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Sampling in Statistics: Understanding Standardized Normal Distribution

Learn about sampling methods, standardized normal distribution, and confidence intervals in statistics. Explore sampling distribution and computation of standard error. Discover how to compute confidence intervals and interpret results using SPSS.

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Sampling in Statistics: Understanding Standardized Normal Distribution

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  1. Statistics in SPSSLecture 5 Petr Soukup, Charles University in Prague

  2. Sampling

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

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

  5. Standardized normal distribution

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

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

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

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

  10. Sampling distribution

  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)

  12. Field’s example

  13. Sampling distribution

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

  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

  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)?

  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.

  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

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