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Lec#5 (feb 6th).docx

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University of Toronto Mississauga
Dax Urbszat

1 SOC 222 -- MEASURING the SOCIAL WORLD Session #5 -- INTRO to INFERENTIAL STATISTICS SPSS: E Notation When numbers are very small SPSS converts to E notation EG: 1.34E-2 = .0134 • 1.34 is the starting number • E means move the decimal point • minus sign – move to the left (negative direction) • 2 is number of spaces to move the decimal point EG: 7.89E-3 = .00789 • If no minus sign, or a plus sign, move decimal point to the right EG: 1.34E+4 = 13400 - Write original and then use ^ method to indicate what to do with the decimal - Test: just round before hand and then write it in. POPULATIONS & SAMPLES Effects size: was the first question we were assessing Q2: if we use a sample how good is the estimate for the population. Inferential because we infer something based on sample data 1. Population: - A population is a group cases were interested in. - We have a research question regarding that group 2. Sample: - Set of cases selected form the population 2 3. Simple random sample • random sample 1. set of cases selected from the population 2. • simple random sample: each case has the same probability of being chosen (SRS)  cases are selected by change  each case in the population has a known probability of being selected • statistic - What we calculate from the sample is the statistic. Sample of students: statistic would be mean age. Case would be one student - Mean, correlation are all statistics calculated from the sample • population characteristic - we estimate population characteristics based on statistics • population value • parameter SAMPLES & POPULATION ESTIMATES • The sample effect size is our estimate of the effect size in the population. - We don’t have time to obtain data from the entire population, thus we draw a sample. - The sample is the source of our data, and then we use that sample data to get a statistic. ACCURACY of ESTIMATES - We cannot be sure that the sample characteristic is the same and represents the entire population - Drawing a second population sample and getting different results will not be a surprise - No sample is 100% accurate Rick Example - Why is the sample inaccurate? 3 • This is his RQ: what is the mean days absent for company employees? • He can only afford a certain number from the population. • We know what rick does not; what the population is. Rick knows: • The company has six employees • He also knows that he can get info on employee from the personal department w/o interviewing employee. Here’s what Rick doesn’t know: (the population data): Employee Days Absent Ann 1 Bob 3 Cathy 3 Donna 5 Ed 7 Farrah 9 ∑ xi 1+3+3+5+7+9 28 x= = = =4.67 N 6 6 Estimating a Population Mean from a Sample • Cathy and Farrah - Rick can only get data from 2 people, so he picks these two randomly. - Next he finds that cathy was absent 3 days and farah was absent 9 days - He concludes sample mean is 6 Summary: • The sample mean is 6.0 days absent, on average • So Rick’s estimate of the population mean is 6.0 days • The true population mean is 4.67 • So Rick’s estimate is inaccurate by 1.33 days. GOOD AND BAD SAMPLES - How accurate is my estimate of 6 days ^. - We know that his estimate is quite off - Why does a sample give an inaccurate sample: o Because you might get a sample that gives a good or maybe a poor estimate. It depends on what sample you draw 4 Employee Days Absent Ann 1 Bob 3 Cathy 3 Donna 5 Ed 7 Farrah 9 15 possible samples of size two - How many sample of size two can we get from population. There are 15 possible samples. • The fourth column is the sample accuracy: • Arbitrary: • High: estimate is off by 1 day or less • Means of 4 or 5 • This is a good sample • Low: estimate is off by 2 days or more • Means of 2 or 7 or 8 • Low accuracy sample Sample Days Absent Sample Mean Sample Accuracy A, B 1, 3 2.0 Low A, C 1, 3 2.0 Low A, D 1, 5 3.0 A, E 1, 7 4.0 High A, F 1, 9 5.0 High B, C 3, 3 3.0 B, D 3, 5 4.0 High B, E 3, 7 5.0 High B, F 3, 9 6.0 C, D 3, 5 4.0 High C, E 3, 7 5.0 High C, F 3, 9 6.0 D, E 5, 7 6.0 D, F 5, 9 7.0 Low E, F 7, 9 8.0 Low Employee Days Absent Ann 1 5 Bob 3 Cathy 3 Donna 5 Ed 7 Farrah 9 Representative sample: A sample with a distribution that matches the population distribution. Employee Days Absent Ann 1 Bob 3 Cathy 3 Donna 5 Ed 7 Farrah 9 • 6 samples give good estimates • 5 are so-so • 4 are bad The quality of the estimate depends on whether the sample is representative Sampling Error Sampling error: the probability of drawing a sample that gives an inaccurate population estimate. - There is always a chance that the sample you draw will not be representative. Rick’s Probability of a Bad Sample In the Rick example: • 15 possible samples • 4 were bad • So probability of drawing a bad sample is 4/15 • = 27% • This is the sampling error for Rick’s sample - Rick does not know the means of all the samples, so he cannot calculate the probability of drawing a bad sample (sampling error) 6 Estimating Sampling Error - If rick can estimate a sampling error, then he can know if the chance of drawing a bad sample is high, then he might have drawn a bad sample. But if he knows that the chance of drawing a bad sample is low, then he mostly likely does not have a bad sample. - So if we know that the chance is high to get a bad sample, then we might have drawn a bad one so we
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