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Statistics in SPSS
Lecture 5
Petr Soukup, Charles University in Prague
Sampling
Why sampling?
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Sample vs. population
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Money, money, money
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We have only sample
Sample types
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Random (probability) – simple, multistage,
cluster,...
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Purposive – quota
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Only for random sampled data we can use
following tools for statistical inference
Standardized normal distribution
Stand. normal distribution
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Author: Karl Fridrich Gauss (Gaussian
distribution)
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Model that is followed by many variables
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It is wise to know about it
Stand. normal distribution
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Mean is equal to 0
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Standard deviation (and variance) is equal to 1
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We use symbol N(0,1)
Stand. normal distribution
Pravidlo
šesti
sigma:
do tří směrodatných
na každou
stranu
SIX
SIGMA
RULE:
NEARLY
ALL VALUESodchylek
ARE COVERD
BY THE
RANGE WITH THE
WIDTHleží
OF celkem
SIX STANDARD
DEVIATIONS
od průměru
99 % případů.
95 %
34,1%
34,1%
68 %
2,1%
13,5%
13,5%
2,1%
Stand. normal distribution
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5 % of values are above 1.96 or below -1,96
Sampling distribution
Sampling distribution
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Basic idea (utopic): We carry out infinite number
of samples and compute some descriptive
statistic* (e.g. mean)
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Sampling distribution = distribution of statistics
for individual samples
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Usually follow some well-known distribution
(mainly normal distr.)
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*in sampling we use only term statistic (instead
of descriptive)
Field’s example
Sampling distribution
Online simulation
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http://onlinestatbook.com/stat_sim/sampling_dist
/index.html
Sampling distribution
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Basic statistic – standard error
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S.E. = standard deviation of sampling
distribution
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Computation:
,
where s=standard deviation of the variable
and N is sample size
Computation of std. deviation for
sampling distribution (STANDARD
ERROR)
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SPSS: ANALYZE-DESCRIPTIVE
STATISTICS-EXPLORE (for mean)

SPSS: ANALYZE-DESCRIPTIVE
STATISTICS-EXPLORE (for proportion of
binary variable) – tip: use 0,1 coding
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? How to compute it for nominal or ordinal data
(one category)?
Confidence interval (CI)
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Try to cover (estimate) unknown parameter for
population by the range
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Mostly 95 % coverage (intervals)
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Normal distribution: MEAN +- 2*SD (95%)
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Conf. Int.: MEAN +- 2*S.E. (95%)
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etc.
Usage of STANDARD ERROR:
Confidence interval for mean

SPSS: ANALYZE-DESCRIPTIVE
STATISTICS-EXPLORE (for mean)

Computation: MEAN +- 2*S.E. (95%)
Usage of STANDARD ERROR:
Confidence interval for proportion

SPSS: ANALYZE-DESCRIPTIVE
STATISTICS-EXPLORE (for proportion)

Computation: MEAN +- 2*S.E. (95%)

Use 0,1 coding
HW
HW5
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Try to compute confidence interval for mean
(one cardinal variable) and for proportion }one
binary variable). Interpret results.
Thanks for your attention