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Confidence Intervals

Confidence Intervals. Terminology Confidence Interval Confidence level (relation to alpha) We can be X% sure that in the population… Procedure How many SE to go out? (1.96, 2.58) based on CL Formula to get value of a standard error for your data (e.g., what is the SE “worth”)

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Confidence Intervals

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  1. Confidence Intervals • Terminology • Confidence Interval • Confidence level (relation to alpha) • We can be X% sure that in the population… • Procedure • How many SE to go out? (1.96, 2.58) based on CL • Formula to get value of a standard error for your data (e.g., what is the SE “worth”) • Means, Proportion  Know Formulas

  2. Significance Testing • Anything found in sample could be due to sampling error (chance) • What are the odds that what we found is due to sampling error • Start by assuming null is true • What are the odds of getting what I found? • If weird enough, it make sense at some point to go ahead and reject the null

  3. Significance Testing 2 • Test statistic (t, F, chi-square) • Sampling distribution for the test statistic • What would happen if we did an infinite number of samples where the null was true. • Known odds for any value of the test statistic • Calculate single test statistic from a sample • If null were true, what are the odds of finding this value? • Small enough = question assumption that null is true

  4. Stating Findings • What do “test statistics” measure? • Some test statistics generate useful information • t • F • Most are simply a way to get the “sig” or “probability” values. • What is the “probability” associated with the test statistic? • What is the relationship between these two things?

  5. What to do with null hypothesis • Obtained test statistic greater than “critical” value of test statistic • What is a “critical value?” • Obtained “sig value” or “probability” less than stated alpha • Why? • Assuming the null is true, the particular finding (mean difference, F value, etc) would be really rare. So rare in fact, (less than 1% or 5% chance) that it makes more sense to reject the null hypothesis.

  6. KEEP IN MIND PROPER df • t • Univariate = N-1 • χ2 • (r-1)(c-1) • I will provide chart for finding critical values

  7. What things influence… The size of a confidence interval? The size of a test statistic (and therefore the likelihood of rejecting the null)?

  8. Other Concepts • Directional vs. Non  1 or 2 tailed tests • Why might want 2-tailed even if hypothesis is directional? • F-test (conceptual) • Within variance (unexplained) • Between variance (explained) • Variation (SS) vs. variance • What the F-ration tells you

  9. Practice with CI • 200 UMD students out of a random sample of 500 UMD students agree that professor Maahs has a bad haircut • Calculate a confidence interval if alpha = .01 and report results in a sentence. Is it likely that a majority of UMD students think Maahs has a bad haircut? • A random sample of 500 inmates in MN prisons reveals that they have an average of 4.5 prior convictions (s = 1.5). • Calculate a confidence interval if alpha = .05 and report results in a sentence.

  10. Be able to tell what test to use based on variables Sex predicts criminal behavior (number of arrests) Grade (pass/fail) is related to attendance (number of days missed) Area of the country (West, South, Midwest, East) predicts income ($/year) Type of job (menial, blue collar, white collar) is related to whether or not a person becomes homeless

  11. Practice with single sample t • Professor Jack believes that Wisconsinites are smarter than the average American. • The national IQ average is 100. Professor Jack finds an average IQ of 105 (s = 9) in his random sample of 17 Wisconsin residents. • Is this a significant difference for alpha = .01? • T(obtained) • T (critical) • Decision about null • Specific information given by t(obtained)?

  12. Contingency Table • Using a random sample of 300 students, professor Pompous asks people whether or not they would take a lead pipe to the head rather than go to statistics class. • Of the 150 males, 85 report they would rather get lead piped. Out of the 150 females 60 report that they would rather get lead piped. • Create a contingency table, putting IV/DV in right spots, and calculate percent. Is there a relationship in the data? • Calculate whether any relationship is significant, with alpha = .05

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