# Confidence Intervals Terminology Confidence Interval Confidence level relation

- Slides: 12

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

Significance Testing Anything found in sample could be due to sampling error (chance) • What are the odds that 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

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

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?

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.

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

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

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

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.

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

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)?

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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