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Lecture 5, Feb 5.docx

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Brock University
Child and Youth Studies
Patricia Kirkpatrick

3P15, Lecture 5, Feb 5 Lecture feedback • Stop.... (things you’d like to stop doing) • Start.... (things you’d like to start doing) • Continue.... (things you’d like to continue doing) • Anything else you’d like to share • You can include your name, or not, according to your preference Chapter 8 • Sampling Introduction to Sampling • Aim to generalize from sample of units to target population • Sampling error: difference between sample and population There are two types of sampling techniques: probability and non-probability. • Probability: o Simple random sample o Systematic random sample o Stratified/Hierarchical Random Sample o (Multi-stage) cluster sample • Non-Probability / Non-Random o Convenience/opportunity sample o Snowball sample o Quota sample • *Know what they are, their strengths & limitations, when they would be used* Chapter 9 • Generalizing from Samples to Populations Learning Objectives • In this chapter, we’ll study • the central limit theorem • confidence intervals and how to calculate them • how t-distributions can be used for small samples • the sampling distribution of means and proportions. Sampling Distribution of Means • What is the average age of students at the U of A? • Take the average from each class. • Each average can be treated as an individual score. • Accumulation of scores have a normal distribution. • Take the average of averages. Sampling Distribution of Means (cont’d) • Sampling distribution of means: a series of plotted samples o The mean of the sample means will be equal to the population mean. o The distribution of means will be quite tightly clustered around the true population mean. o We can estimate how closely the mean of our sample approximates the population mean by using the equation • Central limit theorem: allows us to assume that any sample statistic we generate from a known population will lie somewhere along a normal distribution Sampling Distribution of Means (cont’d) • Asymptotically normal • Has a mean equal to the population mean • Has a standard deviation (standard error) equal to the population standard deviation divided by the square root of N • The mean of means is more likely to be accurate than any one mean. Illustrating the Normal Curve • The central limit theorem states that if any variable (e.g., the number of times a coin toss shows heads) has a known range, it will increasingly approximate the normal curve as the number of samples increases. Illustrating the Normal Curve (cont’d) • Histograms are often used to assess distributions. • With increased coin tosses (from 100 to 1,000), the distribution of data is closer in the normal curve. Illustrating the Normal Curve (cont’d) • When the number of samples is increased to 10,000, there is little difference between the results and the overlaid normal curve. Standard Error of the Sample Mean • The equation gives us the standard error of the sample mean when the population standard deviation is known. • The standard error is described as the standard deviation of the population divided by the square root of the sample size. Standard Error of the Sample Mean (cont’d) • How do you measure the difference between 1 or 2 sample means and the population mean, when you know the population standard deviation? σ = σ X N • What is the probability that our sample mean is close to our population mean? • Also called the theoretical standard deviation Standard Error of the Sample Mean (cont’d) • Do researchers typically take an infinite number of samples? • Do we know the mean of means/population mean? • Can you be confident in your results? Confidence Intervals • Is it possible to determine how close our sample mean is to the population mean? • If not, is there a second-best solution? • The confidence interval gives a range for the mean, and the probability that the true score is within that range. Confidence Intervals (cont’d) • Standard error: A type of standard deviation that refers to the distance that a sample mean is from a population mean. • To indicate level of confidence, we need to employ the standard error, which is derived from the standard deviation. • The standard error allows us to determine how much confidence we have in the accuracy of the mean taken from the sample. • Confidence limits: The upper and lower ranges of the “confidence interval” C.I.= X ± zscore*σ X Confidence Intervals (cont’d) 68%C.I.= X ±0.99*σ X 95%C.I.= X ±1.96*σ X The z-Table…Again A
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