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Course: ENGR 691, Fall 2009
School: Wisconsin
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Word Count: 991

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Statistical Advanced Applications in Continuous Quality Improvement Types of Distributions Discrete Applied to variables with specific outcomes (heads or tails, success or failures, conforming or non-conforming) # of C-Sections Episodes of otitis media Continuous Represent populations that can have infinitely many values usually within a finite range Differentiation between Discrete and Continuous...

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Statistical Advanced Applications in Continuous Quality Improvement Types of Distributions Discrete Applied to variables with specific outcomes (heads or tails, success or failures, conforming or non-conforming) # of C-Sections Episodes of otitis media Continuous Represent populations that can have infinitely many values usually within a finite range Differentiation between Discrete and Continuous Variables Discrete Variable Characteristics Fixed Numeric Values Continuous Variable Infinite Number of Values within an interval Measurement usually an estimate of the true value depending on the measurement toool Body Weight Systolic Blood Pressure Duration of Treatment No intermediate values between fixed values Examples Number of Extremities Episodes of Diabetic Ketoacidosis Number of People with Hypertension Discrete Distributions Binomial Poisson Hypergeometric Binomial Distributions Binomial applies to situations with just two possible outcomes (success or failure) Usually used with small sample sizes Comprised of a limited number of independent experiments (n) Probability of success is the same for each experiment Outcome of one experiment does not influence the other Binomial Distributions Parameters are represented by and n Where is the proportion of successes Where N is the size of the sample Mean of the sample is N* Standard Deviation is 2 = N*(1 - ) When N* ge 5 and N (1 - ) ge 5 the binomial distribution approximates the normal distribution. Poisson Distribution Poisson primarily directed at populations with rare events Used as basis for control charts that deal with nonconformities Basic assumptions Non-conformities should be independent and random Potential number of non-conformities must be quite large (infinite) and the actual number quite small Usually reserved for situations where the nonconformity rate is very small In healthcare, the basic assumptions cannot always be strictly satisfied since decisions are often influenced by factors other than random chance Hypergeometric Distribution Hypergeometric assumes that the sample for measurement is taken from the population without replacement MCO knows rate of fraud is .014 in network of 1,000 providers Use this distribution to determine the probability that a random sample of 50 providers includes at least one fraudulent provider If removed, the sampling operation would influence the number and frequency of fraudulent providers left in the network Application of the hypergeometric distribution in QI occurs when sampling the population can alter the rate of a nonconformity Continuous Distributions Normal or Gaussian T-Distribution Chi-Square Distribution F-Distribution Normal Distribution F(y) = [1/ sqrt(2)]e-[(y)/ ]2 Where is standard deviation of the population Where is the mean of the population Where e is natural log base (2.71828...) Where is the geographic constant (3.14159...) Limits are - and + Normal Distribution (cont) Specific distribution is the standard normal distribution as shown by Z = (X )/ Data characteristics for normal distribution analysis are: Population must be randomly distributed Variables can assume any infinite number of values along the continuum Mean and Standard Deviation can be calculated or measured Normal distributions underlie nearly every commonly used control chart T-Distribution Often called the Student's T- distribution Developed by W.S. Gosset Formula given is as T = (X )/(s/(n) ) Where X is mean of sample Where is mean of population Where s is standard deviation of sample Where n is the sample size T-Distribution (cont) Sample Size defines degrees of freedom (n1) T-Distribution well approximates the normal distribution as n becomes large Specifically designed when the population standard deviation is unknown using the following formula T = ( )/s T-Distribution (cont) Sample Size defines degrees of freedom (n1) T-Distribution well approximates the normal distribution as n becomes large Primary application of the T-distribution in QI is in the performance of hypothesis testing and designing experiments to compare means from different population samples. T-Distribution (cont) Steps in Hypothesis Testing. Establish the hypothesis H0 vs. H1 Perform the experiment to demonstrate the null hypothesis is incorrect P- Value which is the probability that the difference between two means will be as large or larger than observed. Two Tailed P Indicates the probability that the actual difference in the means is as large or larger with either group having the larger mean. One Tailed P Indicates the same probability but only one group has the larger mean Chi-Squared The X2 distribution probability density function assumes only values between 0 and Infinity and the # of degrees of freedom shapes the curve. Advantage lies in the ability to measure the strength of relationship dependent on the size of the sample F-Distribution Compares two sample variances from a given population to determine if the variances are equal. The F-ratio is 1 if the variances are equal Most commonly used in ANOVA to evaluate the equality of sample means P-value Probability that the results of the analysis match the assumption of the null hypothesis. Statistical Inference Large sample sizes means that we can safely assume the presence of a normal distribution. Sample size to make the inference can vary A X2 distribution may mean a sample size of 15 to 20 is sufficient When radically different from a normal dis...

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Wisconsin - ENGR - 691
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** ** Formatted Listing of Model: ** C:\Documents and Settings\default\Desktop\assignment04solution.mod **
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