HDFS 361

1
HDFS 361Research Methods

• Week 2
• Levels of Measurement and Sampling

2
Types of Studies

• Descriptive studies
• These studies describe the results for the
  participants in the study.
• Inferential studies
• These studies seek to generalize beyond the
  participants to a specified, larger population.

3
Sample and Population

• Population
• A population includes the universe of people or
  groups about whom we are interested.
• Sample
• A sample is a subset of a population.
• If a sample is representative of the population
  from which it was drawn, we can make an inference
  from the sample to the population.

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Criteria for Levels of Measurement

• Mutually exclusiveeach observation is assigned a
  single value or label.
• Exhaustiveevery observation is classified
  (measured), even if assigned to a category called
  other.
• Orderedobservations are ranked or ordered on how
  much of the characteristic they have.
• Equal appearing intervalsan equal difference
  between values corresponds to an equal difference
  on the characteristic being measured.
• Meaningful zero pointa value of 0 corresponds to
  the absolute absence of the characteristic being
  measured.

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Level of Measurement and Measurement Criteria
The Traditional Approach
Level of Meas-urement Measurement Criteria Measurement Criteria Measurement Criteria Measurement Criteria Measurement Criteria  
Level of Meas-urement Mutually Exclu-sive Exhaus-tive Ordered Equal Inter-vals Mean-ingful zero Examples
Ratio Yes Yes Yes Yes Yes Age
Interval Yes Yes Yes Yes Scales
Ordinal Yes Yes Yes Religiosity
Nominal Yes Yes Marital Status
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Nominal VariablesFrequency Distributions
Marital status Freq. Percent
Cum. --------------------------------------------
----- married 1,269 45.90
45.90 widowed 247 8.93
54.83 divorced 445 16.09
70.92 separated 96 3.47
74.39 never married 708 25.61
100.00 --------------------------------------
- Total 2,765 100.00
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Ordinal Ranks--Median

• The median is the value of the case in the
  middle.
• Rank observations. If we had two children who
  were tied at the 3rd rank, we would give both of
  them a rank of 3.5. This is because the pair of
  cases occupies both the 3rd and the 4th ranks.
  The average of 3 and 4 is, . The next person
  higher on the scale would have the rank of 5,
  resulting in rankings of 1, 2, 3.5, 3.5, 5, 6, 7,
  and 8.
• If we had 3 people tied for most aggressive (in
  addition to the 2 tied for third), our rankings
  would be (1, 2, 3.5, 3.5, 5, 7, 7, 7).
• The three highest-ranking children occupy the
  6th, 7th, and 8th ranks.
• In sporting events they try to be nice and give
  tied contestants the highest rank they can.

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Ordinal categoriesFrequency Distribution
Health Freq. Percent
Cum. --------------------------------------------
--- excellent 568 30.75
30.75 good 854 46.24
76.99 fair 322 17.43
94.42 poor 103 5.58
100.00 ------------------------------------------
----- Total 1,847 100.00
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Ordinal CategoriesBar Charts
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Nominal LevelBar Charts
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Interval/Ratio LevelUnderlying Continuum
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Interval/Ratio Level

• We can use most statistics and graphs
• Means, standard deviations
• Histograms and other charts
• We will cover these later in the course

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Data CollectionRandom Sample

• Simple Random sample means everybody has the same
  chance of selection.
• Assumes sampling with replacement, but this is
  rarely used in practice.
• Need a list of the entire population to do a
  random sample and this is often hard to obtain.

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Using Stata to Select Random Sample of 1000
People from a Population of 15,000
------- id ------- 1.
5546 2. 4530 3. 6419 4.
5622 5. 8877 ------- 6. 3867
7. 10748 8. 6179 9. 11602
10. 361 -------
set obs 15000 gen id _n sample 1000, count list
id in 1/10
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Sample size and Sampling Error
Sample N Sampling Error
20 21.91
50 13.86
100 9.80
200 6.93
500 4.38
1,000 3.10
1,600 2.45
10,000 0.98



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Graphic of 15 Confidence Intervals, n 500, True
proportion in Population .48
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Estimating Confidence Interval for Proportion
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Stratified Sample

• By dividing the population into two or more
  strata, each of which is homogeneous, we can
  conduct a random sample of each stratum and then
  pool the results.
• This is more powerful than a simple random sample
  to the extent the strata are homogeneous.
• Rather than taking a random sample of the entire
  population, a stratified sample could be used to
  take a random sample of each stratum.

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Stratified Samples
MEN
WOMEN
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Cluster Sample

• Cluster sampling is sometimes confused with
  stratified sampling, but it has a different
  purpose. If our population is geographically
  dispersed, we can often save a great deal of time
  and money by dividing the population into
  geographical clusters, randomly sampling the
  clusters
• Census data can be used on any city in the U.S.
  to list every city block (usually commercial
  blocks are excluded). We could then take a sample
  of blocks (sampling units) and interview all or
  some of the households in each block we included
  in our sample of blocks.

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Cluster Sample

• A person interested in morale of elementary
  school teachers in a large school district could
  obtain a list of elementary schools (sampling
  units) and sample 10 percent of the schools.
• If your clusters are blocks, you can send an
  interviewer to a selected block. Once there the
  interviewer can go to the first house. If nobody
  is home, the interviewer can go to the next
  selected house, and so on.
• Sampling HDFS students by randomly sampling 20
  sections from the class schedule, then giving the
  instrument to everybody in the selected sections.

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Nonprobability SamplesQuota Sample

• Quota Sampling tries to be representative by
  sampling a reasonable number of certain groups.
• We might sample 100 women and 100 men for a 200
  person sample. This would make the sample
  representative on gender.
• This approach is better than nothing, but should
  not be confused with a probability sample. We may
  represent the gender and racial distribution of
  our population, but without probability sampling,
  we should be hesitant to generalize to the
  population.

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Nonprobability SamplesSnowball

• Snowball Sampling is an approach used for rare
  populations.
• What if you wanted to interview lesbian couples?
  It is practically impossible to get a sampling
  list of lesbian couples.
• You could go to a gay and lesbian group and
  interview people, but you would then be limiting
  yourself to lesbians who are activists.

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Nonprobability SamplesSnowball

• When you interview a lesbian who is in the group
  you ask her to share with you the name of other
  lesbians who are not in the group. When you
  interview them, you ask them to give you the name
  of still other lesbians.
• Several points of entry are important
• PFLAG would give you gays/lesbians whose parents
  were supportive
• Gay and Lesbian groups would give you
  gays/lesbians whether their parents were
  supportive or not.
• Snowballing would give you gays/lesbians who were
  out. IRB issues might be a problem.

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Nonprobability Samples for Qualitative Studies

• Purposive or elite sampling has decided
  advantages over probability sampling.
• The researcher wants to tap the range of people
  and because the interviews are so labor intensive
  the sample must be small, at least in most
  qualitative studies.
• If you are limited to interviewing 20
  participants in your study, you want to select
  them purposively.

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Nonprobability Samples for Qualitative Studies

• Suppose you were studying the effects of a change
  in the welfare system on parents.
• You will want the perspective of both mothers and
  father, unemployed and underemployed parents,
  single parents, cohabiting partners, married
  parents, and parents with different racial or
  ethnic backgrounds.
• You may also need the perspective of social
  service providers in the welfare system.
• If you randomly sampled 20 participants, you
  would not get this diversity. You need to
  purposively select each participant based on the
  information value they have.