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33831 - Statistical Inference Dr Mona Hassan Ahmed Prof of...

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Unformatted text preview: Statistical Inference Dr. Mona Hassan Ahmed Prof. of Biostatistics HIPH, Alexandria University Lesson Objectives Know what is Inference Know what is parameter estimation Understand hypothesis testing & the “types of errors” in decision making. Know what the α-level means. Learn how to use test statistics to examine hypothesis about population mean, proportion Inference Use a random sample to learn something about a larger population Inference ◆ Two ways to make inference Estimation of parameters * Point Estimation ( f8e5 X or p) * Intervals Estimation Hypothesis Testing Parameter Parameter Statistic Statistic Mean: Standard deviation: Proportion: s X _μ___ _σ___ _π___ estimates estimates estimates from sample from entire population p Mean, μ , is unknown Population Point estimate I am 95% confident that μ is between 40 & 60 Mean f8e5 X = 50 Sample Interval estimate Parameter = Statistic ± Its Error Sampling Distribution f8e5 X or P f8e5 X or P f8e5 X or P Standard Error SE (Mean) = S n SE (p) = p(1-p) n Quantitative Variable Qualitative Variable 95% Samples Confidence Interval X _ f8e5 X- 1.96 SE f8e5 X + 1.96 SE μ SE SE Z-axis 1 - α α/2 α/2 95% Samples Confidence Interval SE SE π p p + 1.96 SE p - 1.96 SE Z-axis 1 - α α/2 α/2 Interpretation of CI Probabilistic Practical We are 100(1- α )% confident that the s ingle computed CI contains μ In repeated s ampling 100(1- α )% of all intervals around s ample means will in the long run include μ Example (Sample size≥30) An epidemiologist studied the blood glucose level of a random sample of 100 patients. The mean was 170, with a SD of 10....
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33831 - Statistical Inference Dr Mona Hassan Ahmed Prof of...

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