![]() The standard normal distribution is symmetric around zero: one half of the total area under the curve is on either side of zero. ![]() The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. (i.e., the median and the mean are the same). The normal distribution is symmetric about μ. The area under the curve is interpreted as probability, with the total area = 1. ![]() 68% of the distribution lies within 1 standard deviation of the mean 95% lies within two standard deviation of the mean and 99.9% lies within 3 standard deviations of the mean. The degree to which population data values deviate from the mean is given by the standard deviation, σ. The normal distribution is centered at the mean, μ. What is the consequence in this case? Standard Normal DistributionĬharacteristics of the standard normal distribution Type II error-occurs if Drug B is truly more effective, but we fail to reject the null hypothesis and conclude there is no significant evidence that the two drugs vary in effectiveness. Type I error-occurs if the two drugs are truly equally effective, but we conclude that Drug B is better. Efficacy is measured using a continuous variable, Y, and. Two drugs are to be compared in a clinical trial for use in treatment of disease X. ![]() However, in practice we fix α and choose a sample size n large enough to keep β small (that is, keep power large). Ideally, both error types (α and β) are small. ![]()
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