[...]... underlying population or process 18  introduction to statistics for bioMEDical engineers Histogram of 50 Dice Tosses Relative Frequency 0.2 0.1 0.0 1 2 3 4 5 6 Value of Dice Toss Histogram of 2000 Dice Tosses Relative Frequency 0.2 0.1 0.0 1 2 3 4 5 6 Value of Dice Toss FIGURE 3.8: Histograms representing the outcomes of experiments in which a single dice is tossed 50 (top) and 2000 times (lower), respectively... data in graphical or numerical form The numerical form is what we refer to as statistics Before blindly applying the statistical analysis, it is always good to look at the raw data, usually in a graphical form, and then use graphical methods to summarize the data in an easy to interpret format The types of graphical displays that are most frequently used by biomedical engineers include the following:... Temperature (F) FIGURE 3.9: Histogram for 2000 internal body temperatures collected from a normally distributed population 20  introduction to statistics for bioMEDical engineers Once the researcher has estimated the sample statistics from the sample population, he or she will try to draw conclusions about the larger (true) population The most important question to ask when reviewing the statistics and conclusions... mean” and the formula for estimating s2 from a collection of samples, xi, is s2 = 1 n ∑ ( xi − x ) 2 n − 1 i −1 24  introduction to statistics for bioMEDical engineers Sample standard deviation, s, which is more commonly referred to in describing the variability of the data is s = s 2 (same units as original samples) It is important to note that for normal distributions (symmetrical histograms), sample... we need to assume some probability model for the populations from which the samples have been collected Once we have assumed an underlying model, we can select the appropriate statistical tests for comparing two or more populations and then use these tests to draw conclusions about FIGURE 1.2: Steps in statistical analysis   introduction to statistics for bioMEDical engineers our hypotheses for which... describing a histogram are the absolute frequency and relative frequency in one or more bins These quantities are defined as a) fi = absolute frequency in ith bin; b) fi  /n = relative frequency in ith bin, where n is the total number of samples being summarized in the histogram 14  introduction to statistics for bioMEDical engineers Lower Bound Midpoint Upper Bound FIGURE 3.4: One bin of a histogram plot... probability distribution or probability model to describe the real-world phenomenon If we return to the example of the toss of a dice, we can actually toss the dice a number of times and see how close the histogram, obtained from experimental data, matches 16  introduction to statistics for bioMEDical engineers Symmetric Frequency 200 100 0 -4 -3 -2 -1 0 1 2 3 Measure Skewed 400 Frequency 300 200 100... this book, is the most critical step to support the statistical analysis that will lead to meaningful conclusions and hence sound decisions One of the most fundamental questions asked by biomedical researchers is, “What size sample do I need?” or “How many subjects will I need to make decisions with any level of confidence?”   introduction to statistics for bioMEDical engineers We will address these important... natural and normal characteristic of the natural world 3 We like to make decisions with some confidence This means that we need to find trends within the variability 10  introduction to statistics for bioMEDical engineers 3.3 WHAT QUESTIONS DO WE HOPE TO ADDRESS WITH OUR STATISTICAL ANALYSIS? There are several basic questions we hope to address when using numerical and graphical summary of data: 1...  introduction to statistics for bioMEDical engineers assigned a probability to those arrival times, we would have a probability model for the heartbeat intervals If we can find a probability model to describe the likelihood of occurrence of a certain event or experimental outcome, we can use statistical methods to make decisions The probability models describe . Achorn International Introduction to Statistics for Biomedical Engineers Kristina M. Ropella Department of Biomedical Engineering Marquette University SYNTHESIS LECTURES ON BIOMEDICAL ENGINEERING. alive for them. I also thank J. Claypool for his patience and for encouraging me to finally put this text together. Finally, I thank my family for tolerating my time at home on the laptop. MC:. probability to the likelihood that the next heartbeat will arrive in a specified time interval. If we were to consider all possible arrival times and Introduction 2 INTRODUCTION TO STATISTICS FOR BIOMEDICAL