STAT 3BIOSTATISTICS

Introduction

LECTURE ( 2hours/week)

Requirements

•LONG EXAMS 60%

•QUIZZES, ASSIGNMENTS and

CLASS PARTICIPATION 30%

•ATTENDANCE10%

TOTAL 100%

Introduction

LABORATORY (3 hours/week)

Requirements

EXAMS 40%

EXERCISES, QUIZZES, ASSIGNMENTS 30%

RESEARCH PAPER 10%

ATTENDANCE, PORTFOLIO 20%

TOTAL 100%

Introduction

• Lecture 66.67%

•Laboratory 33.33%

•TOTAL 100%

PASSING GRADE: 70%

Introduction

References• Marija J. Norusis,

SPSS 10.0 Guide to Data Analysis

Introduction

References• Ronald E. Walpole,

Introduction to Statistics

Introduction

References• Ronald E. Walpole,

Raymond H. Myers Probability and Statistics for Engineers and Scientists

Introduction

References• George W. Snedecor

William G. Cochran Statistical Methods

Introduction References• Internet Websites

Learning Objectives

1. To understand the meaning and nature of Statistics;

2. To differentiate Descriptive and Inferential Statistics;

3. To understand the concept of population and sample;

4. To distinguish a parameter from a statistic;

5. To appreciate the different uses of statistics;

6. To determine the methods of collecting data

7. To determine the methods of presenting data

8. To evaluate summation notations

“Statistics is the most important science in the whole world; for upon it depends

the practical application of every science and of every art; the one science essential to all political and social administration, all education, all organization based on

experience, for it only gives results of our experience.”

-Florence Nightingale

“Statistics is like a bikini, what is revealed is suggestive, what is concealed is vital.”

-unknown

STATISTICSDefinition

1. PLURAL SENSE

A set of numerical or recorded data

2. SINGULAR SENSE

A branch of Science which deals with the collection, presentation, analysis, and interpretation of data

EXAMPLES

1. Social Weather Station collects and tabulates data from selected voters to predict the political preferences of all voters. The information they gather can help candidates determine their chances of winning in the election and develop strategies that will increase their chances of winning.

2. Population counts of the different regions in the country may help determine resource allocation.

EXAMPLES

3. Inventory of raw materials allow for the development of a suitable procurement design and competitive production strategies.

4. Sales volume, together with information on consumer behavior and preferences, is useful in the formulation of the marketing strategy for the next year.

Two (2) Major Areas of Statistics

1. Descriptive Statistics

Collecting and describing a set of data so as to yield some meaningful information.

2. Inferential Statistics

Concerned with the analysis of a subset of data leading to prediction or generalization about the entire set of data.

Descriptive Statistics

•Collect Data e.g. Survey

•Present Data e.g. Tables and Graphs

•Characterize Data e.g. Meann

x i

A Characteristic of a: Population is a Parameter

Sample is a Statistic.

Inferential Statistics

•Estimation•Hypothesis Testing

Making decisions concerning a population based on sample results.

Determine whether the following statements use the area of descriptive or inferential statistics.

1. A bowler wants to find his bowling average for the past 12 games.

ANSWER: Descriptive Statistics

2. A manager would like to predict based on the previous year’s sales, the sales performance of a company for the next five years.

ANSWER: Inferential Statistics

3. A politician would like to estimate , based on an opinion poll, his chance for winning in the upcoming senatorial election.

ANSWER: Inferential Statistics

Determine whether the following statements use the area of descriptive or inferential statistics.

4. A teacher wishes to determine the percentage of the students who passed the examination.

ANSWER: Descriptive Statistics

5. A teacher wishes to determine the average monthly expenditures on school supplies for the past five months.

ANSWER: Descriptive Statistics

6. A basketball player wants to estimate his chance for winning the most valuable player (MVP) award based on his current season averages and the averages of his opponents.

ANSWER: Inferential Statistics

Types of Data

Categorical

Discrete Continuous

Num erical

D ata

Data at non-measurement level, grouped into categories. For example, nominal – gender, or ordinal – income group

Categorical data

Data measured at least at interval level, but only as whole numbers (integers). For example, household size, or number of siblings

Discrete Data

Continuous Data

data with a potentially infinite number of possible values along a continuum (eg, weight, blood pressure).

Numerical data

VARIABLE

A characteristic or attribute of persons or objects which can assume different values or labels for different persons or objects under consideration

Examples:

Number of students, Course, Gender

Definitions

Definitions

Measurement the process of determining the value or

label of a particular variable for a particular experimental unit.

Experimental Unit The individual or object on which a

variable is measured.

Different Levels of Measurements1. Nominal The weakest level of measurement where

numbers or symbols are used simply for categorizing subjects into different groups

Examples: gender, course, religion

2. Ordinal Contains the properties of the nominal level,

and in addition, the numbers assigned to categories of any variable may be ranked or ordered in some low to high manner

Examples: year level, sizes of t-shirts

Different Levels of Measurements3. Interval Has the properties of the nominal level,

and in addition, the distances between any two numbers on the scale are of known sizes. An interval scale must have a common and constant unit of measurement.

It has no true zero point/no absolute zero

Examples: score, temperature

Different Levels of Measurements4. Ratio Contains all the properties of the

interval level It has true zero point/absolute zero Examples: no. of correct answers,

Weight, height, area, volume of water

Data Sources

PrimaryData Collection

SecondaryData Compilation

Observation

Experimentation

Survey

Print or Electronic

General Classification of collecting data

Census or complete enumeration

-is the process of gathering information from every unit in the population.

not always possible to get timely, accurate and economical data

costly, especially if the number of units in the population is too large.

General Classification of collecting data

Survey sampling

- is the process of obtaining information from the units in the selected sample.

•  

Advantages of Survey Sampling:• reduced cost• greater speed• greater scope• greater accuracy 

DEFINITIONSPROBABILITY AND NON-PROBABILITY SAMPLING

A sampling procedure that gives every element of the population a (known) nonzero chance of being selected on the sample is called probability sampling. Otherwise, the sampling procedure is called non-probability sampling.

TARGET POPULATION

The target population is the population from which information is desired.

SAMPLED POPULATION

The sampled population is the collection of elements from which the sample is actually taken.

POPULATION FRAME

The population frame is a listing of all the individual units in the population.

Quota

Types of Sampling Methods

Samples

Non-Probability Samples

Judgement Chunk

Probability Samples

Simple Random

Systematic

Stratified

Cluster

Methods of Non-probability Sampling

1. purposive sampling- sets out to make a sample agree with the profile of the population based on some pre-selected characteristic

2. quota sampling- selects a specified number (quota) of sampling units possessing certain characteristics

3. convenience sampling - selects sampling units that come to hand or are convenient to get information from

4. judgment sampling - selects sample in accordance with an expert’s judgment

Methods of Probability Sampling

Probability Samples

Simple Random Systematic Stratified Cluster

Subjects of the sample are chosen based on known probabilities.

4

1i

ix

Consider a controlled experiment in which the decreases in weight over a 6-month period were 15, 10, 18 and 6 kilograms, respectively. If we designate the first recorded value x1 , the second x2 , and so on, then we can write

x1 = 15, x2 = 10, x3 = 18 and x4 = 6

Using the greek letter

(capital zigma) to indicate “summation of” we can write the sum of the 4 weights as

Summation Notation

= x1 + x2 + x3 +x4 = 49

3

2i

ix = x2 + x3 = 28

n

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n

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n

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n

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iii zyxzyx11 11

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THEOREM 1The summation of the sum of two or more variables is the sum of their summations. Thus

THEOREM 2If c is a constant then

n

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i

n

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i xccx11

THEOREM 3If c is a constant then

n

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ncc1

THEOREM 4If c is a constant , and m is any integer not equal to 1, then

n

mi

cmnc 1

23

1

3

2

2

1

12)4)15(.2

)3)43(.1

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iii

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xx

yxyx

Example: If x1 = 2, x2 = 4, x3 = -1, x4 = 0 y1 = 3, y2 = -1, y3 = 2, y4 = 5 find the value of