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Statistics in SPSS Lecture 5
Petr Soukup, Charles University in Prague
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Sampling 2
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Why sampling? Sample vs. population Money, money, money
We have only sample 3
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Sample types Random (probability) – simple, multistage, cluster,...
Purposive – quota Only for random sampled data we can use following tools for statistical inference 4
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Standardized normal distribution
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Stand. normal distribution
Author: Karl Fridrich Gauss (Gaussian distribution) Model that is followed by many variables It is wise to know about it 6
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Stand. normal distribution
Mean is equal to 0 Standard deviation (and variance) is equal to 1 We use symbol N(0,1) 7
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Stand. normal distribution
SIX SIGMA RULE: NEARLY ALL VALUES ARE COVERD BY THE RANGE WITH THE WIDTH OF SIX STANDARD DEVIATIONS 8
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Stand. normal distribution
5 % of values are above 1.96 or below -1,96 9
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Sampling distribution
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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
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Field’s example 12
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Sampling distribution
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Online simulation 14
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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
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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
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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
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Usage of STANDARD ERROR: Confidence interval for mean
SPSS: ANALYZE-DESCRIPTIVE STATISTICS-EXPLORE (for mean) Computation: MEAN +- 2*S.E. (95%) 19
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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
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HW 21
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HW5 Try to compute confidence interval for mean (one cardinal variable) and for proportion }one binary variable). Interpret results. 22
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Thanks for your attention
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