Thing!
… statistically speaking ...
What is statistics?
• Statistics is a collection of procedures and
principles for gathering and analyzing
sample data to learn something about a
larger population. (Ch. 1).
• Sample  Population!!!
• NOT just Sample and then !!!
Population, parameters,
samples and statistics
• Parameters are numbers that summarize
population data.
– mean , proportion p, standard deviation .
• Statistics are numbers that summarize the
corresponding sample data. (Ch. 2)
– mean , proportion p-hat, standard deviation
s.
• Use sample statistics to learn about
population parameters. (Unit A4)
Different samples produce
different results
• To use statistics to make decisions about
parameters, we must understand how
sample statistics vary by studying their
sampling distributions. (Units B11, B12)
• The normal curve (Unit B9) can be used to
describe how sample means and sample
proportions vary.
Good answers come from
good data…or junk in = junk out!
• If want to learn about one population, use
principles of good sampling and surveying.
(Ch. 4)
• If conducting an experiment to compare two
or more populations, use principles of good
randomized experiments. (Unit A3)
• If performing an observational study to
compare two or more populations, know
limits of observational studies. (Unit A3)
Two ways to learn
about a population parameter
• Confidence intervals (Units C1, C2) estimate
parameters.
– We can be 95% confident that the proportion of
Penn State students who have a tattoo is between
5.1% and 15.3%.
• Hypothesis tests (Ch. 11) test the value of
parameters.
– There is enough statistical evidence to conclude
that the mean GPA of all Penn State science
majors is greater than 3.0.
In this class, we’ve learned about
a limited set of situations
•
•
•
•
•
One population mean (Unit C6)
Mean of paired differences (Unit C9)
Comparing two population means (Unit C8)
One population proportion (Ch. 10, 11)
Comparing two or more population
proportions (Ch. 6)
Choosing the correct analysis
• Depends on type of data
– numerical or categorical
• Depends on number of groups (populations)
– 1, 2, or more
• Depends on research question
– Testing hypotheses: Does the parameter equal
this? Or is there a difference?
– Interval estimation: What is the value of the
parameter? Or how different are the parameters?
Use what you’ve learned here...
• When conducting your own research.
• When critically evaluating what you read in
newspaper articles.
• When critically evaluating what you read in
scientific journal articles.