Class Notes (811,170)
SOAN 2120 (389)
Lecture

October 2.docx

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School
University of Guelph
Department
Sociology and Anthropology
Course
SOAN 2120
Professor
David Walters
Semester
Fall

Description
Height (Males) October 2, 2012 – SOAN 2120 99% Height (Males) 95% Any individual value cinto a z-scored 99% Any individual value 95% can be converted into a z-score 5 0’!5 ’! Mean 6 2’6 4’! 5 8’ -2.6 -2 Std Dev = 3 inche+2 +2.6 St dev St dev St devSt dev Standard Deviation Scale 5 0’!5 ’! Mean 6 2’6 4’! 5 8’ -2.6 -2 Std Dev = 3 inche+2 +2.6 St dev St dev St devSt dev Standard Deviation Scale Walters Commonly used cut-offs (alpha levels – ! ) SOAN 2120 99% I n t r o d u c t o r y R e 95% a r c h M e t h o d s Commonly used cut-offs (alpha levels – ! ) 99% 95% Lecture: Statistical Inference’! 1-.95 5 6’ •!1/20 = .05 1-.99 Mean •1-.950 = .01 4 5’5 0’! 5 6’ 6 ’!6 ’! •!1/20 = .05 1-.99 1 in 100 would be the outliers (really short or really tall) •!1/100 = .01 Calculating p-values •!Statistics Tables •!How do we know that a z-score of plus or minus 2 translates to a p-value of .05 •!Calculus http://bcs.whfreeman.com/bps3e/ http://bcs.whfreeman.com/bps3e/ z’s converted to p’s 2 2 Commonly used cut-offs (alpha levels – ! ) 99% z’s converted to p’s95% 1-.95 4 ’!5 ’! 5 6’ 6 ’6 ’! •!1/20 = .05 1-.99 •!1/100 = .01 -2 2 integrate that function from -2 to +2 and you end up with .95 – that’s the area b/w those two points .05 versus .01 1 Implications Hypothesis testing http://bcs.whfreeman.com/bps3e/ 2.576 = above the mean -2.576 = below the mean ^^^^^^ use that website that’s on the slide– it will HELP YOU  What have we been doing? •Summarizing distributions 2 –!Normal distribution •!Probabilities •!Is a particular value different from the mean? New Topic •Statistical inference •!Using sample information to estimate population values •!Normal distribution •!Just as variables have distributions, sample statistics have distributions as well 3 sample – first slide we saw today of male heights population- sampling – “from all possible samples” – abstract concept – take multiple samples, we can calculate a mean and plot those means in a histogram (just like the height) – sampling distribution based on calculating a statistic over and over again from samples of the same size – most abstract but the most powerful •! •! •! This is the sampling distribution over repeated samples. randomly take 10 people from that population then calculate the mean of their height How do we know that the mean of a tadistribution of samples is the same as the take third randpopulation mean?an of a distribution of samples is the same as the •!Statistical theory •!Simulationse know that the mean of a •!distribution of samples is the same as the –!Take a sample (Income of 40,000 people) •!Sim•!Populationulation mean? •!Statistical theorythe mean 40,000 people) •!Pop»!1000 random samples •!Simul–!C»!Calculate the mean –!Take »!1000 random samples0,000 people) •!Population –!Calculate the meanan »!1000 random samples »!Calculate the mean Statistics are Variable Statistics are Variable •! The fact that statistics from random samples have definite sampling •!distStatistics are Variable carefulom sestimate of how trustworthy a statistic dis as an estimate of a parameterul •estimate of how trustworthy a statistic •!samples have definite samplinghe spread idistributions allows a more careful •!estimate of how trustworthy a statistic of its sampling distribution is as an estimate of a parameter •! Variability is described by the spread of its sampling distribution –!Larger samples give smaller spread 5 5 5 Statistics and Bias •! The bias of a statistic is the difference between its average value (obtained from the sampling distribution) and the true value of the parameter •! A statStatistics and Biasf the mean of its sampling distribution is equal to the parameter being estimated –!An unbiased statistic will sometimes give an •!
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