1. Statistics in SPSS Lecture 5
Petr Soukup, Charles University in Prague

2. Sampling 2

3. Why sampling? Sample vs. population Money, money, money
We have only sample 3

4. Sample types Random (probability) – simple, multistage, cluster,...
Purposive – quota
Only for random sampled data we can use following tools for statistical inference 4

5. Standardized normal distribution5

6. Stand. normal distribution
Author: Karl Fridrich Gauss (Gaussian distribution)
Model that is followed by many variables
It is wise to know about it 6

7. Stand. normal distribution
Mean is equal to 0
Standard deviation (and variance) is equal to 1
We use symbol N(0,1) 7

8. Stand. normal distribution
SIX SIGMA RULE: NEARLY ALL VALUES ARE COVERD BY THE RANGE WITH THE WIDTH OF SIX STANDARD DEVIATIONS 8

9. Stand. normal distribution
5 % of values are above 1.96 or below -1,96 9

10. Sampling distribution10

11. 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) 11

12. Field’s example 12

13. Sampling distribution13

14. Online simulation 14

15. 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 15

16. 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)? 16

17. 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. 17

18. 18

19. Usage of STANDARD ERROR: Confidence interval for mean
SPSS: ANALYZE-DESCRIPTIVE STATISTICS-EXPLORE (for mean)
Computation: MEAN +- 2*S.E. (95%) 19

20. 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 20

21. HW 21

22. HW5
Try to compute confidence interval for mean (one cardinal variable) and for proportion }one binary variable). Interpret results. 22

23. Thanks for your attention23