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Quantitative Research Methods

Overview

- Intro to quantitative methods
- A Number
- the characteristic of an individual by which

it is treated as a unit or of a collection by

which it is treated in terms of units - A Variable
- A concept or characteristic that contains

variation - Measurement
- The assignment of numbers to indicate different

values of a variable

Techniques or Instruments

Measurement

- Its purposes
- to provide the basis for the results,

conclusions, and significance of the research. - Measurement ltgt Invalid Research ?
- to provide information about the variables that

are being studied. - Measurement ltgt Variables

The way in which the numbers are used to describe

something determines the amount of information

that is communicated

A useful classification of this process is

referred to as scales of measurement

Measurement Scale

Ratio

Or Levels of Measurement

Interval

Ordinal

Nominal

Numbers assigned to categories

N

Numbers ranked-ordered

O

Equal intervals between numbers

I

Numbers expressed as ratios

R

Descriptive Statistics

Descriptive Statistics Used to help describe a

group of numbers

What can we say about the following set of

numbers?

15 24 28 25 18 24 27 16 20 22 23 18

22 28 19 16 22 26 15 26 24 21 19 27

16 23 26 25 18 27 17 20 19 25 23

- II
- III
- I
- III
- III
- II
- I
- III
- III
- III
- III
- III
- III
- II

Frequency distribution It will indicates how

often each score is obtained

Measures of Variability

Range Difference between the highest and lowest

score

(28-15) 13

Standard Deviation Average distance of the

scores from the mean

SD4

Symmetrical Distribution

Positive Skew

Negative Skew

(mean, median, mode)

(mode, median, mean)

(mean, median, mode)

Standard deviations

x individual scoresM meanN number of

scores in group

1s

-1s

2s

0

-2s

Correlation

Correlation Measure of relationship between two

or more quantitative variables

Correlation Coefficient A number between 1 and

1Which indicates the direction and strength of

the relationship.

Pearson Product-Moment Correlation

r .45

Correlation

Some examples

Correlation vs. Causation

Reading Level

Shoe size

Measurement The basics

- Construct a characteristic that cant be

directly measured, e.g., intelligence - Operational definition a breakdown of what the

elements are of that construct (e.g., verbal,

quantitative, and analytical ability), or what

that construct looks like in reality - Measure a numerical representation of part of

the construct, e.g., items on an IQ test - Measures have to be both reliable and valid

Reliability and Validity

- Reliability consistency of results
- No matter when something is measured
- No matter how it is measured (measured well!)
- No matter where it is measured
- Validity accuracy
- Measuring the right thing, and
- Measuring the thing right!

Reliable AND Valid

Reliable but not Valid

Not Reliable (so not valid either)

Construct Validity

- Construct validity (checking we have measured the

right thing and have measured it right) consists

of several elements, including - Content validity the measure covers everything

it needs to cover (e.g., intelligence test covers

verbal, quantitative, analytic abilities) - Convergent and discriminant validity it

correlates with other related tests (e.g., other

cognitive ability tests), and not with what it

shouldnt be related to (e.g., personality) - Criterion-related validity it predicts what it

should predict (e.g., IQ score predicts GPA) - Face validity it looks valid to people

Reliability

- Internal consistency all the items (single

questions) within a scale (set of items added up)

are measuring the same thing - Equivalence different forms of the test

generate about the same scores (incl. split-half

reliability, Cronbachs alpha, and some others) - Stability, a.k.a. test-retest reliability

people score about the same no matter when they

take it (assuming no change has occurred in

between)

Norm-referenced vs. criterion-referenced tests

- Norm-referenced tests tell you where someone is

relative to everyone else, e.g., IQ tests an IQ

of 115 gt 84th percentile - Criterion-referenced tests tell you whether

someone has achieved a certain level of

performance, e.g., written drivers license test,

and the test for this class!

Inferential Statistics and Meta-Analysis

Overview

- What are inferential statistics?
- Error, confidence intervals, statistical power
- Hypothesis testing
- Some of the basics
- t-tests, chi-square, ANOVA
- Correlation and regression analyses
- Synthesizing multiple findings
- The literature review
- Meta-analysis

What are inferential statistics?

- Descriptive statistics
- Show us how a single variable is distributed

(frequency graphs) - Show us a picture of the relationship between two

variables (correlations) - Inferential statistics
- Allow us to get serious about checking hunches

and hypotheses - Usually look at the strength of relationship

between two or more variables

Errors Getting the inference wrong

Example Deciding to let/not let someone

into graduate school on the basis of GRE scores

Confidence intervals 1 margin of error for an

individual score

68

95

-2sd

-1sd

0

1sd

2sd

-3sd

3sd

99

If we took a random individual from this

population, there is a 95 chance that that

persons score will fall between 2sd and 2sd.

For IQ, thats a 95 chance of being between 70

and 130.

Confidence intervals 2 means

Distribution of IQ scores in the normal

population 95 of the individual scores lie

between 70 and 130 (SD 15)

70

85

100

115

130

55

145

If we took 100,000 groups of nine (9) people

each, the mean IQs of those groups would be

distributed like this ? i.e., 95 of the means

would lie between 90 and 110 (SE 15/(SQRT(9))

5)

90

100

110

95

105

85

115

Example Intelligence (IQ)

The normal population Mean 100

A sample of 9 Michigan residents Mean 108

70

85

100

115

130

55

145

Question Are Michigan folks unusually smart, or

did we just accidentally end up with

some particularly smart people in the sample?

Hypothesis testing

- We need to test two alternate hypotheses
- No cause for alarm, America Michigan folks are

just like other regular folks (i.e., the mean for

this sample is not that off-the-wall) - The null hypothesis (H0)
- Holy guacamole it looks like Michigan folks

really are more brilliant than the rest (i.e.,

the mean for this sample is way out there)!! - The alternative hypothesis (H1)

Is our group significantly different?

Remember If we took 100,000 groups of nine (9)

people each, the means of those groups would be

distributed like this ? i.e., 95 of the means

would lie between 90 and 110 (SE 15/(SQRT(9))

5) OK, so is our mean of 108 unusually

high? No! Because its inside the 95 range (90

to 110). gt We fail to reject the null

hypothesis.

95

90

100

110

What if we had a bigger sample?

If we sample groups of 9 people, 95 of the means

for those groups fall between IQ 90 and 110

95

90

100

110

If we sample groups of 25 people, 95 of the

means for those groups fall between IQ 94 and 106

(narrower)

95

94

100

106

gt If our MI sample had been of 25 people with a

mean IQ of 108, we could have been 95 certain

that Michigan people were smarter (wed have had

more power). But with a sample of only 9, we just

couldnt be certain enough (even though it looked

likely).

Why do we want to be 95 sure?

Consider the trade-off we make between errors

Statistical vs. Practical Significance

- Theres a flip-side to the statistical power

issue with a big sample size, you can detect

statistically significant effects that are

trivial in the real world. - Example the Headstart program
- Tens of thousands of children
- A statistically significant effect gt many

researchers claimed it worked! - The size of the change was trivial

Choosing the right statistical test 1

- Figure out which is/are your independent

variable(s) - These are the predictors or the things that go

on the X-axis of a graph

- Figure out which is your dependent variable
- This is usually the main thing you are interested

in, the outcome, the thing that goes on the

Y-axis of a graph

Example IVs and DVs

Choosing the right statistical test 2

The type of test we use depends on the types of

variables we have

- Categorical (multiple categories)
- Caucasian vs. African American vs. Hispanic vs.
- Group 1 vs. 2 vs. 3
- Continuous (interval ratio scales)
- Age
- Test scores
- Shoe sizes

- Dichotomous (just two options)
- Male vs. female
- Experimental group vs. control group
- Pretest vs. posttest time

Choosing the right test 3

Synthesizing Studies Two Methods

- The literature review
- Reviewing, summarizing, and critiquing the main

studies in a particular area, and drawing a

conclusion about the strength of the evidence

over multiple studies - Use when many of the best studies in the area are

qualitative, or when there are not enough quant

studies for a meta-analysis

- Meta-analysis
- A statistical technique for combining information

about effect sizes to come to an overall

conclusion about the strength of the evidence

over multiple studies - Use when there are many quant studies out there

already, some with conflicting results use to

look for meta-effects (e.g., type of sample, type

of intervention, etc)

Experimental and Mixed Methods

- .

Overview

- Experimental methods
- Why use experimental methods?
- Ruling out rival explanations
- Some useful experimental designs
- Using multiple methods
- Balancing weaknesses in methods
- Uses of multiple methods

Why use experimental methods?

- Main point to nail down causality
- Causality involves ruling out rival explanations

for the effects observed, e.g.,

What kinds of rival explanations?

- What else could have accounted for the increase

in math scores of students using the new hearing

aid? - The students were better on the posttest because

of the practice they got on the pretest

testing/practice effect - The students tested happened to score a bit low

on the day of the pretest, so the improvement

was just the posttest moving closer to the

average regression to the mean

Rival explanations (contd)

- The approach to teaching math changed between the

pretest and the posttest history - The lowest-performing students were absent the

day of the posttest mortality - Students of that age naturally get better at math

at about that age maturation - Using the new hearing aid needed parental

consent, and only those parents with a strong

interest in their childs academic performance

consented - selection

Rival explanations (contd)

- Students using the hearing aid felt this was

special treatment, so tried harder Hawthorne

effect - The hearing aid is novel, so the students feel

excited and more motivated about listening

(though the novelty wears off later on, after the

posttest) novelty effect - The teacher expected to see better results among

these students, and subconsciously tended to

grade their answers more favorably researcher

expectancy effect

Simple experimental designs

X treatment, C control, O test/measure

- XO posttest only (no pretest)
- OXO pretest and posttest
- OXO/OCO pretest and posttest on both an

experimental and a nonequivalent control group

- Hard to rule out any of the rival explanations
- Rules out selection and mortality
- Rules out several rival explanations, but weaker

because control group not equivalent

Randomized designs

- R OXO
- OCO
- R XO
- CO
- R OXO
- OCO
- XO
- CO

- randomly assigned experimental and control groups

pre post - posttest only on randomly assigned exptal and

control grps - Solomon four-group design two experimental and

two control groups half pretested, all posttested

What should a control group be?

- Think of the practical question you need to

answer with your research, e.g., - Is this treatment/method better than nothing?
- Is it better than what we are using now?
- Consider the option of using a Placebo
- In drug studies, this is the sugar pill
- In experimental designs, it is an intervention

that is not expected to affect the DV, but make

sure the control group doesnt feel left out of

the experimental group.

Examples without control groups

- Suppose you wanted to see if phonics training in

kindergarten improved students ability to read

in first grade - What would a posttest only design with no control

group (XO) design entail (i.e., what ,whom, and

when would you test)? - How about a pretest-posttest design with no

control group (OXO) entail?

Examples with control groups

- Suppose you wanted to see if phonics training in

kindergarten improved students ability to read

in first grade - What would a pretest-posttest design with a

control group (OXO/OCO) entail? - How about a posttest only design with a control

(XO/CO)? - How would randomization help with each of the

above? Is it practically feasible?

The Solomon four-group design

- Suppose you wanted to see if phonics training in

kindergarten improved students ability to read

in first grade - How would you set up a randomized Solomon

four-group design? - R OXO
- OCO
- XO
- CO

Using multiple methods

What are the weaknesses of qual quant methods?

- Quantitative
- ________________
- ________________
- ________________
- ________________
- ________________
- ________________

- Qualitative
- ________________
- ________________
- ________________
- ________________
- ________________
- ________________

Complementary multiplism

- All research methods have weaknesses
- Complementary multiplism (a.k.a. critical

multiplism) is the practice of deliberately

choosing complementary methods with different

weaknesses, so that the strengths of one make up

for the weaknesses of another

Uses of mixed methods

- To bring dry statistics alive
- To dig into puzzling results and try to

understand them better - To triangulate by getting multiple perspectives

on one issue - If qual and quant data point in the same

direction, you can be more certain that your

results are robust - If they tell you something different, its time

to dig again!

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