BIOM301 Chapter 7 Sample Variability GOAL Making Populations Statements Based on Sample Data 4 Key Concepts Random Sampling Sampling Error Random Sampling Sampling Distribution of Sample Means Central Limit Theorem When a sample is collected randomly implication is o All experimental units equally likely to be selected o Experimental Units are Independently Selected o Sample represents the entire population o Experimental Units selected without bias Sampling Error the difference between a sample statistic and a population parameter due to chance Error an estimate of possible variability When you collect a sample from a population we DO NOT expect x because of the impact of chance o Populations are large while a sample is a small subset o Theoretically an infinite number of samples could be collected Samples from the same population can have different sample means DUE TO CHANCE since you sampled RANDOMLY o We won t ever know the true population value or sampling error BUT we can make a guess The Sampling Distribution of Sample Means SDSM Occurs when o DO take every possible sample from a population o Calculate the mean of each sample o And plot all the means o Remember we are theoretical here The spread of the data is an estimate of sampling error mean values Two key values when you plot a lot of sample means o The Mean o The Standard Deviation or Standard Error With a lot of samples o Sampling Distribution implies that it is the result of repeated sampling theoretically o Distribution of Sample Means just implies that it is a distribution of As the n increases the spread to the distribution of sample means x decreases o When increasing the sample size the distribution of observations in the Population has not changed with sample size Central Limit Theorem the sampling distribution of means will approach a normal distribution as sample size increases Sample size is n the size of each individual sample not the number of samples For most data sets SDSM will look normal if n is 30 or more IF the population is normally distributed the SDSM is also normally distributed Standard Error an estimate of the spread of the SDSM o As n increases the SE decreases outliers impact
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