Levin and FoxElementary Statistics In Social Research

Chapter 1

The Connection Between Theory, Research Questions, and

Hypotheses

The Nature of Social Science Research

Outline: Review

1. Research Process2. Types of Research3. Stages of the Research Process4. Levels of Measurement

The Nature of Social Science Research

Social Scientists attempt to…• To explain and predict human behavior• To take “educated guesses” about the nature of social reality

Variables: Key to understanding and social inquiry:• Independent (presumed cause)• Dependent (presumed effect)

The Research Process: Variables: Researchers must specify variables (characteristics that differ or

vary from one individual to another or from one point in time to another).

Units of Analysis:Additionally, they must determine the unit of observation or analysis (the level or type of data that the researcher wants to study (individuals, groups, nations, cities, states, etc.)

Sometimes researchers may choose to look at aggregate level data (the way certain measures vary for entire collections of a unit of observation)

The Nature of Social Science Research

The Nature of Social Science Research

Types of Research:Social scientists conduct research to increase their understanding of the

problems and issues in their field. This research can take many different forms:

Experiments Surveys Content Analysis Participant Observation Secondary Analysis.

The Nature of Social Science ResearchThe Experiment• The researcher has degrees of

control over the research situation.• When the independent variable is

assigned to a group of randomly selected individuals, this groups becomes the experimental group.

• When the independent variable is withheld from a randomly selected group of individuals, this group becomes the control group.

• The researcher then evaluates the differences in outcome between both groups.

The Survey

• Survey research is retrospective in that the effects of the independent variable(s) on the dependent variable(s) are recorded after the fact.

• Surveys can be administered by face-to-face interviews, telephone interviews, or by email.

Example: Arming Suffolk Police?

Content Analysis

• This type of research includes the evaluation of the content of newspapers, books, magazines, films, letters, music, etc.

• Research is conducted in a systematic fashion that seeks to uncover trends, variations, similarities, commonalities, etc.

Participant Observation• The researcher participates in the

daily lives of the people under study either overtly or covertly.

Secondary Analysis• The researcher evaluates

information collected or assembled by others.

• Since the research is not the primary collector of the data, the analysis is a secondary evaluation of the data.

The Nature of Social Science Research

Types of Research:

The Nature of Social Science Research

The Stages of Social Research:

1. Reduce problem to a testable hypothesis 2. Develop and use the appropriate set of instruments (polls, focus

groups, controlled experiments). 3. Collect the data 4. Analyze the data

5. Interpret results of data analysis 6. Communicate results to an audience, the public

The Nature of Social Science Research

Why test hypotheses?Our everyday, commonsense observations are generally based on narrow,

often biased preconceptions and personal experiences.

Hypothesis: DefinitionsMonroe defines hypotheses as: “empirical statements derived from a theory. They are statements about variables.” Recall: independent (cause) and dependent (effect) variables.

The Nature of Social Science Research

Why test hypotheses?Hypotheses testing allows us to assess our assumptions about how we think

things ought to be using available data. In the end, we may come to see that things are quite different than we thought!

Think about common perceptions of the:• Poverty (Why is someone poor (or rich) in the US?)• Voting (Who votes in the US and why?)• Parties (Are parties in the Decline in the US?)

Questions:How might we test any assumptions we have? Where would you get

relevant data?

The Nature of Social Science Research

Hypothesis Construction/Formulation:

Often we derive our hypotheses from theory:

Party Decline Thesis: Parties have declined (effect) because partisanship (cause) has declined. That is, parties have declined because fewer voters identify with them.

Additional Examples of Hypotheses:There is a relationship between economics and voting:

• The better the state of the economy (cause), the greater the percentage of the vote (effect) received by the party of the president. (direction: positive (variables move in the same direction)).

There is a relationship between income and voting:

• The higher a person’s income (cause), the more likely they are to vote (effect). (positive)

There is a relationship between age and voting, ideology and voting: • Older (cause) people are more likely to vote (effect). (positive)• More moderate (cause) voters are less likely to vote (cause) in midterm

elections. (negative)

The Nature of Social Science Research

The Nature of Social Science ResearchUsing Numbers in Political Research: Levels of MeasurementNumbers serve important functions for researchers, depending on the level of

measurement employed.

Nominal: Refers to discrete or mutually exclusive categories. Individual cases can only fit into one category at a time. Used to classify, categorize or label.

Example: party affiliation, voter, non-voter. Ordinal: Involves the ranking or ordering of cases in terms of the degree to whichthey possess a certain characteristic.

Example: Social class, Measurements of attitudes.

Interval-Ratio: Measurements for all cases are expressed in the same units. There are equal intervals between points on a scale and either a real or theoretical zero point.

Example: Income, temperature, SAT scores, weight

The Nature of Social Science Research

Levels of Measurement: Limitations

Nominal: cannot indicate grade, ranking, a quality scale (better or worse), higher or lower, more or less. It is simply a label.

Ordinal Data: provides a ranking, but not a magnitude of difference between numbers, or points on a scale. Intervals between points on a scale are not known:

Teeth Cleaning --------------Filling----Root Canal 1 2 3 4 5

Difference?

The Nature of Social Science Research

Levels of Measurement: Strengths

Interval-Ratio:Allows you to indicate the order of categories, but also the exact differences

between them. Uses constant units of measurement with equal intervals between them.

Temperature: 80------------90------------100

Difference?

The Nature of Social Science Research

Levels of Measurement: Strengths

Difference between Interval-Ratio:

Interval: artificial zero point: Zero Degree: cold, but a temperature. Ratio: absolute or true zero point: Zero Age: Birth.

Interval-Ratio: Can Be Natural or Invented. Some variables in their natural form are interval level (weight, number of

siblings you have, hours you watch TV per day). Others become interval because we scale them.

Levels of Measurement and Possible Comparisons

Level

Different or

Equivalent

Higher or Lower

How Much Higher

Nominal Yes No No

Ordinal Yes Yes No

Interval -Ratio

Yes Yes YesIt is worth noting that sometimes the distinction between ordinal and interval are not clear cut. The rule of thumb is if the scale has roughly equal intervals to treat the variables as intervals.

The Nature of Social Science Research

The Nature of Social Science Research

Levels of Measurement: Nominal

Affiliation Frequency (f)

Republican 7

Democrat 3

Total N = 10

Party Affiliation of 10 College Students:

The Nature of Social Science Research

Levels of Measurement: Ordinal: Ranked Data

Student Politics*

LisaTomEllenGwenColeBenLinda

1=Extremely liberal2=liberal3=slightly liberal4=moderate5=slightly conservative6=conservative7=extreme conservative

Total N = 7* ANES rankings

The Nature of Social Science ResearchLevels of Measurement: Interval-Ratio:

Student Test Score

LisaTomJorgeGwenColeBenStephenTanyaLuisNicole

949382

81.781.371

70.5 69 68 66

Total N = 10

The Nature of Social Science Research

Functions of Statistics:Statistics are used to describe and to make decisions.

When statistics are used to describe, we often present the information in categories and look at the frequency (f) of occurrence (see Table 1.7).

To make decisions using statistics, we often collect information on a sample of the population so that we can test a hypothesis and make inferences from our findings. (see pg. 20-21).

The Nature of Social Science Research

Note about Rounding Numbers: Do not round numbers until you reach your final answer. To round before

this point may produce the wrong answer.

Round a final answer to two more decimal points (hundredths +2 decimals) than contained in the original scores.

Examples: 1.224 = 1.22 or 1.2247.761 = 7.76 or 7.7611.015 = 1.023.889 = 3.89

A detailed discussion on how to round is in Appendix B.

The Nature of Social Science Research

Order of Operations:

Step One: Parentheses and Brackets: Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.

Step Two: Exponents: Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.

Step Three: Multiplication and Division: Simplify multiplication and division in the order that they appear from left to right.

Step Four Addition and Subtraction: Simplify addition and subtraction in the order that they appear from left to right.

Source: http://www.algebrahelp.com/lessons/simplifying/oops/

The Nature of Social Science Research

Order of Operation: Example: Expression:2 + (3-1) x 3Step One: Parentheses:2 + (3-1) x 32 + (2) x 3Step Two: Exponents: 2 + (2) x 32 + (2) x 9Step Three: Multiplication and Division: (Left to Right)2 + (2) x 92 + 18Step Four Addition and Subtraction: (Left to Right)2 + 1820

Source: http://www.algebrahelp.com/lessons/simplifying/oops/

2

2

2

2

The Nature of Social Science Research

Order of Operation: Example: