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AMS 7 – BIOSTATISTICS PDF

382 Pages·2009·5.65 MB·English
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AMS 7 – B IOSTATISTICS 1 Abel Rodriguez Spring 2009 W ? HAT IS STATISTICS A collection of methods for planning experiments, obtaining data and then organizing, summarizing, analyzing, interpreting, presenting and drawing conclusions based on data. The word statistics comes from status (meaning “state”). Early uses involved compilations of data (numbers) describing various aspects of a state or country. 2 L EARNING FROM DATA Steps in learning from data: Designing the data collection process (study   design / experimental design). Preparing and analyzing the data (descriptive   statistics, models). Reporting conclusions.   3 S E N TUDY OF THE FFECTS OF ITROGEN F ERTILIZER IN WHEAT PRODUCTION Setting: 15 fields and 5 nitrogen rates. Three   fields were randomly assigned to each of the nitrogen rates. The same variety of wheat was planted in all fields and they were cultivated in the same manner. The number of pounds of wheat per acre was recorded. Goal: to determine the amount of nitrogen that   yielded the largest production of wheat, the experimenter concluded that similar results would hold for fields with the same characteristics as the ones in the study. Is this conclusion justified? 4 P S OPULATION AND AMPLE In this case it is important to measure soil   characteristics of the fields and environmental conditions to obtain results that can be generalized to fields not included in the study  the design of the experiment is crucial. A population is the set of all elements of interest   to the sample collector. A sample is any subset of elements selected from   the population. 5 P S OPULATION AND AMPLE We typically refer to the values of the variables   on the N individuals of the population as X , …, 1 X . Sometimes N can be infinite. N We typically refer to the observations as in a   sample of size n as x , …, x 1 n 6 P S OPULATION AND AMPLE The descriptive characteristics of a population   can be summarized by some population parameters. These are measures that are typical of each population. Usual examples are the central tendency of the population or its dispersion. Parameters are usually unknown quantities. Parameters are estimated using values from a   sample. Sample values are used to obtain a statistic. Actually, any function of a sample is called a statistic. The observed value of a statistic depends on how the sample is obtained, thus statistics are random variables. 7 D T ATA YPES Quantitative data consists of numbers   representing counts or measurements. Discrete data: the number of possible values is either   a finite number or a countable number. Continuous data: are the result from infinitely many   possible values not restricted to certain specified values (such as integers). 8 D T ATA YPES Qualitative data, also called categorical or   attribute data. These can be separated into different categories that are distinguished by some non-numeric characteristics. Nominal data consist of names, labels or categories   only. There is no natural ordering to this categories. Ordinal data can be arranged in some order but   differences between data values either cannot be determined or are meaningless. 9 E XAMPLES This scale is used to classify the performance status of patients in a clinical trial. Description 0 Fully active, able to carry on all pre-disease performance without restriction. 1 Restricted in physically strenuous activity but ambulatory and able to carry out work of a light or sedentary nature. 2 Ambulatory and capable of all self-care but unable to carry out any work activities; up and about more than 50% of waking hours. 3 Capable of only limited self-care; confined to bed or chair more than 50% of waking hours. 5 Completely disabled; not capable of any self-care; totally confined to bed or chair. Note that differences in magnitude are 10 meaningless this is an example of ordinal data.

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AMS 7 – BIOSTATISTICS The word statistics comes from status (meaning “ state”). Early uses involved generalized to fields not included in the study →.
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