By Kristina Ropella

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Extra resources for Introduction to Statistics for Biomedical Engineers

Example text

59. 861). 005) × 100% confidence and state that mean heart rate for fibrillatory rhythms is greater than mean heart rate for normal rhythms. Thus, the rate algorithm should perform fairly well in differentiating normal from fibrillatory rhythms. However, we have only tested the population means. 3, there is some overlap in individual samples between normal and fibrillatory rhythms. Thus, we might expect the device to make errors in administering shock inappropriately when the heart is in normal but accelerated rhythms (as in exercise), or the device may fail to shock when the heart is fibrillating but at a slow rate or with low amplitude.

3. It is important to remember these few numbers, because we will frequently use this 95% interval when drawing conclusions from our statistical analysis. Another means for determining how well our sampled data, x, represent a normal distribution is the estimate Pearson’s coefficient of skew (PCS) [5]. The coefficient of skew is given by PCS = 3 x − xmedian . 5, we assume that our samples were not drawn from a normally distributed population. ). For us to use tables that have been developed for probability models, we need to normalize the data so that the normalized data will have a mean of 0 and a standard deviation of 1.

In such cases, we replace s with s to get the following expression:   Pr( a ≤ x ≤ b ) = Pr a−µ b − µ ≤z≤ , s/ n s / n where s n is called the sample standard error and represents the standard deviation for x−. Let us assume now for large n, we want to estimate the 95% confidence interval for x−. We first scale the sample mean, x−, to a z value (because the central limit theorem says that x− is normally distributed) z= x −µ . 95. Substituting for z, z= x −µ . 96 .  s/ n If we use the following notation in terms of the sample standard error: SE( x ) = s .