• Study Resource
• Explore

Survey
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Central limit theorem wikipedia, lookup

Transcript
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
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
Related documents