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.
Undergraduate Research work
The Beauty of Mathematics<br />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<br />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<br />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<br />
And look at this symmetry:<br />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<br />
PROJECT TITLE <br />Estimation Of The Age Distribution Of Patients Operated And Effect Of Salmonella Typhi On The Incidence Of Typhoid Complications At The Main Surgical Theatre<br />Supervisor<br />Mr. S. K. Appiah<br />
6/9/2008<br />4<br />INTRODUCTION<br /><ul><li>Komfo Anokye Teaching Hospital (Kath) is not</li></ul>performing<br /><ul><li>Many lives lost both medically and surgically
The ministry of health ensure well being of the populace </li></li></ul><li>6/9/2008<br />5<br />PROBLEM RECOGNITION<br /><ul><li>Reconnaissance Visits
An Interview With A Medical (Surgical) Doctor </li></li></ul><li>6/9/2008<br />6<br />THE NEED<br /><ul><li>Conduct a survey so as to seek information to questions unanswered
Find certain conditions that exist in this hospital</li></li></ul><li>6/9/2008<br />7<br />QUESTIONS RAISED<br /><ul><li>What age group has more surgical complications?
The mean age of the patients is in the thirty’s</li></li></ul><li>6/9/2008<br />9<br />ASSERTION BY “EMEDICINE GROUP” ON TYPHOID<br /><ul><li>Children aged 1 - 5 years have the highest risk of infection, morbidity and mortality
Typhoid fever in patients is highest in adolescents and young adults
Disease is generally highest in children aged 3 - 9 years</li></li></ul><li>6/9/2008<br />10<br />RESEARCH OBJECTIVES <br /><ul><li>IDENTIFY THE CONDITIONS IN THE MAIN SURGICAL THEATRE
To estimate the average age of patients and age range who visit the department
Minitab</li></li></ul><li>6/9/2008<br />14<br />ORGANIZATION OF THE STUDY <br /><ul><li>CHAPTER ONE </li></ul>Overview of the study<br /><ul><li>CHAPTER TWO </li></ul>Literature review<br /><ul><li>CHAPTER THREE </li></ul>Profile of the coverage<br /><ul><li> CHAPTER FOUR </li></ul>Analysis of data<br /><ul><li> CHAPTER FIVE </li></ul>Findings and Recommendations<br />
TYPHOID FEVER<br />is also known as <br />ENTERIC FEVER<br />
ENDEMIC<br />Developing Countries<br />AFRICA & South America <br />
THEIR VISION <br />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)<br />
THEIR MISSION <br />“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”.<br />
OVERVIEW OF CONCEPTS<br />6/9/2008<br />32<br /><ul><li>Sampling theory is a study of relationships existing between a population and samples drawn from the population.
Why sampling over complete enumeration:-saves time, reduce cost ,saves labour</li></li></ul><li>6/9/2008<br />33<br />Sampling Distribution:-<br /><ul><li> 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.</li></li></ul><li>STATISTICAL HYPOTHESIS<br />6/9/2008<br />34<br /><ul><li>It is a statementabout the parameters of the model
Used to test the claim about the average age obtained in stratification and the average age obtained by the random sample generated by minitab
P-value as the smallest level at which the data is significant.
State if the null hypothesis was or was not rejected at a specified α -value or level of significance</li></li></ul><li>CONFIDENCE INTERVAL<br />6/9/2008<br />36<br /><ul><li>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.
In many engineering and industrial experiments, the experimenter already knows that the means µ1differ µ2, consequently, the hypothesis testing on is of little interest.
The experimenter would usually be more interested in a confidence interval on the difference in means . The interval</li></ul> is called a percent confidence interval for the parameter.<br />
CORRELATION ANALYSIS<br />6/9/2008<br />37<br />CONCERNED WITH THE STRENGTH OF ASSOCIATION BETWEEN THE VARIABLE OF INTEREST AND THE OTHERS <br />An error term which caters for the errors due to chance and neglected factors which we assume are not important<br />
CORRELATION COEFFICIENT<br />6/9/2008<br />38<br /><ul><li>This is a quantitative measure of the strength of linear relationship between two variables, say x and y. There are two types of measure:</li></ul> Pearson Product – Moment<br /><ul><li>This is used for quantitative data measured on interval or ratio scale.
This is used when the data is ranked</li></li></ul><li>Scatter diagram<br />6/9/2008<br />39<br />The scatter diagram is a useful tool in examining relationships; especially between two variables. <br />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.<br />
TYPES OF REGRESSION MODEL<br />6/9/2008<br />40<br /> Regression models are classified according to the number of predicted variables and also the form of the regression function.<br /><ul><li> Simple Regression model
Multiple regression model</li></li></ul><li>Simple Linear Regression Model<br />6/9/2008<br />41<br />Definition and features of model<br />The simple linear regression model is given by Y = β0 + β1 x + ε<br /> x - is the value of the response variable in the observation<br /> is the known value of the predictor variables in the ith observation<br /> ε - is the random error term which caters for the errors due to chance are neglected factors which we assumed not important.<br /> are the parameters of the model<br /> β0 - gives the intercept on y axis<br />β1 - measures the slope of the linear model <br />
ESTIMATION OF LINEAR REGRESSION MODEL<br />6/9/2008<br />42<br /><ul><li>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.</li></li></ul><li>6/9/2008<br />43<br />METHOD OF LEAST SQUARES<br />This method finds the estimates <br /> respectively by minimizing the total sum of squares error( SSE ).<br />
ANALYSIS OF VARIANCE IN REGRESSION MODEL<br />6/9/2008<br />44<br />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.<br />
DEFINITION OF SOME TERMS(ANOVA):-<br />6/9/2008<br />45<br /><ul><li>The three quantities SSyy, SSE and SSR are measures of dispersion.
The total sum of squares of deviation (SSyy, ) is a measure of dispersion of the total variation in the observed values, y.
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.
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 ).</li></ul> <br />
COEFFICIENT OF DETERMINATION<br />6/9/2008<br />46<br />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. <br />
6/9/2008<br />47<br />MULTIPLE REGRESSION ANALYSIS<br /><ul><li>Multiple regression analysis will include fitting an appropriate model to a collected set of data, testing for the adequacy of the model
The analysis involves a large array of data system of equations which are conveniently and effectively performed in matrix
When you have q linear combinations of the k random variables X 1 , X2…., X k . </li></li></ul><li>6/9/2008<br />48<br />That is, for n independent observations on Yi<br /> and the associated independent variables X1, X 2, …, Xk<br />We have<br />
6/9/2008<br />50<br />MULTIPLE LINEAR REGRESSIONMODEL<br /><ul><li>From the general linear regression model for a multiple regression analysis takes the form</li></li></ul><li>6/9/2008<br />51<br />Forms of Multiple Linear Regression Models<br /> 1. Polynomials regression models:-<br /><ul><li>They contain one or more predictor variables in various powers.</li></ul> 2. Transformed regression models:- <br /> Some non-linear functions may be transformed to linear regression models.<br /> 3.Interaction effects regression model:-<br /> It is the joint effect of two or more predictor variables(you can use Log etc)<br />
THE BEAUTY OF MATHEMATICS<br />ANALYSIS OF DATA AND DISCUSSION <br />6/9/2008<br />53<br />
ANALYSIS OF DATA AND DISCUSSION <br />6/9/2008<br />54<br />“An unexamined life is not worth living”, similarly an unexamined organization will not be able to move forward in the right direction <br />At the end of this analysis, we will be able to make well informed decisions as to;<br /><ul><li>How to raise public awareness on the age group, gender (sex) that should be extremely vigilant, cared, and etc.
Which class or nature of surgical equipments or devises that should not be limited in number.
Which complications will need to be attended by the ministry of health.</li></li></ul><li>6/9/2008<br />55<br />CLASSIFICATION OF THE VARIOUS COMPLICATIONS REPAIRED <br />
6/9/2008<br />73<br />Each sample was used for the hypothesis testing of the claim that the mean age was 29 years. <br />One-Sample Z: sample1<br />Test of mu = 29 vs mu not = 29<br />The assumed sigma = 21.6<br />Variable N Mean StDev SE Mean<br />Sample 1 150 27.53 19.68 1.76<br />Variable 95.0% CI Z P<br />Sample 1 ( 24.07, 30.98) -0.84 0.403<br />One-Sample Z: sample 2<br />Test of mu = 29 vs mu not = 29<br />The assumed sigma = 21.6<br />Variable N Mean StDev SE Mean<br />Sample 2 150 28.48 21.37 1.76<br />Variable 95.0% CI Z P<br />Sample 2 ( 25.02, 31.94) -0.29 0.768<br />One-Sample Z: sample 3<br />Test of mu = 29 vs mu not = 29<br />The assumed sigma = 21.6<br />Variable N Mean StDev SE Mean<br />Sample 3 150 28.70 21.90 1.76<br />Variable 95.0% CI Z P<br />Sample 3 ( 25.24, 32.16) -0.17 0.865<br />One-Sample Z: sample 4<br />Test of mu = 29 vs mu not = 29<br />The assumed sigma = 21.6<br />Variable N Mean StDev SE Mean<br />Sample 4 150 29.47 21.47 1.76<br />Variable 95.0% CI Z P<br />Sample 4 ( 26.01, 32.92) 0.26 0.791<br />One-Sample Z: sample 5<br />Test of mu = 29 vs mu not = 29<br />The assumed sigma = 21.6<br />Variable N Mean StDev SE Mean<br />Sample 5 150 30.69 23.36 1.76<br />Variable 95.0% CI Z P<br />Sample 5 ( 27.24, 34.15) 0.96 0.337<br />
6/9/2008<br />86<br />The regression equation is<br />patients = - 18.5 + 6.87 Ln(zonagefem)<br />where patients represents the number of patient admitted with typhoid at the Pediatric Unit;<br />zonagefem represents the product of the environment, age below six years and number of females. The Ln is the natural logarithm function.<br />
MAJOR FINDINGS AND IMPLICATIONS<br />6/9/2008<br />87<br />
<ul><li>The mean age of patients operated was 29 years
The age range which had more surgical complications was 0-9 years.
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
The complete data indicates that out of a total of 1831patients 27.1%and 22.17% suffered from hernia and typhoid complications</li></ul>6/9/2008<br />88<br />
<ul><li>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.
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.
The ratio of the male to female was nearly 1:1 respectively
The known dirty environs (“Zongo”) did not contribute a high percentage in the case of typhoid.</li></ul>6/9/2008<br />89<br />
<ul><li>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;
Nature of the water they drink or use in cooking
Poor keeping of the kitchen and toilet facilities
Parent Inadequate education of nursing children </li></ul>6/9/2008<br />90<br />
RECOMMENDATIONS<br /><ul><li>The findings and Implications explained above gives an idea to make good recommendation based on the sample survey.
The hospital administrators should provide more equipments and surgical devices to accommodated patients especially those with age less 16 years.
The public should be informed as to the risk of complications of people aged in interval 0-10 years so as to minimize these cases.
Counseling on ways to minimize some of these related complications should be carried out.</li></ul>6/9/2008<br />91<br />
<ul><li>The general public should be educated on the incidence and severity of typhoid fever; ways they can minimize its infection.
The Ministry of Health can help create animations (Cartoons) on our visual media stations so as to educate the children faster.
Rural Water Projects should be encouraged in way to enhance proper distribution of water to various locations.</li></ul>6/9/2008<br />92<br />
CONCLUSION<br /><ul><li>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.
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</li></ul>6/9/2008<br />93<br />