IntroductionIntroduction

The Role of Statistics in The Role of Statistics in ScienceScience• Research can be qualitative or Research can be qualitative or

quantitativequantitative• Where the research results are Where the research results are

numbers, this information is called numbers, this information is called datadata• Statistics are mathematical techniques Statistics are mathematical techniques

used to manipulate and analyze dataused to manipulate and analyze data– Allow us to answer research questions or Allow us to answer research questions or

test theoriestest theories– Example of fertility ratesExample of fertility rates

Fertility Rate ExampleFertility Rate Example

• What causes overpopulationWhat causes overpopulation– Things found to correlate with high Things found to correlate with high

fertility ratesfertility rates•Low levels of education—particularly for Low levels of education—particularly for

womenwomen

•Absence of social security systemAbsence of social security system

•Low incomesLow incomes

•Absence of birth control and fertility clinicsAbsence of birth control and fertility clinics

•The wealthiest people in the world make The wealthiest people in the world make money from overpopulation, so they do what money from overpopulation, so they do what they can to encourage itthey can to encourage it

What the wealthy gain from What the wealthy gain from overpopulationoverpopulation

• When there are too many people When there are too many people looking for jobs, wages go downlooking for jobs, wages go down– So, profits go up dramaticallySo, profits go up dramatically

• When there are too many people When there are too many people buying products, especially with buying products, especially with shortages of resources, prices go upshortages of resources, prices go up– So, profits go up dramaticallySo, profits go up dramatically

Ways the Wealthy Ways the Wealthy Encourage GrowthEncourage Growth• Republicans speak for the wealthy, so Republicans speak for the wealthy, so

listen to what they saylisten to what they say– They have a Club for GrowthThey have a Club for Growth– They oppose abortion globallyThey oppose abortion globally– They oppose birth control, particularly They oppose birth control, particularly

funding for it in family planning clinicsfunding for it in family planning clinics– They talk endlessly about “family values” They talk endlessly about “family values”

hoping that will translate to larger hoping that will translate to larger familiesfamilies

StatisticsStatistics

• They are summary numbersThey are summary numbers

• Needed because our minds can only Needed because our minds can only remember and make sense out of remember and make sense out of small sets of numberssmall sets of numbers

Why Do Quantitative Why Do Quantitative ResearchResearch• Some of the most important works in the Some of the most important works in the

social sciences do not use any statssocial sciences do not use any stats– Example of study of med school studentsExample of study of med school students

• Your audience will be persuaded if you use Your audience will be persuaded if you use statisticsstatistics– They are powerfulThey are powerful– They make a stronger case in favor of a positionThey make a stronger case in favor of a position– ItIt’’s easier to get quantitative research publisheds easier to get quantitative research published– Your expertise with stats helps you to evaluate Your expertise with stats helps you to evaluate

the research of othersthe research of others

Descriptive and Inferential Descriptive and Inferential StatisticsStatistics

Descriptive StatisticsDescriptive Statistics

• Used to describe the distribution of a single Used to describe the distribution of a single variable in a sample (the first four chapters in variable in a sample (the first four chapters in your book)your book)– Example, the ages of all the people in a communityExample, the ages of all the people in a community

•So, use So, use data reductiondata reduction– Allows a few meaningful numbers to Allows a few meaningful numbers to

summarize large masses of datasummarize large masses of data•CanCan’’t list all the agest list all the ages

– Use percentages, averages, graphs, and Use percentages, averages, graphs, and chartscharts

– Called univariate statisticsCalled univariate statistics

Explanatory StatisticsExplanatory Statistics

• Sometimes also classified as descriptiveSometimes also classified as descriptive– Bivariate if two variablesBivariate if two variables– Multivariate if more than two (last two Multivariate if more than two (last two

chapters in your book)chapters in your book)

• Explanatory statistics are used to Explanatory statistics are used to understand the relationship between understand the relationship between two or more variables in a sampletwo or more variables in a sample– Use measures of association Use measures of association

Measures of AssociationMeasures of Association

• Will tell you three thingsWill tell you three things– Existence of a relationshipExistence of a relationship– Direction of a relationshipDirection of a relationship

• E.g., the older you get, the higher your incomeE.g., the older you get, the higher your income– As one goes up, the other goes up (a positive As one goes up, the other goes up (a positive

association or a direct relationshipassociation or a direct relationship

• E.g., the higher your level of education, the less E.g., the higher your level of education, the less prejudiced you tend to beprejudiced you tend to be

– A negative association A negative association

– Strength of a relationshipStrength of a relationship• Is it true for all people, most people, or just a slight Is it true for all people, most people, or just a slight

tendencytendency

Depending on Strength and Depending on Strength and DirectionDirection• We can find evidence for We can find evidence for causationcausation

– Correlation is not causation—just Correlation is not causation—just evidence for itevidence for it•You have to use your own logic to You have to use your own logic to

decide if the association is causaldecide if the association is causal– We want to know if there is a cause and We want to know if there is a cause and

effect relationshipeffect relationship•The cause is the independent The cause is the independent

variable, represented by the letter variable, represented by the letter ““XX ””•The effect is the dependent variable, The effect is the dependent variable,

represented by the letter “Yrepresented by the letter “Y””

HypothesisHypothesis

– An An hypothesishypothesis is a statement about the is a statement about the predicted relationship between the predicted relationship between the variablesvariables•It comes from theoryIt comes from theory•Example: the more education you Example: the more education you

receive, the higher your income will bereceive, the higher your income will be– Which is the independent variable Which is the independent variable

and which is the dependentand which is the dependent• We can also find evidence for We can also find evidence for predictionprediction

– Can predict your score on one variable Can predict your score on one variable from your score on anotherfrom your score on another

Inferential StatisticsInferential Statistics

• We want to We want to generalizegeneralize the findings from the findings from the sample to a larger populationthe sample to a larger population

• We donWe don’’t have the money or time to t have the money or time to survey every personsurvey every person

• So we draw a small So we draw a small randomrandom sample from sample from the larger populationthe larger population

• Inferential statistics Inferential statistics involve using involve using information from samples to make information from samples to make inferences about populationsinferences about populations

Discrete and Continuous Discrete and Continuous VariablesVariables• DiscreteDiscrete

– A variable is discrete if it has a basic unit of measurement A variable is discrete if it has a basic unit of measurement that cannot be subdividedthat cannot be subdivided• Example, number of people per householdExample, number of people per household

– The basic unit is peopleThe basic unit is people– The fewest you can have is oneThe fewest you can have is one

• ContinuousContinuous– It can be subdivided infinitely, at least theoreticallyIt can be subdivided infinitely, at least theoretically

•Example, time, which can be subdivided into Example, time, which can be subdivided into seconds or nanoseconds (one billionth of a seconds or nanoseconds (one billionth of a second)second)

•Do actually report these scores as discreteDo actually report these scores as discrete• Mostly, this information is needed to decide between a Mostly, this information is needed to decide between a

bar graph and a histogrambar graph and a histogram

Level of MeasurementLevel of Measurement

Nominal Level of Nominal Level of MeasurementMeasurement• Very important, in that it decides which statistics to useVery important, in that it decides which statistics to use• Nominal Level of MeasurementNominal Level of Measurement

– The word “nominal” means The word “nominal” means namingnaming– With nominal variables, you classify people into With nominal variables, you classify people into

categories, and look at how many people are in each categories, and look at how many people are in each categorycategory

– The categories are not thought of as The categories are not thought of as ““higherhigher”” or or ““lowerlower”” than the others, or than the others, or ““greater thangreater than”” or or ““lesser lesser thanthan””

– Examples: religion, sex, race, political party, marital Examples: religion, sex, race, political party, marital status, and variables with only two choices—like status, and variables with only two choices—like ““YeYess”” or or ““NoNo””

Ordinal Level of Ordinal Level of MeasurementMeasurement• Also classifies cases into categoriesAlso classifies cases into categories• Additionally, it allows the categories to be rankedAdditionally, it allows the categories to be ranked

– Ordinal categories can be ranked from Ordinal categories can be ranked from ““lowlow”” to to ““highhigh””, , ““moremore”” or or ““lessless””

• Examples of ordinal level variablesExamples of ordinal level variables– Occupation, social class, grade point average, education Occupation, social class, grade point average, education

measured by degrees, degree of religiositymeasured by degrees, degree of religiosity– Also SES, measured as upper class, middle class, Also SES, measured as upper class, middle class,

working class, or lower classworking class, or lower class– Also, all attitude and opinion scales, like prejudice, Also, all attitude and opinion scales, like prejudice,

alienation, or political conservatismalienation, or political conservatism• Usually measures in a Likert ScaleUsually measures in a Likert Scale

• The limitation of ordinal level variables is that you cannot The limitation of ordinal level variables is that you cannot describe the distance between the scores or categories in describe the distance between the scores or categories in precise termsprecise terms

Interval/Ratio Level of Interval/Ratio Level of MeasurementMeasurement• Variables measured at the interval-ratio level permit Variables measured at the interval-ratio level permit

classification like nominal onesclassification like nominal ones• Permit ranking like ordinalPermit ranking like ordinal• But also exactly define the distance from category to But also exactly define the distance from category to

categorycategory• Examples of interval-ratio level of measurementExamples of interval-ratio level of measurement

– AgeAge• The unit of measurement (years) has equal intervalsThe unit of measurement (years) has equal intervals• Also, income, number of children, and number of Also, income, number of children, and number of

years marriedyears married• All math operations are permitted for data measured All math operations are permitted for data measured

at this levelat this level

Levels of MeasurementLevels of Measurement

• A single variable can be measured in A single variable can be measured in any of the three levelsany of the three levels– Example of educationExample of education

•Nominal, if asking Nominal, if asking ““do you have a college do you have a college degree?degree?”” with a yes or no response with a yes or no response

•Ordinal, if asking Ordinal, if asking ““what educational degrees what educational degrees do you have?”do you have?”

• Interval/ratio if asking Interval/ratio if asking ““how many years how many years have you been in school?have you been in school?””