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# Choosing the Correct Analysis

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?.

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## Choosing the Correct Analysis

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1. Choosing the Correct Analysis

2. 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

3. Who Cares? The type(s) of data collected in a study determine the type of statistical analysis used. That’s almost the whole story ….

4. 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?

5. One Group, Categorical (Binary) Data • Hypotheses: Z-test for one proportion • Estimation: Z-interval for one proportion • In Minitab: • Stat >> Basic Stat >> 1 proportion ...

6. 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

7. 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 ...

8. 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.

9. One Group, Measurement Data • Hypotheses: t-test for one mean • Estimation: t-interval for one mean • In Minitab: • Stat >> Basic Stat >> 1-sample t ...

10. 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

11. TwoPaired 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

12. 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.

13. TwoIndependent 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 ...

14. 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.

15. One Group, Two Measurement Variables • Correlation: Does a linear relationship exist? • Linear regression: What is the linear relationship?

16. 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?

17. 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”)?

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