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Lecture

# Lec 7.docx

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Department
Sociology
Course Code
SOC222H5
Professor
John Kervin

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SOC 222 -- MEASURING the SOCIAL WORLD Session #7 -- INF STAT: TABLES October 24, 2013 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 variables: either nominal (such as religion) or ordinal (logical ordered fashion). • Percentage Difference: measuring effect sizes. • Problem: we do not know what is the population after drawing a sample. 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? → Estimate the population correlation. For example: 0.35. • Answer: a confidence interval around a population estimate. But only looked at one variable. • 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 Procedure #2: Statistical Significance • Question: Is there a relationship in the population? • Question is different here than the first procedure. Asking whether it exists. • Does what we found in the sample exist in the population? • Answer to this question: statistical significance of the relationship WHAT IS STATISTICAL SIGNIFICANCE? Linneman: chi-squared used as statistical test. See Kranzler: 108-109 The Logic of Hypothesis Testing 2 THEORIES: 1. Two groups are different OR 2. Two variables are related → Either of those two theories can lead us to research hypothesis. Research hypothesis. With statistics, you can’t show something is true • It is easier to disprove a statement; show that something is false. SO: • We create an opposite hypothesis since we cannot prove anything. We can only disprove something. • And we try to disprove that! • NULL HYPOTHESIS NOTE: If we keep doing research attempting to disprove the null hypothesis, it gives us a little more confidence that our research hypothesis is right. KNOW ABOUT IT BUT SET IT ASIDE; NOT ON THE TEST! 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. That’s just a sampling error. If we can disprove the null hypothesis, they we have support for our research hypothesis. Type I Error • We find in our sample that X  Y • Could the sample relationship occur just because it’s a non-representative sample? • Ex: female students are more likely to have jobs than male students. Could it be just a sampling error? We conclude there’s a relationship in the population when there really isn’t. TYPE 1 ERROR → Sample is misleading us. → We are saying something is happening in the population when in fact it doesn’t. → It is almost always the MOST IMPORTANT! HOW DO WE DO IT? • We estimate the probability of making a type 1 error If this probability is LOW, • We say the relationship has statistical significance because probability of type 1 error is low. Hence, it exists in the population. In most research, we want to minimize type I error. Type II Error • Concluding no relationship in the population when there really is one. It is the opposite of type 1 error. • Normally this is less important. • The cost of missing a relationship is less than the cost of drawing a relationship when really there isn’t one. INTERESTING FACT: the smaller the chance of a type I error, the larger the chance of a type II error → You run the risk of missing something important if you consider type 1 error than type 2 error. Find balancing act between the two. STATISTICAL SIGNIFICANCE FROM CHI-SQUARE CHI-SQUARED TEST! What is Chi-Square? 1. Chi-square is a statistic • Calculated from your sample • Remember: anything you calculate from your sample is a STATISTIC. (Ex: mean, hours you study, etc) 2. Chi-square is calculated from crosstabs • The chi-square statistic compares the expected frequencies with the observed frequencies. • Comes up with a chi-squared number that tells us how similar they are. • The less similar they are the bigger the value of the chi-squared. The bigger the chi-squared the less similarity between the expected frequencies and observed frequencies. 3. We know the shape of the sampling distribution for chi-square • Not symmetrical; CHI-SQUARED CURVE! • Changes with the size of the crosstab • Number of rows and columns gives you the size of the crosstab
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