Lecture 1-introduction To Statistics

‫بسم ال الرحمن الرحيم‬

INTRODUCTION TO BIOSTATISTICS Dr. Aesha Farheen Department of Community and Family Medicine, Medical College(Girls center) King Khaled University, Abha

• The word 'Statistics' is derived from the Latin word 'Statis' which means a "political state." Clearly, statistics is closely linked with the administrative affairs of a state such as facts and figures regarding defense force, population, housing, food, financial resources etc.

• What is Statistics? • aggregate of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to reasonable standard of accuracy, collected in a systematic manner for a predetermined purpose and placed in relation to each other." • IN SIMPLE WORDS: • Methods for organizing, summarizing, presenting, & interpreting information (data).

WHY WE NEED STATISTICS •

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To present the data in a concise and definite form : Statistics helps in classifying and tabulating raw data for processing and further tabulation for end users. To make it easy to understand complex and large data : This is done by presenting the data in the form of tables, graphs, diagrams etc., or by condensing the data with the help of means, dispersion etc.

• For comparison : Tables, measures of means and dispersion can help in comparing different sets of data.. • In measuring the magnitude of a phenomenon:- Statistics has made it possible to count the population of a country, the industrial growth, the agricultural growth, the educational level (of course in numbers(

QUANTITATIVE MEDICINE • Everything in medicine, be it research, diagnosis or treatment depends on counting/measurement. • High/ Low B.P?? • Pulse rate. • Incidence of disease. • Death rate. • Enlargement of liver/ spleen

Statistics and Health • • • •

BIOSTATISTICS HEALTH STATISTICS MEDICAL STATISTICS VITAL STATISTICS NOT MUTUALLY EXCLUSIVE TERMS

Examples of uses of biostatistics • To define what is normal/ healthy in a population (Setting limits of normality). • To compare drug action –potency/efficacy • Confirm association between two attributes:Cancer and smoking or Socioeconomic status and malnutrition • Usefulness of vaccines

Uses in Public Health Planning • Recording of vital events • Incidence/prevalence of disease. • Leading causes of death/ morbidity in the community • Demographic characteristics of a community. • Health system research.

Statistical presentation • Two ways of representing statistics : Numerical and Pictorial. • Numerical statistics are numbers. But some numbers are more meaningful such as mean, standard deviation etc. • When the numerical data is presented in the form of pictures (diagrams) and graphs, it is called the Pictorial statistics. This statistics makes confusing and complex data or information, easy, simple and straightforward, so that even the layman can understand it without much difficulty.

Types of statistics • The branch of statistics wherein we record and analyze observations for all the individuals of a group or population and draw inferences about the same is called "Descriptive statistics" or "Deductive statistics".

• On the other hand, if we choose a sample and by statistical treatment of this, draw inferences about the population, then this branch of statistics is known as Statical Inference or Inductive Statistic or Inferential statistics. • Tools for generalizing beyond actual observations • Generalize from a sample to a population

COMMON TERMS • DATA: • Collection of information, comprised of 2 parts • (1) Individuals (also called cases or observation units) • Individuals are ANY OBJECTS described by data • Do NOT have to be people

• (2)Variables are characteristics recorded on/from the individuals • A variable is something that varies—has at least 2 values • Something that changes over time OR • Something that varies across individuals.

• Pick out the individuals and variables in these examples: • 100 business executives were asked their age • 8 farmers obtained the weight of 25 pigs • 4 technicians measured the sound quality of 10 stereos

Types of Data • Categorical /(QUALITATIVE): • records which group or category an individual/observation belongs in; • it classifies; • doesn’t make sense to perform arithmetic on this type of variable • E.g., gender (Female or Male)

Quantitative • a true numerical value; • it indicates an amount; • often obtained from a measuring instrument; • it makes sense to perform arithmetic on these types of variables • E.g., Weight in pounds

:Variables can also be divided into

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Discrete (a) Indivisible units (b) Restricted to whole numbers (c) Can be counted e.g. # of children in a family # of houses in a neighborhood

• Continuous: • (a) Unlimited number of possible values • (b) Infinite number of values can fall b/n any 2 observed values • (c) No gaps between units • e.g. time taken to solve a problem height or weight

• Variables can be measured on four different types of scales: • 1.Nominal: (a) Consists of a set of categories or labels • (b) The ‘score’ does NOT indicate an amount • (c) The ‘score’ is arbitrary • (d) Example: Color of cars: 1=red, 2=blue, 3=green •

• 2.Ordinal: (a) Score indicates rank order along some continuum • (b) It is a relative score, not an absolute score • Might have the highest score on the exam, but we still don’t know how well you did • (c) There is NOT an equal distance between scores • Finish 1st,2nd, or 3rd in a race; could be a difference of 2 seconds b/n 1st & 2nd but a difference of 10 minutes b/n 2nd & 3rd

• 3.Interval: (a) Score indicates an actual amount • (b) There is an equal distance between each unit • (c) Can include the number 0, but it is not a ‘true’ 0 • (d) Zero on this scale does not mean an absence of the variable; thus cannot speak to ratios • (e) Example: temperature, in degrees Fahrenheit :80 degrees is not twice as hot as 40°

• 4.Ratio: (a) Score indicates an actual amount • (b) There is an equal distance between each unit • (c) It includes a ‘true’ zero point; thus ratios are valid • (d) Example: # of friends you have

.COMMON TERMS CONTD • VARIABLE • A characteristic that takes on different values in different persons/ places/tjhings. • Eg. Height, Weight,B.P, Age etc. • CONSTANT: • Quantities that do not vary eg in biostatistics, for a particular population;mean, SD, SE,Correlation coeff.,and proportion are considered as constants

• OBSERVATION: • An event and its measurement eg B.P=120 mm Hg • OBSERVATION UNIT • The source of observation, often called the individual or subject.

Population and sample Population • The entire collection of events of interest eg., collection of people you want to study about. • The total number of objects (individuals) in a population is known as the size of the population. This may be finite or infinite. • Doesn’t necessarily mean “big” but often is.

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SAMPLING UNIT: Each member of a population. SAMPLE: Part of population Subset of events selected from a population • Intended to represent the population

• PARAMETER: • It is a summary value or constant of a variable that describes the population such as the mean,variance, correlation coefficient,etc. • (Against which we measure a statistic of a sample) • STATISTIC: is a summary value that describes the sample:eg mean SD, SE, Correlation coeff. etc.

• PARAMETRIC TEST; • It is one in which population constants such as that described above are used and data tend to follow one assumed or established distribution such as Poisson, normal, binomial etc.

NONPARAMETRIC TEST • Tests such as Chi square in which no constant of a population is used. Data do not follow any specific distribution and no assumptions are made in these tests.

Symbols and Notations • For Parameter i.e Values describing POPULATIONS • Greek letters eg., • µ =Mean ∀ σ2 =Variance ∀ σ =SD ∀ ρ =Proportion

• For Statistics i.e Values describing SAMPLES • Roman letters,eg. X =Mean s2=Variance s =Standard Deviation p =Proportion

methods of research 1.Correlational :(non-experimental) 2.Experimental:Begin with an hypothesis, a hunch/guess/belief about how variables might be related or influence each other: • Meditation can reduce stress

Co relational Research Measure variables as they occur naturally • Questionnaires, interviews, observational or archival research • Test hypotheses about association between 2 or more variables • Theory may be causal, but conclusions cannot be.

:Example • • • •

Survey 100 people Measure how often (if ever) they meditate Measure their level of life stress Look at association between meditation and stress • Can we draw a causal inference?

Experimental Research • Manipulate one variable; examine its effect on an outcome variable • Independent Variable (IV) Dependent Variable (DV) • Goal is to draw causal inferences • Cause - Effect • The IV presumed to cause changes in DV • IV DV

Example • Recruit 100 people • Randomly assign 50 to a meditation task & 50 to a neutral task • Measure stress after task • Look at group differences in stress • Can we draw a causal inference?

Two key elements of an :experiment • 1.IV with at least two “levels” • treatment group = meditation • control group = no meditation • 2.Random assignment to groups/conditions • Assignment of participants to groups is based on a random process

LIMITATIONS WITH STATISTICS •

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Statistics does not deal with individual measurements. Since statistics deals with aggregates of facts, it can not be used to study the changes that have taken place in individual cases. Statistics cannot be used to study qualitative phenomenon like morality, intelligence, beauty etc. as these can not be quantified. However, it may be possible to analyze such problems statistically by expressing them numerically. Statistical results are true only on an average- The conclusions obtained statistically are not universal truths. They are true only under certain conditions. This is because statistics as a science is less exact as compared to the natural science.