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Lecture 7

SOC222 Lecture 7

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University of Toronto Mississauga
John Kervin

SOC 222 -- MEASURING the SOCIAL WORLD Session #7 -- INF STAT: TABLES TODAY’S OBJECTIVES 1. Know the difference between confidence intervals and statistical significance 2. Know the difference between a Type I and a Type II error 3. Know the meaning of “expected frequencies” and their role in chi-square calculations 4. Know the commonly used levels of statistical significance 5. Know how to run a chi-square test on SPSS 6. Know the meaning of “degrees of freedom” Terms to Know statistical significance significance level research hypothesis null hypothesis type I error type II error chi-square expected frequencies observed frequencies (counts) degrees of freedom SITUATION 2 category vars 2 procedures we can use to make inferences about the relationship REFRESHER: THE TWO INFERENTIAL STATISTICS PROCEDURES Procedure #1: confidence intervals • Question: How much confidence do we have in our estimate of the effect size in the population? • Answer: a confidence interval around a population estimate • Typically 95% • We’re 95% sure that the population estimate falls within this interval • If we drew all possible samples of size N, 95% of them would give a population estimate within this interval We did this last week but with one variable at a time Procedure #2: statistical significance • Question: Is there a relationship in the population? • Answer to this question: statistical significance of the relationship This question is different from the first procedure – asking if an relationship exist in the population if we found in the sample – so is the relationship found in the sample is statistically significant? WHAT IS STATISTICAL SIGNIFICANCE? Linneman See Kranzler: 108-109 The Logic of Hypothesis Testing We start with a theory (below) which leads us to the RH 1. Two groups are different OR 2. Two variables are related research hypothesis. With statistics, you can’t show something is true • It is easier to disprove a statement (Carl Pauper) SO: • We create an opposite hypothesis • And we try to disprove that! • null hypothesis Linneman, p. 140 Kranzler, p. 105-106 • Null hypotheses state that nothing is happening: • In particular, any differences or relationship you find in your sample is purely by chance If we can disprove the null hypothesis, they we have support for our research hypothesis  confidence that RH is true; null won’t be on any test Type I Error • We find in our sample that X  Y (related) • Could the sample relationship occur just because it’s a non-representative sample? (could it be sampling error) We conclude there’s a relationship in the population when there really isn’t. (mistake that we can make  sample misleads us  type I error) type I error • We estimate the probability of making a type 1 error If this probability is low, • We say the relationship has statistical significance In most research, we want to minimize type I error Type II Error • Concluding no relationship when there really is one (opposite mistake) • Normally this is less important Interesting fact: the smaller the chance of a type I error, the larger the chance of a type II error Need to find a balance between the two types of error keeping in mind that I is more imp STATISTICAL SIGNIFICANCE FROM CHI-SQUARE What is Chi-Square? 1. Chi-square is a statistic • Calculated from your sample (anything you calculate from your sample is a stat) 2. Chi-square is calculated from crosstabs (Linneman) • The chi-square statistic compares the expected frequencies with the observed frequencies (less similarity between expected and observed frequencies = bigger value of chi-square) 3. We know the shape of the sampling distribution for chi-square - Has its own curve: chi-curve • Not symmetrical • Changes with the size of the crosstab (columns and rows  degrees of freedom) 1. Calculating Expected Frequencies First step: Calculating expected frequencies • What would be expected in the population if no relationship • Based solely on the marginals (sums we find) • Marginals: the row and column totals in the margins Male Female Not working 161 Working 116
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