Class Notes (806,507)
Brock University (11,827)
CHYS 3P15 (11)
Lecture

# Lecture 5, Feb 5.docx

7 Pages
125 Views

School
Brock University
Department
Child and Youth Studies
Course
CHYS 3P15
Professor
Patricia Kirkpatrick
Semester
Winter

Description
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
More Less

Related notes for CHYS 3P15

OR

Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.