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? –H 0 : p = 0.5 versus H A : 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? –H 0 :  = 100 versus H A :  > 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”)?