Assessing normality and sampling distributions in statistics
Assessing normality and sampling distributions in statistics STAT 205 001
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This 3 page Class Notes was uploaded by Janay Notetaker on Sunday September 25, 2016. The Class Notes belongs to STAT 205 001 at University of South Carolina taught by in Fall 2016. Since its upload, it has received 23 views.
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Date Created: 09/25/16
th Stat 205 Sept 19-24 Sampling variability and Normality assessment Asessing Normality: Why? Because in statistical analysis all of the functions or tests (ANOVA, t-test…) assume that the data is normal. Ways to check: Modified boxplot: see where the lower fence (Q1 - 1.5*IQR) and the upper fence (Q3 + 1.5*IQR) are Ask= Are the lower fence, the upper fence, and the box all approximately the same size? If not, then the data are probably not normal. Quantile-Quantile Plot (aka Normal probability plot): in small sample sizes especially, use a quantile- quantile plot (qq plot) Rcode= qqnorm(insert data file name here) 1. Order data from smallest to largest 2. Find the sample mean and sample standard deviation 3. Plot these values against appropriate quantiles from the standard normal distribution If it’s a straight line (or looks reasonably straight, it’ll probably not be 100% straight) then your data is normal QQ plot axis: y-axis=observed data, x-axis=the observed percentile (the z score) Sampling Variability: Sampling variability = variability among random samples Meta study= a study to test variability (how variability is assessed) Sampling distribution= a histogram of all of the ȳ (sample means) The sampling distribution of ȳ theorem The mean of the sampling distribution of ȳ equals the population mean μ =ȳμ The standard deviation of the sampling distribution of ȳ equals the population standard deviation divided by the square root of sample size σ =ȳ If the population Y is normal then the sampling distribution ȳ is normal regardless of n sample size Central Limit Theorem = if n is large, the sampling distribution of ȳ is normal (the sampling distribution density of Y¯ will look more and more like a normal distribution as n gets bigger) Hope the exam went well this week.
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