What is statistics? Prof. Jacob M. Montgomery. Quantitative Political Methodology (L32 363) August 31, 2016

Transcription

1 What is statistics? Prof. Jacob M. Montgomery Quantitative Political Methodology (L32 363) August 31, 2016 Lecture 2 (QPM 2016) Measurement August 31, / 8

2 Topics for today A (very) broad view of statistical methods Group exercise on measures, sampling, and error. Lecture 2 (QPM 2016) Measurement August 31, / 8

3 What is statistics? Statistics A body of methods for collecting and analyzing data. Lecture 2 (QPM 2016) Measurement August 31, / 8

4 What is statistics? Statistics A body of methods for collecting and analyzing data. Let s break that down. Research design: Gathering data that will allow us to answer research questions by testing empirical hypotheses. Lecture 2 (QPM 2016) Measurement August 31, / 8

5 What is statistics? Statistics A body of methods for collecting and analyzing data. Let s break that down. Research design: Gathering data that will allow us to answer research questions by testing empirical hypotheses. Description: Summarizing the data. Lecture 2 (QPM 2016) Measurement August 31, / 8

6 What is statistics? Statistics A body of methods for collecting and analyzing data. Let s break that down. Research design: Gathering data that will allow us to answer research questions by testing empirical hypotheses. Description: Summarizing the data. Inference: Using data to make (probabilistic) statements about the real world. Testing our hypotheses. Lecture 2 (QPM 2016) Measurement August 31, / 8

7 Lecture 2 (QPM 2016) Measurement August 31, / 8

8 Example: What percent of this class supports Gary Johnson for President? Using that information, what is the percent of WashU undergraduates that support ACA? Lecture 2 (QPM 2016) Measurement August 31, / 8

9 Some big concepts How it all works: Populations Lecture 2 (QPM 2016) Measurement August 31, / 8

10 Some big concepts How it all works: Populations have parameters Lecture 2 (QPM 2016) Measurement August 31, / 8

11 Some big concepts How it all works: Populations have parameters (often denoted µ) Lecture 2 (QPM 2016) Measurement August 31, / 8

12 Some big concepts How it all works: Populations have parameters (often denoted µ) Example? Lecture 2 (QPM 2016) Measurement August 31, / 8

13 Some big concepts How it all works: Populations have parameters (often denoted µ) Example? Why can t we know it? Lecture 2 (QPM 2016) Measurement August 31, / 8

14 Some big concepts How it all works: Populations have parameters (often denoted µ) Example? Why can t we know it? Choose a sample (randomly or otherwise) Gather data from this sample (e.g.,?) Lecture 2 (QPM 2016) Measurement August 31, / 8

15 Some big concepts How it all works: Populations have parameters (often denoted µ) Example? Why can t we know it? Choose a sample (randomly or otherwise) Gather data from this sample (e.g.,?) Calculate statistics Lecture 2 (QPM 2016) Measurement August 31, / 8

16 Some big concepts How it all works: Populations have parameters (often denoted µ) Example? Why can t we know it? Choose a sample (randomly or otherwise) Gather data from this sample (e.g.,?) Calculate statistics (e.g., x = x i n ) Lecture 2 (QPM 2016) Measurement August 31, / 8

17 Some big concepts How it all works: Populations have parameters (often denoted µ) Example? Why can t we know it? Choose a sample (randomly or otherwise) Gather data from this sample (e.g.,?) Calculate statistics (e.g., x = x i Is this descriptive or inferential? n ) Lecture 2 (QPM 2016) Measurement August 31, / 8

18 Some big concepts How it all works: Populations have parameters (often denoted µ) Example? Why can t we know it? Choose a sample (randomly or otherwise) Gather data from this sample (e.g.,?) Calculate statistics (e.g., x = x i Is this descriptive or inferential? Use statistics to make a statement about the real world Is this descriptive or inferential? n ) Lecture 2 (QPM 2016) Measurement August 31, / 8

19 Data types and why we care Continuous Discrete Interval ex., Income ex, Family size Ordinal NA ex., Love mornings Nominal (Qualitative) NA ex., Eye color Note: You will use different statistical approaches and calculations depending on where your data falls on this table. Lecture 2 (QPM 2016) Measurement August 31, / 8

20 Class business Problem set 1 will be posted online today(ish). Lecture 2 (QPM 2016) Measurement August 31, / 8

21 Class business Problem set 1 will be posted online today(ish). Sign up for the Facebook page. Last warning. Lecture 2 (QPM 2016) Measurement August 31, / 8

22 Class business Problem set 1 will be posted online today(ish). Sign up for the Facebook page. Last warning. Look at the online content we provide before class and lab. Lecture 2 (QPM 2016) Measurement August 31, / 8

23 Class business Problem set 1 will be posted online today(ish). Sign up for the Facebook page. Last warning. Look at the online content we provide before class and lab. Take the class survey. Lecture 2 (QPM 2016) Measurement August 31, / 8

24 Class business Problem set 1 will be posted online today(ish). Sign up for the Facebook page. Last warning. Look at the online content we provide before class and lab. Take the class survey. Quiz grading Lecture 2 (QPM 2016) Measurement August 31, / 8

25 Class business Problem set 1 will be posted online today(ish). Sign up for the Facebook page. Last warning. Look at the online content we provide before class and lab. Take the class survey. Quiz grading Group activity Lecture 2 (QPM 2016) Measurement August 31, / 8

26 Class business Problem set 1 will be posted online today(ish). Sign up for the Facebook page. Last warning. Look at the online content we provide before class and lab. Take the class survey. Quiz grading Group activity Engage all your group members Lecture 2 (QPM 2016) Measurement August 31, / 8

27 Class business Problem set 1 will be posted online today(ish). Sign up for the Facebook page. Last warning. Look at the online content we provide before class and lab. Take the class survey. Quiz grading Group activity Engage all your group members Rules Lecture 2 (QPM 2016) Measurement August 31, / 8

28 Class business Problem set 1 will be posted online today(ish). Sign up for the Facebook page. Last warning. Look at the online content we provide before class and lab. Take the class survey. Quiz grading Group activity Engage all your group members Rules Write out a copy for class discussion/one to turn in Lecture 2 (QPM 2016) Measurement August 31, / 8

29 Data types and why we care Data basics Categorical Qualitative: Unordered categories Lecture 2 (QPM 2016) Measurement August 31, / 8

30 Data types and why we care Data basics Categorical Qualitative: Unordered categories Quantitative: Categories differ in magnitude Lecture 2 (QPM 2016) Measurement August 31, / 8

31 Data types and why we care Data basics Categorical Qualitative: Unordered categories Quantitative: Categories differ in magnitude Lecture 2 (QPM 2016) Measurement August 31, / 8

32 Data types and why we care Data basics Categorical Qualitative: Unordered categories Quantitative: Categories differ in magnitude Scale of measurement: Interval: A real scale for measurement (the units mean something). Lecture 2 (QPM 2016) Measurement August 31, / 8

33 Data types and why we care Data basics Categorical Qualitative: Unordered categories Quantitative: Categories differ in magnitude Scale of measurement: Interval: A real scale for measurement (the units mean something). Ordinal: A natural ordering, but distances have no concrete meaning. Lecture 2 (QPM 2016) Measurement August 31, / 8

34 Data types and why we care Data basics Categorical Qualitative: Unordered categories Quantitative: Categories differ in magnitude Scale of measurement: Interval: A real scale for measurement (the units mean something). Ordinal: A natural ordering, but distances have no concrete meaning. Nominal: Categories with no clear or meaningful ordering. Lecture 2 (QPM 2016) Measurement August 31, / 8

35 Data types and why we care Data basics Categorical Qualitative: Unordered categories Quantitative: Categories differ in magnitude Scale of measurement: Interval: A real scale for measurement (the units mean something). Ordinal: A natural ordering, but distances have no concrete meaning. Nominal: Categories with no clear or meaningful ordering. Lecture 2 (QPM 2016) Measurement August 31, / 8

36 Data types and why we care Data basics Categorical Qualitative: Unordered categories Quantitative: Categories differ in magnitude Scale of measurement: Interval: A real scale for measurement (the units mean something). Ordinal: A natural ordering, but distances have no concrete meaning. Nominal: Categories with no clear or meaningful ordering. Granularity: Continuous Lecture 2 (QPM 2016) Measurement August 31, / 8

37 Data types and why we care Data basics Categorical Qualitative: Unordered categories Quantitative: Categories differ in magnitude Scale of measurement: Interval: A real scale for measurement (the units mean something). Ordinal: A natural ordering, but distances have no concrete meaning. Nominal: Categories with no clear or meaningful ordering. Granularity: Continuous Discrete (sometimes called categorical) Lecture 2 (QPM 2016) Measurement August 31, / 8