chapter 13 sampling: quantitative and qualitative

Chapter 13 Sampling:

quantitative and qualitative

CONTENTS

• Samples and populations• Representativeness• Sample size• Weighting• Sampling for qualitative research

Samples and populations• Population:

– Total category of subjects that is the focus of attention in a particular research project (can be non-human)

• Sample:– A number of subjects drawn from the population

• Two key issues:1. What procedures must be followed to ensure that the

sample is representative of the population?2. How large should the sample be?

A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

Representativeness

• Achieved by Random sampling: • A systematic selection process which ensures that all

members of the population have an equal chance of inclusion in the sample

• Designed to ensure representativeness• An unrepresentative sample is: biased• How is random sampling achieved in practice?


Sampling for household surveys

• Ideally – Eg. 10 million population – sample of 1000: all 10 m.

names put in a drum and 1000 drawn.• In practice:

– For national/regional surveys – multi-stage sampling used 1. Select states/regions2. Within state/region select local government areas (lga) or

constituencies/electorates3. Within lgas or constituencies/electorates for face-to-face

interviews select streets (telephone surveys select numbers at this point)

4. Select ‘clusters’ of 10-15 houses


Sampling for telephone surveys

• Telephone numbers selected at random from telephone directory

• For large-scale surveys: automated by Computer-Aided telephone Interviewing (CATI)

• Requires access to electronic directory with residential/business numbers identified

• No directories for mobile phones• For household and telephone surveys: select person

in household randomly: eg person with next birthday


Sampling for site/user/visitor surveys

1. ISUM: Interviewer stationary – user mobile: – eg. interviewing at entrance/exit– Sample by selecting: ‘next person to pass entrance/exit point

2. USIM: User stationary – interviewer mobile– eg. interviewing people on a beach– Interviewers should have a set route/rules to follow – eg.

‘interview every third person/group’

3. Handouts– Handing out questionnaires to (all) visitors for self-completion– Not generally recommended unless closely supervised –

generally very poor response rates


Sampling for street/quota surveys

• Can be used when data are available on key characteristics of population:– age/sex structure of a community – from Census

• Interviewing target numbers determined by population characteristics– Eg. if Population Census indicates 12% retired: if overall

sample size is 200: interview 24 retired people


Sampling for mail surveys

• Sample from mail-out list• 100% sample often used


Sampling for complex events and destination surveys

• Different components will conform to above guidelines – mostly site surveys

• Problem lies in combining data from different sources for an overall result, if required.


Sampling/ random assignment for experimental research

• Samples of subjects often ‘convenience’ samples – eg. Students

• Assignment to control and experimental groups: – Use of random numbers– Online: eg. www.random.org


http://www.random.org/

Sample size

• Required sample size is not related to population size (except for small populations – see later)

• Criteria:o The required level of precision in the resultso The level of detail in the proposed analysiso The available budget


Level of precision – confidence intervals

• A statistic (finding) from a sample survey is an estimate of the population statistic

• In a randomly drawn sample the sample value has a certain probability of being in a certain range either side of the population value– Eg. 95% probability of being within 2 ‘standard errors’

• See ‘Normal distribution’– Theoretical: imagine drawing lots of samples: some would

be accurate, some not– Discussed further in Ch. 17


Normal curve (Fig. 13.1)

NUMBER OF SAMPLES

-4 -3 -2 -1 +1 +2 +3 +4

Popn Value

2.5%2.5%

95%

Standard errors Standard errors


Confidence intervals (CIs) (Table 13.1: Extract)

Sample size (N)

Percentages found from sample (‘results’)50% 40/60% 30/70% 20/80% 10/90% 5/95% 2/98% 1/99%

Confidence intervals (CIs) + %

500 +4.4 +4.3 +4.0 +3.5 +2.6 +1.9 +1.2 +0.9


Confidence intervals (CIs) (Table 13.1)

Sample size (N)

Percentages found from sample (‘results’)

50% 40/60% 30/70% 20/80% 10/90% 5/95% 2/98% 1/99%


500 +4.4 +4.3 +4.0 +3.5 +2.6 +1.9 +1.2 +0.9

So CI for 20% finding is 30% +4.0 = a range of: 26.0% to 34.0%.CI is not related to population size.NB. • CI for p = CI for 100-p – eg. CI is the same for 40% and 60%• CI for 50% is the largest in absolute terms• This table refers to 95% probability CIs – others can be calculated – eg. 99%


Confidence intervals (CIs) contd (Table 13.1)

Sample size (N)

Percentages found from sample (‘results’)50% 40/60% 30/70% 20/80% 10/90% 5/95% 2/98% 1/99%


500 +4.4 +4.3 +4.0 +3.5 +2.6 +1.9 +1.2 +0.92000 + 2.2 +2.1 +2.0 +1.7 +1.3 +1.0 +0.6 +0.4

So to halve the CI it is necessary to increase the sample fourfold.


Confidence intervals (CIs) contd (Table 13.2)

Table 13.1 can be changed to present necessary sample size for a given CI – see Table 13.2

Percentages found from sample (‘results’)

Conf.Interval

50% 40/60% 30/70% 20/80% 10/90% 5/95% 1/99%

Necessary sample sizes

+1 9600 9216 8064 6144 3456 1824 380+2 2400 2304 2016 1536 864 456 *

+4 600 576 504 384 216 114 *

+8 150 144 126 96 53 * *


Suggested appendix on sample size and CIs

• See Appendix 13.1• table indicating levels of Cis• statement indicating that they have been

taken into account


Detail of proposed analysis

Sample size

% CI Range, % Comment

Survey with sample of 200

200 Bowling 20 +5.5 14.5 – 25.5 Ranges overlap

Tennis 30 +6.3 23.7 – 36.3

Survey with sample of 500

500 Bowling 20 +3.5 16.5 – 23.5 Ranges do not overlap

Tennis 30 +4.0 26.0 – 34.0


Budget

• Key issue: halving the CI requires 4-fold increase in sample size– Eg. N = 250 CI for 50% = +6.2 Survey Cost = 200 x $20 = $5000 N = 1000 CI for 50% = +3.1 Survey Cost = 1000 x $20 = $20,000

• If resources not available for adequate sample size, consider:– Pilot/exploratory study– Qualitative study


Confidence intervals and population estimates (Table 13.3)

Item Source Number

Population Census 500,000

Sample Survey 1,000

% visiting facility/year Survey 12%

% confidence interval Table 13.1 + 2.0%

Estimated no. persons 12% of 500,000 60,000

CI in no. persons + 2% of 500,000 + 10,000

CI as % of persons (10,000/60,000) x 100 + 16.7%

Frequency of visit/year Survey 2.5

Estimated total visits Calc.: (12% of 500,000) x 2.5 150,000

CI in no. visits Calc: (2% of 500,000) x 2.5 +25,000

CI in % visits Cals.: (25,000/150,000) x 100 +16.7%


Sampling for small populations

• CIs are affected by population size if population is below about 50,000

• See Table 13.3


Sample size & population size: small pop’ns (Table 13.3)

Population size Minimum sample size to achieve CI of +5% or +1% on a sample finding of 50%

+5% +1%Infinite 384 96025 million 384 95841 million 384 9511500,000 384 9422100,000 383 876150,000 381 805610,000 370 48995000 357 32881000 278 906100 80 99


Weighting (Tables 13.4 & 13.5)

Time # of Interviews

% Actual # of users (counts)

%

9-11 am 10 22.2 25 5.711.01-1 pm 12 26.7 240 55.21.01-3 pm 11 24.4 110 25.33.01-5 pm 12 26.7 60 2.7Total 45 100.0 435 100.0

Sample does not reflect the pattern of use

Example: one survey at a site


Weighting contd (Table 13.5)

A B C DTime No. of

InterviewsNo. of Users Weighting

FactorsWeighted

Sample No.Source: Survey Counts B/A CxA9-11 am 10 25 2.5 2511.01-1 pm 12 240 20.0 2401.01-3 pm 11 110 10.0 1103.01- 5pm 12 60 5.0 60Total 45 435 435


Sampling for qualitative research

• Number of subjects generally be small, but:– sampling process is still important– should be fully described in research report

• A range of approaches is possible


Method CharacteristicsConvenience Conveniently located persons or organisations -

Sampling for qualitative research contd (Table 13.6)

Criterion Selected on key criterion - eg. age-group.Homogeneous Deliberately homogeneous group: eg. university-

educated male cyclists aged 20-30.Opportunistic Taking advantages of opportunities as they arise - eg. a

major sporting event taking place locally.

Maximum variation Deliberately studying contrasting cases. Opposite of 'homogeneous'.

Purposeful Similar to 'criterion' but may involve other considerations, such as 'maximum variation', typicality.

Snowball Interviewees source of suggestions for contacts.Stratified purposeful A range of cases based on set criteria, eg.

representatives of a range of age-groups or nationalities.


chapter 13 sampling: quantitative and qualitative

Documents

sport studies

sport management

research methods

practical guide

qualitative research

population sample

streets telephone surveys

particular research