Topic_7.1___Statistical_Inference___Significance_Tests___Examples

# Topic_7.1___Statistical_Inference___Significance_Tests___Examples

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Significance Tests for Single Samples – Examples Ash Genaidy

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Case study — example 1 Is the average back pain at baseline significantly lower from 10 (worst imaginable pain)? Assume type I error =0.05 Mean =7.83; sd =1.8; N=35 H 0 : μ =10 H a : μ <10 P-Value corresponding to Z=0.0000 <<0.05 Conclusion: Reject the null hypothesis and conclude that the mean of lower back pain at base line is significantly lower than 10 09 . 7 306 . 0 17 . 2 35 81 . 1 83 . 7 10 0 = = - = - = se Y Z μ
Case Study – example 2 Is the average back pain at 3 months after surgery significantly lower/differently than 7.83? Assume type I error =0.05 H 0 : μ =7.83 H a : μ <7.83 P-value corresponding to Z=0.0000<<0.05 Conclusion: Reject the null hypothesis and conclude that the mean of lower back pain is significantly less than 7.83 18 . 8 441 . 0 61 . 3 35 61 . 2 22 . 4 83 . 7 0 = = - = - = se Y Z μ

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Case Study – example 2 H 0 : μ =7.83 H a : μ 7.83 P-value corresponding to Z=0.0000<<0.025 Same Conclusion 18 . 8 441 . 0 61 . 3 35 61 . 2 22 . 4 83 . 7 0 = = - = - = se Y Z μ
Case study – example 3 Is the proportion of smokers significantly different from 0.5? , type I error =0.05 sd = se = 457 . 0 ˆ = π 497 . 0 543 . 0 457 . 0 ) ˆ 1 ( ˆ = × = - π π 084 . 0 35 / 497 . 0 = = n sd

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Example 3 Test statistic: P-value corresponding to Z-value =0.305>>0.025 Conclusion: Accept the null hypothesis and conclude that it is not significantly different from 0.50. 512 . 0 084 . 0 457 . 0 5 . 0 ˆ ˆ 0 = - = - = se z π π
Use of CI as an Alternative to Significance Test Is the average back pain at baseline significantly different from 10 (worst imaginable pain)? Assume type I error =0.05 Mean =7.83; sd =1.81; n =35; CI: 10 is outside the interval; Conclusion: The average back pain at the baseline is significantly different from 10 ) 43 . 8 , 23 . 7 ( 5997 . 0 83 . 7 35 81 . 1 96 . 1 83 . 7 = ± = × ±

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Use of CI as an Alternative to Significance Test Is the average back pain at baseline is significantly lower than 10? Conclusion: The mean back pain at baseline is significantly lower than 10. 33 . 8 503 . 0 83 . 7 35 81 . 1 645 . 1 83 . 7 = + = × +
Use of CI as an Alternative to Significance Test Is the proportion of smokers significantly different from 0.5? , type I error =0.05 sd = se = CI: 0.457 ± 1.96 × 0.084 =0.457 ± 0.1646 =(0.29, 0.62) Conclusion: The confidence interval does include 0.5. Conclude that the proportion of smokers is not significantly different from 0.5.

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