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Lecture 6

lecture 6

9 Pages
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Department
Sociology
Course Code
SOC222H5
Professor
John Kervin

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1 SOC 222 -- MEASURING the SOCIAL WORLD Session #6 INFERENTIAL STATS II: SIGNIFICANCE & CONFID. INTERVALS Linneman: ch. 5 Kranzler: chs. 6, 7 WHERE WE ARE samples populations standard error sampling error sampling distribution Today Today’s Objectives: Know… 1. The difference between statistical significance and confidence intervals 2. The logic of hypothesis testing and null hypotheses 3. The difference between Type I and Type II errors 4. How Type I error is calculated 5. The role of the normal distribution in calculating Type I errors 6. The five conventional significance levels 7. How confidence intervals are calculated 8. how sample size is related to statistical significance and confidence intervals 9. The SPSS procedures for getting statistical significance and confidence intervals for single variables Terms to Know confidence interval mu (μ) t-curve normal curve statistical significance significance level research hypothesis null hypothesis type I error type II error degrees of freedom 2 USING the STANDARD ERROR STATISTICAL SIGNIFICANCE • Could the population characteristic actually be zero? • Cat-cat: the percentage difference is really zero • Cat-rat: the difference in means is really zero • Rat-rat: the correlation coefficient “r” is really zero the slope “b” is really zero the coefficient of determination “R ” is really zero Does not say or ask anything about size or strength of a relationship HYPOTHESIS TESTING 1. A research question: • Do students who study more hours achieve higher grades? 2. A research hypothesis: • Hypothesis: students who study more hours achieve higher grades. The Problem of “Truth” Logically, it is very difficult to show something is true- cant test all swans in the world(all swans are white) So instead its easier to prove the opposite- no swans are not white Disprove reverse hypothesis Null Hypotheses null hypothesis: the opposite EG: • Research hypothesis: students who study more hours achieve higher grades. • X and Y are related • Null hypothesis: students who study more hours do not achieve higher grades • X and Y are not related NOTE: • Disproving a null hypothesis does not prove the research hypothesis It just supports the research hypothesis, hypothesis are never proven true, theyre just supported Null Hypotheses, Samples, and Populations • sampling error- what you found in sample was a mistake, there is nothing going on in population. 3 we try to disprove that null hypothesis- then we have support and we can test null hypothesis reputedly . We keep on disproving null, then belief in research gets stronger INFERENCE ERRORS Population Reality (unknown) Sample Results: Relationship No Relationship Relationship OK Type I Error No relationship Type II Error OK Type I Error We can never know if we make a type 1 error Say there’s relationship but there really isn’t We estimate the probability of making a type 1 error The statistical significance of an X-Y relationship is related to • Probability of a Type I error Standard Error and Chance of a Type I Error Bad samples are found in tail of distribution, more spread out the more the chance of bad sample • The more spread out the sampling distribution, the more chance of a bad sample • The more chance of a bad sample, the higher the chance of a type I error • IE, the more spread in the sampling distribution, the higher the chance of a type I error • Statistical significance is the chance of a type I error. Calculating Chance of a Type I Error We can never REALLY know if we made a type 1 error To do this, we need to know the shape of the sampling distribution curve 1. The mean of the sampling distribution statistic 2. The standard error of the sampling distribution statistic 3. The overall shape of the sampling distribution curve Estimate of standard error comes from what we can calculate from standard deviation There are different distribution curves (4 in this class) The Normal Distribution This is a bell-shaped curve. • The statistic is said to be normally distributed • The sampling distribution of means is normally distributed 4 • Distance from the mean is in terms of SEs from the mean • These are the Z scores • The size of the area under the curve corresponds to the number of possible samples in particular part of the curve -3 -2 -1 0 1 2 3 Standard Errors from the Mean sample mean Our null hypothesis: the population mean is zero- there’s nothing going on Our sample finding: a mean with a Z score of 1.25 5 -3 -2 -1 0 1 2 3 Standard Errors from the Mean sample mean Probability of a type I error = Proportion of samples with Z scores of 1.25 or more = 6/36 So chance of a type I error is 1/6,
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