Week 5 Measurement, Sampling and Data Analysis

Measurement Chapter 4

- If it exists, it is measurable!
- Measurement is used to gain mathematical insight

into our data - Measurement is a comparison We compare our data

to a standard such as the norm, average or

expected outcome - Measurement is a standard used for evaluation

- Measurement is an essential component of

quantitative research - Through measurement we can inspect, analyze and

interpret our information

The Language of Variables

- A variable is any observation that can take

different values - Gender, Age, Religion, Ethnicity are variables
- Attributes are specific values on a variable
- Attributes of Gender 1. Male 2. Female
- Are discreet values
- Age (may be continuous 0-100)

- An indicator is the responses to a single

question The main concept in the question is

the variable being measured - Concept A mental image that summarizes a set of

similar observations, feelings or ideas - We may not all agree on the same definition

of a concept Concepts are abstracts - Conceptualization specifying the dimensions of

and defining the meaning of the concept

- We often use concepts in our theories
- i.e. crime, abuse, deterrence, eating disorder
- What do we mean by crime? How is it measured.

How can we measure our concepts for research?

- Devise operations that actually measure the

concepts we intend to measure - Operationalization of concepts connect concepts

to observations by identifying specific

observations that we will use to indicate that

concept in empirical reality. - The process of choosing the variable to

represent the concept

- We use variables which are derived from concepts

in our hypotheses - The variables move the concepts into the realm of

testability i.e. The indicator of crime is

spousal abuse - Through the indicators of a variable we are able

to ascertain the characteristics, behaviors,

attitudes of our subjects

How it Works

- Define the concept
- We have a theory that Punishment deters criminal

behavior - Choose and indicator of the concept to represent

it - The concept, punishment, is operationalized

by using the variable, arrest to represent it.

The indicators of the variable, arrest are 1.

arrest on first offense 2. Dont arrest on first

offense

- The concept crime is represented in our research

as physical spousal abuse. - The resulting hypothesis is
- If subjects are arrested on the first reported

offense of physical spousal abuse then they will

be less likely to offend again (recidivism) - The indicators of the variable, recidivism are 1.

re-offend 2. doesnt re-offend - Our concepts are now defined in measurable,

testable terms

- Through conceptualization and operationalization,

measurement becomes the process of linking

abstract concepts to empirical indicants - Measurement validity The operations we devise

to measure our data must assure that we measure

the variables we intended to measure

- For the concept social class, we can use the

variables income, education and occupation. - Now we get a much clearer picture of what

indicators are necessary to measure the abstract

concept, social class - Income can be measured by actual income
- Education can be measured by years of education
- Occupation can be measured by levels from not at

all professional to being very professional

- Measuring social variables is often done through

questions posed to people - A single question may not be adequate for

measuring a concept. Multiple questions may be

necessary - The concepts age, gender, ethnicity, religion,

income, education, occupation, are what is called

demographic variables. These can be measured with

one question. What is your age? - But more than one question is necessary to

measure Social Class, ADD, Prejudice, Nurture - May need to construct an Index of question

Levels of Measurement

- Levels of measurement have important implications

for the type of statistics that can be used in

analyzing the data for a variable - 4 Levels of measurement Nominal, Ordinal,

Interval and Ratio - These levels are determined by the indicators

(response/answer categories) for a variable

- Nominal qualitative, has no mathematical

interpretation, even if numbers are attached to

the value label - These are called categorical variables
- For example, we may ask What is your gender?

And the answer categories are 1. male 2. female.

However, the numbers 1 2 do not indicate

anything mathematical about the differences in

the answers. Female is not more or higher of

gender than Male.

Quantitative Levels of Measurement

- Ordinal the numbers assigned to the response

categories indicate order. 1 is lower in order

than 2 and 2 is lower in order than 3. - 1. Very Unimportant is lower in order than 2.

Unimportant and 2. is lower in order than 3.

Important

- Interval The numbers indicating values in the

response categories have mathematical meaning. - They represent fixed measurement units, but have

no absolute or fixed zero point. - This is important mathematically because having a

fixed zero point allows us to use the highest

level of statistics - Often researchers try to use ordinal level

variables as interval (i.e. Likert Scales)

- In interval level variables the numbers can be

added and subtracted but ratios are not

meaningful - Fahrenheit Temperature is an interval level

variable. 60 degrees is 30 degrees hotter than

30 degrees. But, 60 degrees can not be said to be

twice as hot as 30 degrees because temperature

has no absolute zero. - There are very few true interval-level measures

in social science. This is why researchers use

ordinal level data as interval level data and

score it in ways that allow them to do so

- Ratio The numbers attached to these response

categories represent fixed measuring units and an

absolute zero point. Age is a ratio level

variable. Test Scores can be ratio. i.e. 0-100

SamplingHow to choose survey subjects?

- Sample A subset of people (population) selected

for study i.e. 100 students from Webster selected - Population larger group from which sample comes

(will infer back to this group) i.e. All Webster

students participate

Why Sample

- If cant access entire population (too costly,

too huge) - Sampling Goal
- Representativeness smaller group (sample) is

representative of larger group (population) - Larger the sample, more confidence in it being

representative - More homogeneous the population, more confidence

of sample representativeness

- If sample is representative, findings can be

generalized to population. You can infer that

your sample will respond in same way as whole

population - But, generalizing from sample to population

involves risk - Ecological Fallacy cant draw conclusions about

individuals from group level sample of data - Reductionist Fallacy cant draw conclusions

about groups from individual level sample of data

Generalizability

- Not easy to achieve in experiment
- Cant really apply findings to larger population
- Experiments occur in artificial setting
- Subjects recruited or selected, not chosen

through random sampling

Types of Sampling Procedures

- Probability Random Sampling selects subjects

out of a large population on the basis of chance - ( a technique used most effectively with survey

research)

Probability Sampling

- Participants drawn by chance (random)
- Every subject has equal chance of being chosen

(known probability, 110 1100) - How to do Simple Random Sample
- 1. Arbitrarily select a number from a random

number table - 2. Match it to number in numbered subject list

for starting point - 3. Continue selecting numbers and subjects
- Until desired number of subjects is obtained

Systematic Random Sample

- Arrange population elements sequentially
- Determine size of sample wanted
- Divide sample into of subjects in population
- Randomly select a starting point in list
- Select every nth subject
- If need 5 subjects and have 45 in population,

select every 9th person

Stratified Random Sampling

- Characteristics of population are known to the

researcher before taking the sample - Sample is selected with mirror proportions on

characteristics such as ethnic, age, gender,

religion,education level, income level etc.

Cluster Sampling

- Unit chosen is not an individual, but is a

cluster of individuals naturally grouped together

such as Churches, Schools, Blocks, Counties,

Businesses etc. - They are alike with respect to characteristics

relevant to the study

Non-Probability Sampling-

- Participants are not chosen by chance
- They are Chosen due to economical and

convenience reasons - Example Study on student attitudes. Stop

students at the gym only and ask them to take the

survey. They are not necessarily representative

of the total student population

Types of Non-Probability Sampling

- Accidental just encounter a of people and ask

to be in your study - It is extremely weak, but popular method
- Psychological research is often accidental
- Convenience Similar to accidental Individuals

seek out individuals who are available - Likely to be biased
- Not representative of any population
- Should be avoided

- Snowball - used for hard to reach but

interconnected populations - One person identifies and recommends another

people and those people recommend other people

and on and on. - Typical subjects drug dealers, prostitutes,

practicing criminals, gang leaders, AA members

Data Analysis Chapter 12

Why are Statistics Important

- Statistics give numeric meaning to our data
- Helpful tool for understanding social world and

are used to - 1.describe social phenomena
- 2. identify relationships among them
- 3. explore reasons for relationships
- 4. test hypotheses
- 5. interpret cause and effect

Drawbacks

- Can use statistics to distort reality
- Lying with statistics is unethical
- Easy to be careless when using statistics
- Must use appropriate level of measurement for

variables in our data

Preparing for Statistics

- After data is collected it must b cleaned,

checked and coded before statistics are run - There is software available to do this

Displaying Statistics

- Graphics Bar Charts, histograms, pie charts,

frequency tables and curve graphs describe the

shape of the data visually

Statistics for One Variable

- Univariate - describes statistical

characteristics of one variable frequency

distributions, summary statistics, measures of

central tendency (mean, median mode), skewness,

measures of dispersion (range, variance, standard

deviation), reliability tests - Display the distribution of cases across the

categories of one variable

Univariate Stats

- Frequency distribution (1xtables) displays the

number and percentage or cases corresponding to

each of a variables values or group of values - Measures of Central Tendency
- 1. Mean (arithmetic average of the values in a

distribution) sum the values of the cases and

divide by the number of cases

- 2. Median (the point that divides the

distribution in half) One in the middle - 3. Mode (most frequent value in a

distribution) - The Mean is the most frequently used because it

is the foundation for more advanced statistics

- Skewness If there is a lack of symmetry in the

data (symmetric would be Bell curve) - If data clustered to right of center- Positive

skew - If data clustered to left of center Negative or

inverse skew

- Measures of Variation or Dispersion
- Are the data spread out or clustered?
- 1. Range- highest value minus the lowest value

plus one - 3. Variance the average squared deviation of

each case from the mean (takes into account the

amount by which each case differs from the mean)

- 4. Standard Deviation Preferred measure of

variability because of its mathematical

properties ( sq. root of the variance)

Bivariate/multivariate Analysis

- Describes the association between two or more

variables - Some types Cross-tabulation, Regression,

Correlation - Measures of Association- descriptive statistics

that summarized the strength of an association

(Variation in one variable is related to

variation in another. - For example Chi Sq. and Gamma are used to

summarize the relationship between two or more

variables in Cross-tabulation

CROSS-TABULATION

- The tables display the distribution of one

variable for each category of another variable

(see text pgs. 392-398) - Sex of voter determines party.
- If Man then Republican

Rep M E 80 N Dem 20

W O M 30 E N 70

What to Look for

- The IV is Gender
- Do percentages distributions vary at all between

categories of the independent variable? - (existence)
- How much? (strength)
- (This example is nominal level data)

Rep M E 80 N Dem 20

W O M 30 E N 70

Interval Level Data

- Hypothesis - As education level (IV) increases,

income level (DV) increases - Total N300
- 100 with BAs
- 100 with MAs
- 100 with PhDs
- Do values of the DV increase with increase in IV?

(Direction) - Are changes in DV fairly regular increasing

fairly regularly? (pattern)

BA MA PhD

LT 50 60 20 5

50- 100 30 50 30

GT 100 10 30 65

Inferential Statistics

- They estimate the degree of confidence that can

be placed in generalizations from a sample to the

whole population from which the sample was

selected - Chi-Square used in bivariate analysis to

estimate probability that an association between

DV IV is not due to chance alone.

- A probability level of .05 (p.05) from Chi Sq.

means the probability that the association was

due to chance is less than 5 out of 100 (5) - The lower the probability score the higher the

significance level. - A relationship between variables is said to be

statistically significant when the analyst feels

reasonably confident (often 95) that an

association was not due to chance.

- Inferential statistics with Crosstabulation can

tell us if there is an association more than

would be expected by chance (coin toss 50/50) - But! Does not tell us how strong that

relationship is (See pgs. 405-407)

Elaboration Analysis

- Controlling for the effect of a third variable
- Sometimes a 3rd variable could be effecting the

association or strength of the association

without us realizing it. - Example in Text The strength of the

relationship between Arrest and Abuse is actually

dependent on how much the perpetrator is vested

in society. i.e. employed or not and married or

not.

- In fact, if the seemed relationship disappears

when an extraneous (3rd variable) is controlled,

it is probably a spurious relationship. The IV we

think is effecting the DV isnt Its an

extraneous variable we havent considered. - We hypothesize that Income level (IV) effects how

we vote (DV) - In reality, income is a reflection of education

(IV) and its education that really effects how

we vote (DV).

Regression Analysis

- Regression analysis and Correlation analysis-

advantages over simple crosstabs give strength

of association between two or more variables - Often collapse values of variables into

categories for crosstabs - Better to leave values as continuous for upper

level summary stats - Example Age 10-20 21-30 31-40 (grouped or

categorical age)

Ethics in Data Analysis

- l. When just letting computer search around in

the data for relationships without a testable

hypothesis, relationships may appear just on the

basis of chance but mean nothing. - A reasonable balance needed between doing

deductive data analysis (theorygthypothesisgtsignifi

cant association) - And inductive data analysis (exploration of

patterns in a dataset) - If findings are Serendipitous (based on inductive

analysis) must be reported as such

- 2. Report findings honestly (do not lie with

statistics even though it is possible to do so) - 3. Do not mislead people by choosing summary

statistics that accentuate a particular feature

of a distribution. Use statistical techniques

appropriately

Tools for Data Analysis and Statistics

- Computer software ranges from easy, but not very

comprehensive to difficult, very robust and very

expensive - Excel, Access, Lotus limited, elementary

statistics, moderately expensive - Easy NCSS user friendly, cheap (lt100), only

numeric data entry, outputso-so - SPSS Very comprehensive, user

friendly,excellent graphics, small learning curve - Not very expensive for students (200-500)
- SAS most robust, sort of user friendly, big

learning curve, - CRISP, STATBasic, SYSstat expensive, not user

friendly, More for programmers than average user