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Class notes Biostatistic in Public Health BSPH 209 $10.39   Add to cart

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Class notes Biostatistic in Public Health BSPH 209

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This detailed classnote is an essential resource for students enrolled in a public health degree program, focusing on biostatistics. It covers fundamental and advanced concepts in statistical methods, including probability theory, hypothesis testing, regression analysis, and more. Whether you're pr...

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  • August 27, 2024
  • 50
  • 2023/2024
  • Class notes
  • Mr. moses wollo
  • All classes
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Learning Objectives

► Upon completion of this lecture section, you will be able to:
► Summarize a binary outcome across a group of individual observations via the sample
proportion
► Explain why, with binary data, the sample proportion is the only summary statistic
(besides sample size n) necessary to describe characteristics of the sample
► Compute the sample proportion based on the results of a study




3

, Example: Treatment Response to ART, HIV+ Individuals—1

► Response to therapy in a random sample of 1,000 HIV-positive patients from a citywide
clinical population

► 206 of the 1,000 patients responded. The summary measure used for binary outcomes is
the sample proportion 𝑝𝑝̂ (pronounced p-hat!), given by

# 𝑜𝑜𝑜𝑜 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 206
𝑝𝑝̂ = = = 0.206 𝑜𝑜𝑜𝑜 20.6%
𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 # 𝑖𝑖𝑖𝑖 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 1,000

► Why the hat? To distinguish 𝑝𝑝,̂ the sample estimate, from the underlying true (population)
proportion p (which can only be estimated)


Source: http://inclass.kaggle.com/ 4

,p-hat, Generally Speaking

► Response to therapy in a random sample of 1,000 HIV-positive patients from a citywide
clinical population

► The sample proportion 𝑝𝑝� is just a sample mean of data that takes on two values, 0 and 1

► Generally, binary data values are given a value of x=1 for observations that have the
outcome, and x=0 for observations that do not have the outcome




5

, Example: Treatment Response to ART, HIV+ Individuals—2

► Response to therapy in a random sample of 1,000 HIV-positive patients from a citywide
clinical population

► So, with 206 of the 1,000 responding, we have xi=1 for 206 observations, and xi=0 for 794
observations

∑𝑛𝑛𝑖𝑖=1 𝑥𝑥𝑖𝑖 ∑1000
𝑖𝑖=1 𝑥𝑥𝑖𝑖 206
𝑝𝑝̂ = = = = 0.206 𝑜𝑜𝑜𝑜 20.6%
𝑛𝑛 1,000 1,000




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