Choosing the Correct Analysis

Class #2, First Activity

• Analyzed first and last names– # of letters in first name– letter E in first name– length, in mm, of first name

• Collected other data, too– semester standing– home state

Who Cares?

The type(s) of data collected in a study determine the type of statistical analysis used.

That’s almost the whole story ….

Choosing the Correct Analysis

• Depends on type of data– measurement or categorical

• Depends on number of groups – 1, 2, or more

• Depends on research question– Testing hypotheses: is there a difference? – Estimation: how much of a difference is there?

One Group, Categorical (Binary) Data

• Hypotheses: Z-test for one proportion

• 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-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

• Do male and female students differ with respect to virginity?– Two groups: Males, Females– Binary Data: Virgin or Not– Determine proportion of male virgins and proportion

of female virgins.

• Hypothesis testing: Tells us if proportions are different. Estimation: Tells us by how much the proportions differ.

One Group, Measurement Data

• Hypotheses: t-test for one mean

• Estimation: t-interval for one mean

• In Minitab: – Stat >> Basic Stat >> 1-sample t ...

Examples: One Group, Measurement 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

Two Paired Groups, Measurement Data

• Hypotheses: Paired t-test for mean difference

• Estimation: Paired t-test for mean difference

• In Minitab: – Stat >> Basic Stat >> Paired t-test

Examples: Two Paired Groups, Measurement Data

• Do people’s pulse rates increase after exercise?– Two paired groups: People before, same people after– Measurement 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, Measurement 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-test ...

Examples: Two Independent Groups, Measurement Data

• Do male and female pulse rates differ?– Two independent groups: Males, Females– Measurement 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.

One Group, Two Measurement 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)?

• Then: hypothesis testing (“is there a difference”) or estimation (“how much”)?