Statistics in SPSS Lecture 5

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Presentation transcript:

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

Sampling 2

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

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

Standardized normal distribution 5

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

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

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

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

Sampling distribution 10

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

Field’s example 12

Sampling distribution 13

Online simulation http://onlinestatbook.com/stat_sim/sampling_dist/index.html 14

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

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

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

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

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

HW 21

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

Thanks for your attention 23