Ch7

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Unformatted text preview: erent treatment conditions Sometimes also called related samples or repeated measures t test K310 Statistical Techniques Inference for Distributions 10 / 26 Matched pairs example Research question: Does the moon influence the behavior of dementia patients? Moon days: Average number of disruptions per day for three days surrounding a full moon Other days: Average number of disruptions per day on other days Patient 1 2 3 4 5 6 7 8 Moon days 3.33 3.67 2.67 3.33 3.33 3.67 4.67 2.67 Other days 0.27 0.59 0.32 0.19 1.26 0.11 0.30 0.40 K310 Statistical Techniques Difference Patient 3.06 3.08 2.35 3.14 2.07 3.56 4.37 2.27 9 10 11 12 13 14 15 Moon days 6.00 4.33 3.33 0.67 1.33 0.33 2.00 Other days 1.59 0.60 0.65 0.69 1.26 0.23 0.38 Inference for Distributions Difference 4.41 3.73 2.68 −0.02 0.07 0.10 1.62 11 / 26 Matched pairs example (cont’d) 1 Hypotheses: K310 Statistical Techniques Inference for Distributions 12 / 26 Matched pairs example (cont’d) 2 H0 : µ = 0 Ha : µ = 0 Sample information: x = 2.433, s = 1.460 ¯ 3 P -value: 4 Conclusion for α = 0.001: 1 Hypotheses: K310 Statistical Techniques Inference for Distributions 12 / 26 Comparing two means Use two-sample t procedures when: The goal of inference is to compare the responses in two groups Each group is considered to be a sample from a distinct population The responses in each group are independent of those in the other group K310 Statistical Techniques Inference for Distributions 13 / 26 Notation for hypothesis testing Q: Is there a difference between the two populations’ means? Notation: Population 1 2 Hypotheses: Variable x1 x2 Mean µ1 µ2 Standard deviation σ1 σ2 H0 : µ1 = µ2 =⇒ µ1 − µ2 = 0 Ha : µ1 = µ2 =⇒ µ1 − µ2 = 0 Population 1 2 Sample size n1 n2 K310 Statistical Techniques Sample mean x1 ¯ x2 ¯ Sample standard deviation s1 s2 Inference for Distributions 14 / 26 Two-sample t procedure Suppose we don’t know the populations’ standard deviations σ1 and σ2 . K310 Statistical Techniques Inference for Distribu...
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This note was uploaded on 04/16/2013 for the course MATH-M 310 taught by Professor Palanivelmanoharan during the Spring '13 term at Indiana.

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