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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