THE estimate for the mean age WAS 28.55549 WITH STANDARD ERROR 1.281085
the estimate for the mean age is 30.76648 WITH STANDARD ERROR 1.787193
the estimate for the mean age is 29.01362 years WITH STANDARD ERROR 0.3770333
DONE TO CHECK IF THE ANOVA WAS NOT DECEIVING US
After you have plotted data for Normality Test, Check for P-value.P-value < 0.05 = not normal. normal = P-value >= 0.05. Comment:since the p-value was <0.001 the age distribution was not normally distributed but skewed.(P-value=0.65>0.05)
8.84% of the cases handled by the theatre were children below 16 years with typhoid fever; this was relatively high.
If any of the predictor variables is zero then the product is zero; number of patients becomes negative. Since, there exists no negative number of patients it implies the number of patients is zero. Therefore, most patients that visit the hospital and are admitted in the pediatric ward are very likely to be females aged below six years from the zongo community. All the three predictor variables have a positive influence in the number of patients admitted with typhoid in the pediatric ward as observed from the correlation analysis.
Transcript
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The Beauty of Mathematics 1 x 9 + 2 = 1112 x 9 + 3 = 111123 x 9 + 4 = 11111 234 x 9 + 5 = 1111112345 x 9 + 6 = 111111123456 x 9 + 7 = 11111111234567 x 9 + 8 = 1111111112345678 x 9 + 9 = 111111111123456789 x 9 +10= 1111111111 1 x 8 + 1 = 912 x 8 + 2 = 98123 x 8 + 3 = 9871234 x 8 + 4 = 987612345 x 8 + 5 = 98765123456 x 8 + 6 = 9876541234567 x 8 + 7 = 987654312345678 x 8 + 8 = 98765432123456789 x 8 + 9 = 987654321 9 x 9 + 7 = 8898 x 9 + 6 = 888987 x 9 + 5 = 88889876 x 9 + 4 = 8888898765 x 9 + 3 = 888888987654 x 9 + 2 = 88888889876543 x 9 + 1 = 8888888898765432 x 9 + 0 = 888888888
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And look at this symmetry: 1 x 1 = 111 x 11 = 121111 x 111 = 123211111 x 1111 = 123432111111 x 11111 = 123454321111111 x 111111 = 1234565432111111 11 x 1111111 = 123456765432111111111 x 11111111 = 123456787654321111111111 x 111111111=12345678987654321
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PROJECT TITLE Estimation Of The Age Distribution Of Patients Operated And Effect Of Salmonella Typhi On The Incidence Of Typhoid Complications At The Main Surgical Theatre Supervisor Mr. S. K. Appiah
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THEIR VISION To become a medical centre of excellence offering Clinical and Non-Clinical services of the highest quality standards comparable to any international standards within 5 years (2003-2008)
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THEIR MISSION “to provide quality services to meet the needs and expectations of all clients. This will be achieved through well-motivated and committed staff applying best practices and innovation”.
Sampling theory is a study of relationships existing between a population and samples drawn from the population.
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Why sampling over complete enumeration:-saves time, reduce cost ,saves labour
6/9/2008 33 Sampling Distribution:-
It is when samples of size N is been drawn from a given populationWhy Use Stratification:-Different classes of surgeryDifferent age groupsDifferent sexesThe Principle Objective Of Stratification:-stratification divides the population into a relative more homogenous age distribution groups with regard to average age sent to the surgical ward for treatment.
STATISTICAL HYPOTHESIS 6/9/2008 34
It is a statementabout the parameters of the model
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Used to test the claim about the average age obtained in stratification and the average age obtained by the random sample generated by minitab
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P-value as the smallest level at which the data is significant.
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State if the null hypothesis was or was not rejected at a specified α -value or level of significance
CONFIDENCE INTERVAL 6/9/2008 36
Although hypothesis testing is a useful procedure, it sometimes does not tell the entire story. It is often preferable to provide an interval within which the value of the parameter would be expected to lie.
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In many engineering and industrial experiments, the experimenter already knows that the means µ1differ µ2, consequently, the hypothesis testing on is of little interest.
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The experimenter would usually be more interested in a confidence interval on the difference in means . The interval
is called a percent confidence interval for the parameter.
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CORRELATION ANALYSIS 6/9/2008 37 CONCERNED WITH THE STRENGTH OF ASSOCIATION BETWEEN THE VARIABLE OF INTEREST AND THE OTHERS An error term which caters for the errors due to chance and neglected factors which we assume are not important
Scatter diagram 6/9/2008 39 The scatter diagram is a useful tool in examining relationships; especially between two variables. A plot of the sample data on a graph gives a visual indication of the degree of association between two variables say x and y.
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TYPES OF REGRESSION MODEL 6/9/2008 40 Regression models are classified according to the number of predicted variables and also the form of the regression function.
Simple Linear Regression Model 6/9/2008 41 Definition and features of model The simple linear regression model is given by Y = β0 + β1 x + ε x - is the value of the response variable in the observation is the known value of the predictor variables in the ith observation ε - is the random error term which caters for the errors due to chance are neglected factors which we assumed not important. are the parameters of the model β0 - gives the intercept on y axis β1 - measures the slope of the linear model
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ESTIMATION OF LINEAR REGRESSION MODEL 6/9/2008 42
The linear regression model is estimated by fitting a best prediction line through the scatter diagram. This can be done by estimating the parameters of the model.
6/9/2008 43 METHOD OF LEAST SQUARES This method finds the estimates respectively by minimizing the total sum of squares error( SSE ).
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ANALYSIS OF VARIANCE IN REGRESSION MODEL 6/9/2008 44 The application of analysis of variance (ANOVA) in regression analysis is based on the partitioning of the total variation and its degree of freedom into components.
The three quantities SSyy, SSE and SSR are measures of dispersion.
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The total sum of squares of deviation (SSyy, ) is a measure of dispersion of the total variation in the observed values, y.
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The explained sum of squares, (SSR ), measures the amount of the total deviation in the observed values of y that is accounted for by the linear relationship between the observed values of x and y. This is also referred to as sum of squares due to the linear regression model.
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The unexplained sum of squares is a measure of dispersion of the observed y values about the regression which is sometimes called the error residual sum of squares (SSE ).
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COEFFICIENT OF DETERMINATION 6/9/2008 46 r2 is called the coefficient of determination which is explained variation expressed as fraction of total variation. It is also defined as a square of the correlation coefficient.
From the general linear regression model for a multiple regression analysis takes the form
6/9/2008 51 Forms of Multiple Linear Regression Models 1. Polynomials regression models:-
They contain one or more predictor variables in various powers.
2. Transformed regression models:- Some non-linear functions may be transformed to linear regression models. 3.Interaction effects regression model:- It is the joint effect of two or more predictor variables(you can use Log etc)
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THE BEAUTY OF MATHEMATICS ANALYSIS OF DATA AND DISCUSSION 6/9/2008 53
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ANALYSIS OF DATA AND DISCUSSION 6/9/2008 54 “An unexamined life is not worth living”, similarly an unexamined organization will not be able to move forward in the right direction At the end of this analysis, we will be able to make well informed decisions as to;
How to raise public awareness on the age group, gender (sex) that should be extremely vigilant, cared, and etc.
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Which class or nature of surgical equipments or devises that should not be limited in number.
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Which complications will need to be attended by the ministry of health.
6/9/2008 55 CLASSIFICATION OF THE VARIOUS COMPLICATIONS REPAIRED
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6/9/2008 71 One-way ANOVA: formulation1 versus factor Analysis of Variance for formulation Source DF SS MS F P factor 4 842 210 0.45 0.771 Error 745 347210 466 Total 749 348051 Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ----------+---------+---------+------ 1 150 27.53 19.68 (-----------*----------) 2 150 28.48 21.37 (-----------*----------) 3 150 28.70 21.90 (-----------*----------) 4 150 29.47 21.47 (----------*-----------) 5 150 30.69 23.36 (----------*-----------) ----------+---------+---------+------ Pooled StDev = 21.59 27.0 30.0 33.0
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6/9/2008 73 Each sample was used for the hypothesis testing of the claim that the mean age was 29 years. One-Sample Z: sample1 Test of mu = 29 vs mu not = 29 The assumed sigma = 21.6 Variable N Mean StDev SE Mean Sample 1 150 27.53 19.68 1.76 Variable 95.0% CI Z P Sample 1 ( 24.07, 30.98) -0.84 0.403 One-Sample Z: sample 2 Test of mu = 29 vs mu not = 29 The assumed sigma = 21.6 Variable N Mean StDev SE Mean Sample 2 150 28.48 21.37 1.76 Variable 95.0% CI Z P Sample 2 ( 25.02, 31.94) -0.29 0.768 One-Sample Z: sample 3 Test of mu = 29 vs mu not = 29 The assumed sigma = 21.6 Variable N Mean StDev SE Mean Sample 3 150 28.70 21.90 1.76 Variable 95.0% CI Z P Sample 3 ( 25.24, 32.16) -0.17 0.865 One-Sample Z: sample 4 Test of mu = 29 vs mu not = 29 The assumed sigma = 21.6 Variable N Mean StDev SE Mean Sample 4 150 29.47 21.47 1.76 Variable 95.0% CI Z P Sample 4 ( 26.01, 32.92) 0.26 0.791 One-Sample Z: sample 5 Test of mu = 29 vs mu not = 29 The assumed sigma = 21.6 Variable N Mean StDev SE Mean Sample 5 150 30.69 23.36 1.76 Variable 95.0% CI Z P Sample 5 ( 27.24, 34.15) 0.96 0.337
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6/9/2008 81 THE PRODUCT TRANSFORMATION Regression Analysis: patients versus zonagefem This modification considers the product of the predictor factors as a single variable. The regression equation is patients = 24.3 + 0.00230 zonagefem Predictor Coef SE Coef T P Constant 24.293 4.256 5.71 0.000 zonagefe 0.0022960 0.0008795 2.61 0.028 S = 9.824 R-Sq = 43.1% R-Sq(adj) = 36.8% Analysis of Variance Source DF SS MS F P Regression 1 657.66 657.66 6.82 0.028 Residual Error 9 868.52 96.50 Total 10 1526.18
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6/9/2008 82 THE SQUARE ROOT TRANSFORMATION Regression Analysis: patients versus sqrt (zonagefem) This modification considers the square root of the product of the predictor factors as a single variable. The regression equation is patients = 14.1 + 0.353 sqrt(zonagefem) Predictor Coef SE Coef T P Constant 14.079 4.162 3.38 0.008 sqrt(zon 0.35299 0.07059 5.00 0.001 S = 6.700 R-Sq = 73.5% R-Sq(adj) = 70.6% Analysis of Variance Source DF SS MS F P Regression 1 1122.2 1122.2 25.00 0.001 Residual Error 9 404.0 44.9 Total 10 1526.2
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6/9/2008 83 THE NATURAL LOG TRANSFORMATION The regression equation is patients = - 18.5 + 6.87 Ln(zonagefem) Predictor Coef SE Coef T P Constant -18.480 5.142 -3.59 0.006 Ln(zonag 6.8658 0.6790 10.11 0.000 S = 3.704 R-Sq = 91.9% R-Sq(adj) = 91.0% Analysis of Variance Source DF SS MS F P Regression 1 1402.7 1402.7 102.24 0.000 Residual Error 9 123.5 13.7 Total 10 1526.2
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6/9/2008 86 The regression equation is patients = - 18.5 + 6.87 Ln(zonagefem) where patients represents the number of patient admitted with typhoid at the Pediatric Unit; zonagefem represents the product of the environment, age below six years and number of females. The Ln is the natural logarithm function.
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The age range which had more surgical complications was 0-9 years.
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The percentage of cases were relatively high for males. It was realized that about that 62.64 of the cases worked on were males. The ratio of males to femaleswas 1.7:1
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The complete data indicates that out of a total of 1831patients 27.1%and 22.17% suffered from hernia and typhoid complications
The investigations proved that out of the 22.17% of the typhoid related complications, 44.58% were children. That implied 9.88% of the total cases were children with typhoid complications.
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It was also observed that 39.9% of the children with typhoid complication were aged below 16years.In other words, approximately 8.84% of the cases handled by the theatre were children below 16 years with typhoid fever.
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The ratio of the male to female was nearly 1:1 respectively
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The known dirty environs (“Zongo”) did not contribute a high percentage in the case of typhoid.
This could mean that even though most of the patients lived in well sanitary locations, they probably do not take absolute good care of themselves since typhoid is water and food bone. That is to say;
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Nature of the water they drink or use in cooking
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Poor keeping of the kitchen and toilet facilities
Our way of Life, is based on the decisions we make. As such, there is a need for us as citizens to be cautious on the food and water we take into our body.
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This survey has revealed to as certain conditions at the main theatre of the KATH. The recommendations outlined, based on the survey, above should be considered so as to ensure that the health of all are stabilize
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