1. Introduction

2. The Role of Statistics in Science Research can be qualitative or quantitative Research can be qualitative or quantitative Where the research results are numbers, this information is called data Where the research results are numbers, this information is called data Statistics are mathematical techniques used to manipulate and analyze data Statistics are mathematical techniques used to manipulate and analyze data –Allow us to answer research questions or test theories –Example of fertility rates

3. Fertility Rate Example What causes overpopulation What causes overpopulation –Things found to correlate with high fertility rates Low levels of education—particularly for women Low levels of education—particularly for women Absence of social security system Absence of social security system Low incomes Low incomes Absence of birth control and fertility clinics Absence of birth control and fertility clinics The wealthiest people in the world make money from overpopulation, so they do what they can to encourage it The wealthiest people in the world make money from overpopulation, so they do what they can to encourage it

4. What the wealthy gain from overpopulation When there are too many people looking for jobs, wages go down When there are too many people looking for jobs, wages go down –So, profits go up dramatically When there are too many people buying products, especially with shortages of resources, prices go up When there are too many people buying products, especially with shortages of resources, prices go up –So, profits go up dramatically

5. Ways the Wealthy Encourage Growth Republicans speak for the wealthy, so listen to what they say Republicans speak for the wealthy, so listen to what they say –They have a Club for Growth –They oppose abortion globally –They oppose birth control, particularly funding for it in family planning clinics –They talk endlessly about “family values” hoping that will translate to larger families

6. Statistics They are summary numbers They are summary numbers Needed because our minds can only remember and make sense out of small sets of numbers Needed because our minds can only remember and make sense out of small sets of numbers

7. Why Do Quantitative Research Some of the most important works in the social sciences do not use any stats Some of the most important works in the social sciences do not use any stats –Example of study of med school students Your audience will be persuaded if you use statistics Your audience will be persuaded if you use statistics –They are powerful –They make a stronger case in favor of a position –It ’ s easier to get quantitative research published –Your expertise with stats helps you to evaluate the research of others

8. Descriptive and Inferential Statistics

9. Descriptive Statistics Used to describe the distribution of a single variable in a sample (the first four chapters in your book) Used to describe the distribution of a single variable in a sample (the first four chapters in your book) –Example, the ages of all the people in a community So, use data reduction So, use data reduction –Allows a few meaningful numbers to summarize large masses of data Can ’ t list all the ages Can ’ t list all the ages –Use percentages, averages, graphs, and charts –Called univariate statistics

10. Explanatory Statistics Sometimes also classified as descriptive Sometimes also classified as descriptive –Bivariate if two variables –Multivariate if more than two (last two chapters in your book) Explanatory statistics are used to understand the relationship between two or more variables in a sample Explanatory statistics are used to understand the relationship between two or more variables in a sample –Use measures of association

11. Measures of Association Will tell you three things Will tell you three things –Existence of a relationship –Direction of a relationship E.g., the older you get, the higher your income E.g., the older you get, the higher your income –As one goes up, the other goes up (a positive association or a direct relationship E.g., the higher your level of education, the less prejudiced you tend to be E.g., the higher your level of education, the less prejudiced you tend to be –A negative association –Strength of a relationship Is it true for all people, most people, or just a slight tendency Is it true for all people, most people, or just a slight tendency

12. Depending on Strength and Direction We can find evidence for causation We can find evidence for causation –Correlation is not causation—just evidence for it You have to use your own logic to decide if the association is causal You have to use your own logic to decide if the association is causal –We want to know if there is a cause and effect relationship The cause is the independent variable, represented by the letter “ X ” The cause is the independent variable, represented by the letter “ X ” The effect is the dependent variable, represented by the letter “Y ” The effect is the dependent variable, represented by the letter “Y ”

13. Hypothesis –An hypothesis is a statement about the predicted relationship between the variables It comes from theory It comes from theory Example: the more education you receive, the higher your income will be Example: the more education you receive, the higher your income will be –Which is the independent variable and which is the dependent We can also find evidence for prediction We can also find evidence for prediction –Can predict your score on one variable from your score on another

14. Inferential Statistics We want to generalize the findings from the sample to a larger population We want to generalize the findings from the sample to a larger population We don ’ t have the money or time to survey every person We don ’ t have the money or time to survey every person So we draw a small random sample from the larger population So we draw a small random sample from the larger population Inferential statistics involve using information from samples to make inferences about populations Inferential statistics involve using information from samples to make inferences about populations

15. Discrete and Continuous Variables Discrete Discrete –A variable is discrete if it has a basic unit of measurement that cannot be subdivided Example, number of people per household Example, number of people per household –The basic unit is people –The fewest you can have is one Continuous Continuous –It can be subdivided infinitely, at least theoretically Example, time, which can be subdivided into seconds or nanoseconds (one billionth of a second) Example, time, which can be subdivided into seconds or nanoseconds (one billionth of a second) Do actually report these scores as discrete Do actually report these scores as discrete Mostly, this information is needed to decide between a bar graph and a histogram Mostly, this information is needed to decide between a bar graph and a histogram

16. Level of Measurement

17. Nominal Level of Measurement Very important, in that it decides which statistics to use Very important, in that it decides which statistics to use Nominal Level of Measurement Nominal Level of Measurement –The word “nominal” means naming –With nominal variables, you classify people into categories, and look at how many people are in each category –The categories are not thought of as “ higher ” or “ lower ” than the others, or “ greater than ” or “ lesser than ” –Examples: religion, sex, race, political party, marital status, and variables with only two choices—like “ Yes ” or “ No ”

18. Ordinal Level of Measurement Also classifies cases into categories Also classifies cases into categories Additionally, it allows the categories to be ranked Additionally, it allows the categories to be ranked –Ordinal categories can be ranked from “ low ” to “ high ”, “ more ” or “ less ” Examples of ordinal level variables Examples of ordinal level variables –Occupation, social class, grade point average, education measured by degrees, degree of religiosity –Also SES, measured as upper class, middle class, working class, or lower class –Also, all attitude and opinion scales, like prejudice, alienation, or political conservatism Usually measures in a Likert Scale Usually measures in a Likert Scale The limitation of ordinal level variables is that you cannot describe the distance between the scores or categories in precise terms The limitation of ordinal level variables is that you cannot describe the distance between the scores or categories in precise terms

19. Interval/Ratio Level of Measurement Variables measured at the interval-ratio level permit classification like nominal ones Variables measured at the interval-ratio level permit classification like nominal ones Permit ranking like ordinal Permit ranking like ordinal But also exactly define the distance from category to category But also exactly define the distance from category to category Examples of interval-ratio level of measurement Examples of interval-ratio level of measurement –Age The unit of measurement (years) has equal intervals The unit of measurement (years) has equal intervals Also, income, number of children, and number of years married Also, income, number of children, and number of years married All math operations are permitted for data measured at this level All math operations are permitted for data measured at this level

20. Levels of Measurement A single variable can be measured in any of the three levels A single variable can be measured in any of the three levels –Example of education Nominal, if asking “ do you have a college degree? ” with a yes or no response Nominal, if asking “ do you have a college degree? ” with a yes or no response Ordinal, if asking “ what educational degrees do you have?” Ordinal, if asking “ what educational degrees do you have?” Interval/ratio if asking “ how many years have you been in school? ” Interval/ratio if asking “ how many years have you been in school? ”