Download Normal distribution

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