Choosing the correct analysis
Some research questions
• How many times each semester do Penn
State students go “home”?
• What percentage of Penn State students
smoke cigars?
• Do a higher percentage of Alaskans commit
suicide than non-Alaskans?
• How much heavier are male students than
female students?
Choosing the correct analysis
• Depends on the type of data
– continuous or categorical
• Depends on the number of groups
– 1, 2, or more
• Depends on the research question
– Testing hypotheses: is it this?
– Estimation: what is it?
• Depends on the assumptions made
One Group,
Categorical (Binary) Data
• One- or two-sided hypothesis: Z-test for
one proportion
• Two-sided hypothesis: Chi-square test
• Estimation: Z-interval for one proportion
• In Minitab:
– Stat >> Basic Stat >> 1 proportion ...
Examples:
One Group, Binary Data
• Estimation (Z-interval): What proportion
of students have an E in their last name?
• Hypothesis (Z-test): Do a majority of
students work during the semester?
– H0: p = 0.5 versus HA: p > 0.5
Two Groups,
Categorical (Binary) Data
• One- or two-sided hypothesis: Z-test for
two proportions
• Two-sided hypothesis: Chi-square test
• Estimation: Z-interval for two proportions
• In Minitab:
– Stat >> Basic Stat >> 2 proportions …
– Stat >> Tables >> Chi-Square Test ...
Examples:
Two Groups, Binary Data
• Different proportions of male students who
snore and female students who snore?
– Two groups: Males, Females
– Binary Data: Snore or not
– Determine proportion of male snorers and
proportion of female snorers.
• Hypothesis testing: Tells us if proportions
are different. Estimation: Tells us by how
much the proportions differ.
More than two Groups,
Categorical Data
• Two-sided hypothesis: Chi-square test for
more than two proportions
• In Minitab:
– Stat >> Tables >> Chi-Square Test ...
Examples:
> 2 Groups, Categorical Data
• Is rate of cigarette smoking independent of
semester standing?
– Four groups: Freshmen, sophomores, juniors,
seniors
– Categorical (binary) data: Smoker or not
– Determine proportion of freshman smokers,
sophomore smokers, junior smokers, senior
smokers.
One group,
Continuous data
• Hypotheses:
– t-test for one mean
– sign test or signed rank test for one median
• Estimation: t-interval for one mean
• In Minitab:
– Stat >> Basic Stat >> 1-sample t …
– Stat >> Nonparametrics >> 1-sample sign…
– Stat >> Nonparametrics >> 1-sample Wilcoxon…
Examples:
One Group, Continuous Data
• Estimation (t-interval): What is the mean
length of student’s middle finger?
• Hypothesis (t-test): Is mean IQ larger than
100?
– H0:  = 100 versus HA:  > 100
• Hypothesis (sign test): Is median income
greater than 40,000?
– H0: m = 40,000 versus HA: m >40,000
Two Paired Groups,
Continuous Data
• Hypotheses:
– Paired t-test for mean difference
– Sign test or signed rank test for median difference
• Estimation: Paired t-test for mean difference
• In Minitab:
– Stat >> Basic Stat >> Paired t…
– Stat >> Nonparametrics >> 1-sample sign…
– Stat >> Nonparametrics >> 1-sample Wilcoxon…
Examples: Two Paired Groups,
Continuous Data
• Do people’s pulse rates increase after
exercise?
– Two paired groups: People before, same people
after
– Continuous Data: Pulse rates
– Determine average difference in pulse rates.
• Hypothesis testing: Tells us if mean
difference is 0. Estimation: Tells us how
much mean differs from 0.
Two Independent Groups,
Continuous Data
• Hypotheses: Two-sample t-test for
difference in means.
• Estimation: Two-sample t-interval for
difference in means.
• In Minitab:
– Stat >> Basic Stat >> 2-sample t...
Examples: Two Independent
Groups, Continuous Data
• Do male and female pulse rates differ?
– Two independent groups: Males, Females
– Continuous data: Pulse rates
– Determine difference in average pulse rates.
• Hypothesis testing: Tells us if difference in
means is 0. Estimation: Tells us by how
much the means differ.
More than two independent
Groups, Continuous data
• Hypotheses: Analysis of variance
• In Minitab:
– Stat >> ANOVA >> One-way ...
– Stat >> ANOVA >> One-way (unstacked)...
One Group, Two Continuous
Variables
• Correlation: Does a linear relationship
exist?
• Linear regression: What is the linear
relationship?
Example: One Group, Two
Measurement Variables
• Correlation: Does a relationship exist
between number of nights out and GPA?
• Linear regression: If someone goes out 10
times each month, what kind of a GPA can
they expect?
Choosing the correct analysis
• First ask: how many groups?
• Then: what type of data? Summarized by
a proportion (percentage) or average (mean)
or median?
• Then: hypothesis testing (“is there a
difference”) or estimation (“how much”)?
• Then: don’t forget assumptions….
Some more research questions
• Do seniors earn higher semester grade point
averages than freshmen?
• What is the relationship between amount of
alcohol consumed (in ounces) and level of
coordination (on a scale from 1 to 10)?
• Are number of skipped classes and student’s
course grade linearly related?
Some more research questions
• Is there a difference in the percentage of
NCAA football players who graduate and
NCAA basketball players who graduate?
• How many hours per week do PSU students
study outside of class?
• How much more prevalent is lupus in
women than in men?
Some more research questions
• Do PSU students drink, on average, more
than 1 cup of coffee per day during finals
week? (During finals week, a sample of
students will record how many cups of
coffee they drink each day.)
• Is recovery time from migraine related to
treatment (A, B, C)?
Some more research questions
• Is there a relationship between political
affiliation and income?
• How much heavier (in pounds) are 15-year
old boys than 13-year old boys?
• A random sample of 64 students were
asked: “Do you study regularly at Pattee?”
One last research question
• Do Goodyear tires have better tread wear
than Firestone tires? Tread wear is
measured in millimeters of tread remaining
after 30,000 miles. Thirty cars are selected
for experiment. On each car, one Goodyear
tire and one Firestone tire is placed
randomly in one of two front positions.