Introduction to Introduction to STATISTICSSTATISTICS

Biostatistics

Week 1

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ContentContent

1.1 What is Statistics

1.2 Descriptive and Inferential Statistics

1.3 Variables and Types of Data

1.4 Data Collection and Sampling Techniques

1.5 Observational and Experimental Studies

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ObjectivesObjectivesBy the end of this chapter, you should be able to

Demonstrate knowledge of statistical terms. (1.1)

Differentiate between the two branches of statistics. (1.2)

Identify types of data. (1.3)

Identify the measurement level for each variable. (1.3)

Identify the four basic sampling techniques. (1.4)

Explain the difference between an observational and an experimental study. (1.5)

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1.1: What is Statistics?1.1: What is Statistics?

Most people become familiar with probability and statistics through radio, television, newspapers, and magazines. For example, the following statements were found in newspapers.

• Only 2 out of 11864 National Service dodgers have been hailed to the court

• Based on the 2000 census, 40.5 million households have two vehicles.

• The average annual salary for a professional football player for the year 2001 was $1,100,500.

• The average cost of a wedding dress is nearly 50,000.

• In USA, the median salary for men with a bachelor’s degree is $49,982, while the median salary for women with a bachelor’s degree is $35,408.

• Based on a survey of 250,000 individual auto leases signed from March 1 through April 15, 2002, 73% were for a Jaguar.

• Women who eat fish once a week are 29% less likely to develop heart disease.

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Various uses of Statistics Statistics is used in almost all fields of human endeavor.

In sports, statistician may keep records of the number of yards a running back gains during

a football game, or the number of hits a baseball player gets in a season.

In public health an administrator might be concerned with the number of residents who contract a

new strain of flu virus during a certain year.

In education A researcher want to know if new methods of teaching are better than old ones.

Furthermore, statistics is used to analyze the results of surveys and as a tool in scientific research to make decisions based on controlled experiments.

Other uses of statistics include operations research, quality control, estimation, and prediction.

Is STATISTICS important in our life?Is STATISTICS important in our life?

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Why you should study STATISTICS?Why you should study STATISTICS?

1. Students, like professional people, must be able to read and understand the various statistical studies performed in their fields. To have this understanding, they must be knowledgeable about the vocabulary, symbols, concepts, and statistical procedures used in these studies.

2. Students and professional people may be called on to conduct research in their fields, since statistical procedures are basic to research. To accomplish this, they must be able to design experiments; collect, organize, analyze, and summarize data; and possibly make reliable predictions or forecasts for future use. They must also be able to communicate the results of the study in their own words.

3. Students and professional people can also use the knowledge gained from studying statistics to become better consumers and citizens. For example, they can make intelligent decisions about what products to purchase based on consumer studies about government spending based on utilization studies, and so on.

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Statistics is the branch of science that deals with the collecting, organizing, summarizing, analyzing, presenting, interpreting and drawing conclusions from data.

Any values (observations or measurements) that have been collected

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The basic idea behind all statistical methods of data analysis is to make inferences about a population by studying small sample chosen from it

PopulationThe complete collection of

measurements, outcomes, objects or individuals under study

SampleA subset of a population,

containing the objects or outcomes that are actually observed

ParameterA number that describes a population characteristic

StatisticA number that describes a sample

characteristic

Example: A researcher wants to determine the average income of the residents of a certain barangay and there are 2,000 residents in the barangay. Then all of these residents comprise the population, and is usually denoted by N. Therefore, N = 2,000.

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1.2 Descriptive & Inferential Statistics1.2 Descriptive & Inferential Statistics

Inferential statisticsInferential statistics

consists of generalizing from samples to populations, performing estimations hypothesis testing, determining relationships among variables, and making predictions.

Used when we want to draw a conclusion for the data we obtained from the sample

Used to describe, infer, estimate, approximate the characteristics of the target population

Descriptive statisticsDescriptive statistics

consists of the collection, organization, classification, summarization, and presentation of data obtain from the sample.

Used to describe the characteristics of the sample

Used to determine whether the sample represent the target population by comparing sample statistic and population parameter

Descriptive vs. Inferential Statistics

Tell whether the following make use of descriptive or inferential statistics: A teacher computes the average grade of her

students then determines the top ten students. A psychologist investigates if there is a significant

relationship between mental age and chronological age.

A manager of a business firm predicts future sales of the company based on the present sales.

A janitor counts the number of various furniture inside the school.

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An overview of descriptive An overview of descriptive statistics and statistical inferencestatistics and statistical inference

START

Gathering of Data

Classification, Summarization, and Processing of data

Presentation and Communication of

Summarized information

Is Information from a sample?

Use cencus data to analyze the population

characteristic under study

Use sample information to make inferences about

the population

Draw conclusions about the population

characteristic (parameter) under study

STOP

Yes

No

Statistical Inference

Descriptive

Statistics

Statistical Inference

Descriptive Statistics

No

Yes

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1.3 Variables and Types of Data1.3 Variables and Types of Data

To gain knowledge about seemingly haphazard events, statisticians collect information for variables, which describe the event.

Variables whose values are determined by chance are called random variables

Variables

•is a characteristic or attribute that can assume different values.

•is also a characteristics of interest, one that can be expressed as a number that is possessed by each item under study.

•The value of this characteristic is likely to change or vary from one item in the data set to the next.

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Data are also the values that variables can assume.

A data set is a collection of data values.

Each value in the data set is called a data value or a datum.

Variables can be classified

By how they are categorized, counted

or measured - Level of

measurements of data

As Quantitative and Qualitative

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Types Types of Dataof Data

Qualitative (categorical/Attributes) 1* Data that refers only to name classification (done

using numbers)2* Can be placed into

distinct categories according to some

characteristic or attribute.

Quantitative (Numerical)

1* Data that represent counts or measurements

(can be count or measure)

2* Are numerical in nature and can be ordered or

ranked.

Nominal Data (can’t be rank)Gender, race, citizenship. ext

Ordinal Data (can be rank)Feeling (dislike – like),

color (dark – bright) , ext

Discrete Variables Assume values that can be

counted and finiteEx : no of something

Continuous variables Can assume all values

between any two specific values & it obtained by

measuringEx: weight, age, salary, height,

temperature, ext

Use code numbers (1,

2,…)

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Level of Measurements of Data Level of Measurements of Data

Nominal-level data

Ordinal-level data

Interval-level data

Ratio-level data

classifies data into mutually exclusive (non overlapping), exhausting

categories in which no order or

ranking can be imposed on the

data

classifies data into categories

that can be ranked;

however, precise differences between the ranks do not

exist

ranks data, and

precise differences

between units of measure do exist; however, there is no meaningful

zero

Possesses all the characteristics of

interval measurement,

and there exists a true zero.

Examples

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ExampleExample

1. A meteorologist classifies cities as having winter weather that is “dreary” (0) or “not dreary” (1). Type of winter weather (0 vs. 1) is measured at what level of measurement?

2. A neurologist measures how many times per minute a specific neuron in the brain “fires” when a person is in dim light as opposed to when a person is in bright light. She is measuring the neuron firing at what level of measurement?

3. A social worker obtains suicide rates for students at colleges. If the college has a suicide rate that is below average, it classifies a – 1. If the suicide rate is average, the college gets a 0; and if the suicide rate is , above average, it gets a +1. Suicide rate (– 1, 0, 1) is being measured at what level of measurement?

4. Classify each of the measurements as quantitative, ordinal or categorical:a. Response to treatment coded as 1 = no response, 2 = minor

improvement, 3 = major improvement, 4 = complete recoveryb. Annual incomec. Body temperature (degree Celsius)d. Area of a parcel of land (acres)e. Population density of peoplef. Political party affiliation coded 1 = Democrat, 2 = Republican, 3 = Ind.;

4 = Other

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1.4 Data Collection and 1.4 Data Collection and Sampling TechniquesSampling Techniques

Method of Data Collection

Data resulting from an experiment

(experimental study)

Data that are made available by others (secondary data)

Data collected in an observational study

(survey/ questionnaires)

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4 Sampling Techniques4 Sampling Techniques

Random samples Selected using chance method or random methods

Systematic samples Numbering each subject of the populations & select every kth

number

Stratified samples Dividing the population into groups according some

characteristic that is important to the study, then sampling from each group

Cluster samples Dividing the population into sections/clusters, then randomly

select some of those cluster & then chose all members from those selected cluster

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Identify the type of sampled obtain

Example 1A physical education professor wants to study the

physical fitness levels of students at her university. There are 20,000 students enrolled at the university, and she wants to draw a sample of size 100 to take a physical fitness test. She obtains a list of all 20,000 students, numbered it from 1 to 20,000 and then

invites the 100 students corresponding to those numbers to participate in the study. Is this a simple random sample?

Example 2A quality engineer wants to inspect rolls of wallpaper in order

to obtain information on the rate at which flows in the printing are occurring. She decides to draw a sample of 50 rolls of wallpaper from

a day’s production. Each hour for 5 hours, she takes the 10 most recently produced rolls and counts the number of flaws on each. Is

this a simple random sample?

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Example 3

Suppose we have a list of 1000 registered voters in a community and we want to pick a probability sample of 50. We can use a random number table to pick one of the first 20 voters (1000/50 = 20) on our list. If the table gave us the

number of 16, the 16th voter on the list would be the first to be selected. We would then pick every 20th name after this random start (the 36th voter, the 56th

voter, etc) to produce a systematic sample.

Example 4

Consumer surveys of large cities often employ cluster sampling. The usual procedure is to divide a map of the city into small blocks each blocks

containing a cluster are surveyed. A number of clusters are selected for the sample, and all the households in a cluster are surveyed. Using a cluster

sampling can reduce cost and time. Less energy and money are expended if an interviewer stays within a specific area rather than traveling across stretches of

the cities.

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Example 5

Suppose our population is a university student body. We want to estimate the average annual expenditures of a college

student for non school items. Assume we know that, because of different lifestyles, juniors and seniors spend more than freshmen

and sophomores, but there are fewer students in the upper classes than in the lower classes because of some dropout factor. To

account for this variation in lifestyle and group size, the population of student can easily be stratified into freshmen, sophomores, junior and seniors. A sample can be stratum and each result

weighted to provide an overall estimate of average non school expenditures.

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1.5 Observational and Experimental 1.5 Observational and Experimental Studies (Types of statistical studies) Studies (Types of statistical studies)

In an observational study, the researcher merely observes what is happening or what has happened in the past and tries to draw conclusions based on these observations.

Example data from the Motorcycle Industry

Council (USA TODAY) stated that “Motorcycle owners are getting older and richer.” Data were collected on the ages and incomes of motorcycle owners for the years 1980 and 1998 and then compared. The findings showed considerable differences in the ages and incomes of motorcycle owners for the two years. In this study, the researcher merely observed what had happened to the motorcycle owners over a period of time. There was no type of research intervention.

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In an experimental study, the researcher manipulates one of the variables and tries to determine how the manipulation influences other variables.

the subjects should be assigned to groups randomly.

Also, the treatments should be assigned to the groups at random.

Example a study conducted at Virginia Polytechnic

Institute and presented in Psychology Today divided female undergraduate students into two groups and had the students perform as many sit-ups as possible in 90 sec. The first group was told only to “Do your best,” while the second group was told to try to increase the actual number of sit-ups they did each day by 10%. After 4 days, the subjects in the group that were given the vague instructions to “Do your best” averaged 43 sit-ups, while the group that was given the more specific instructions to increase the number of sit-ups by 10% averaged 56 sit-ups by the last day’s session. The conclusion then was that athletes who were given specific goals perform better than those who were not given specific goals.

This study is an example of a statistical experiment since the researchers intervened in the study by manipulating one of the variables, namely, the type of instructions given to each group.

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Statistical studies usually include one or more independent variables and one dependent variable.

The independent variable in an experimental study is the one that is being manipulated by the

researcher. The independent variable is also called the explanatory variable.

The resultant variable is called the dependent variable or the outcome variable.

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SummarySummary The two major areas of statistics are descriptive and inferential.

When the populations to be studied are large, statisticians use subgroups called samples.

The four basic methods for obtaining samples are: random, systematic, stratified, and cluster.

Data can be classified as qualitative or quantitative.

The four basic types of measurement are nominal, ordinal, interval, and ratio.

The two basic types of statistical studies are observational and experimental.

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ConclusionConclusion

The applications of statistics are many and varied. People encounter them in everyday life, such as in reading newspapers or magazines, listening to the radio, or watching television.

Thank you Thank you