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Published byGraham Alman Modified over 3 years ago

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Difference in Proportions

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We’re trying out 4 different sugar cookie products. The following intervals are the result of a 95% confidence interval of likeability. Do the intervals provide convincing evidence? Product A: 0.05 to 3.1 Product B: 0 to 4.2 Product C: -0.01 to 0.02 Product D: -2.3 to -2.0 Ye s No

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H 0 : Hamilton has the same ABILITY to get a hit at home and on the road in the 2010 regular season. H a : Hamilton has a greater ABILITY to get at home than on the road in the 2010 regular season. Test statistic = BA home - BA away = 103/264 – 83/254 = 0.390 – 0.327 = 0.063 Hamilton’s batting average is estimated to be 0.063 greater at home than on the road.

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Simulation gives a p-value of 0.15 There is a 15% chance that Hamilton’s difference in BA will be at least 0.063 by RANDOM CHANCE. We do not have convincing evidence that Hamilton’s ABILITY to get a hit at home was better than on the road.

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Hypothesis Test OR Confidence Interval

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Confidence Interval = center ± margin of error Where P = PERFORMANCE n = # of attempts

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Remember, BA home = 103/264=0.390 & BA away =83/254=0.327 Confidence Interval Margin of Error Standard Deviation

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We are 95% confident the interval of plausible values from -0.021 to 0.147 includes the difference in Hamilton’s ABILITY to get a hit at home and on the road.

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positive possibilities, then the athlete's ABILITY is better in context 1 than context 2. a a 0, then the athlete's ABILITY is the same in both contexts. negative possibilities, then the athlete's ABILITY is worse in context 1 than context 2.

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(Hamilton’s difference in BA interval is from -0.021 to 0.147 ) We do not have convincing evidence that Hamilton’s ABILITY to get a hit at home was better than getting a hit on the road.

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If we want to estimate the difference in an athlete's ABILITY in two contexts, we can calculate a confidence interval for a difference in proportions (if the data are categorical). We can decrease the margin of error in a CI by: increasing the sample size decreasing the number of standard deviations (AKA the multiplier)

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