Ebd1 lecture 3 2010

General Studies 1

(Community Dentistry1)

Dr Nizam Abdullah

Introduction to Statistics

© The University of Adelaide, School of Dentistry

Content of this lecture

What is ‘statistics’?

Data and statistics

Variable types

Measurement scales


What is Statistics ?Statistics is a science that deals with the

collection,organizing,analysis,interpretation, andpresentation

of information that can be stated numerically.(Daniel WW, 1999)

The application of statistics in biological sciences & medicine - Biostatistics


2 Broad areas of statistics

Descriptive statistics- describe, organise, or summarise data; referring only to the actual data available

Inferential statistics- making inferences that go beyond actual data. ( Generalising to a population after having observed only a sample)


Why should I study Statistics??


Why should I study Statistics?

A tool for researchEasier to communicate with Statisticians/BiostatisticiansUnderstanding medical literature (improve literature appraisal-skills)


Statistics in dentistry

Statistics are a pervasive force in the practice of dentistry.

They are involved in the entire spectrum of clinical decision making.

Manufacturers may provide details of the effectiveness of their products in an attempt to persuade practitioners to purchase them.

Individual practitioners may choose to alter the way in which they practise as a result of published research findings.


Statistics in dentistry (cont.)

Government departments and professional bodies may produce guidelines or regulations on the basis of a body of evidence concerning a particular area of practice.

In each case it is likely that statistics will have been used in the process of evaluating the strength of evidence in favour of (or against) taking a particular course of action.

Without a basic understanding of statistics it is difficult for the individual practitioner to assess the value of a particular piece of published research, or to make their own mind up as to whether new guidelines are reasonable.


(Williamson et al., 1986)

“The study assessed 30 medical journals

(including BMJ, JAMA, N Engl J Med, CMAJ,

The Lancet, ….) involving 4,235 articles …

Only 20% met the assessor's criteria for

validity …..”


Williamson & colleagues (1986) suggested ..

1. Avoid relying on abstracts as a primary source of information

2. Seek reviews, meta-analysis articles based on validated research results

3. Make at least a moderate effort to develop the skills necessary for evaluating the medical literature


Data & Statistics

• Data is the information obtained about a particular area of research

- Data comprise of observations on one or more variables of interest eg. Age, sex or height of patients


What is a variable?Variable

We observe a characteristic of variables of interest (e.g. age, gender, family income, decay, miss, etc.) any quantity

that varies is termed a variable

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Types of Data

The choice of an appropriate statistical technique depends on the type of data in question

4 Scales of measurements: - Nominal - Ordinal - Interval - RatioData may also be characterized as discrete or

continuous


1. Nominal scale (Qualitative)

The lowest level of measurement - the naming level.

Distinguishes a person, object or event on the basis of a name. For example, we can classify or name: - a newborn infant as male or female- tooth as sound, decayed, missing or filled- people as being single, married, divorced- the outcome of a coin toss as a head or a tail- blood type as either A, B or O.

Data is not rankable, e.g. you can’t say that single (as a name) ranks higher or lower than married.


Nominal scale (example) Numbers can assigned to categories as

‘names’. Which number is assigned to which category is completely arbitrary.

Classifying people according to sex is a common application of a nominal scale.

In this example, the number 1 is assigned to Male and the number 2 is assigned to Female. We can just as easily assign the number 1 to Female and 2 to Male. The purpose of the number is merely to name the characteristic or give it identity. The only mathematical operation we can perform with nominal data is to count.


2. Ordinal scale (Qualitative) Distinguishes objects or events from one another on the

basis of the relative amounts of some characteristic they possess, i.e. elements can be arranged in some meaningful kind of order that corresponds to their relative position or size.

Ordinal measurements make it possible for persons, objects etc to be ranked, e.g. students may receive grades A, B, C, or D according to the their performance on a test, or illnesses can be ranked from least severe to most severe.

Puts participants in order from high to low, but this rank does not indicate how much higher or lower one subject is from another.


Ordinal scale (example)

Students may receive grades A, B, C, or D according the their performance on a test. They can be ranked accordingly:

– student with grade A is ranked 1st

– student with grade B is ranked 2nd

– student with grade C is ranked 3rd

– student with grade D is ranked 4th

The difference in grade scores between the students ranked 1 and 2 is not necessarily the same as the difference between those ranked 2 and 3.

Student grade scores might be, respectively, 80% (A), 68% (B), 52% (C).

The interval between ranks is not the same and is arbitrarily changeable.

-12% -16%


3. Interval scale (Quantitative) Same like ordinal data - can be placed in a

meaningful order. In addition they have meaningful intervals between item, which are usually measured in quantities

So, we can not only say that one element is larger than or smaller than another, but also by how much.

Basically, the interval scale uses a set scale, so the researcher knows both the order of the data points in relation to each other and on absolute terms, but it has no set zero.

More informative that the nominal or ordinal scales.


Interval scale (example) A good example of an interval scale is the

measurement of temperature on Fahrenheit or Celsius scales.

The units on a thermometer represent equal volumes of mercury between each interval on the scale. The thermometer identifies for us how many units of mercury correspond to the temperature measured.

We know that 60° is hotter than 30° and that there is the same 10-degree difference in temperature between 20° and 30° as between 50° and 60°.

But zero degrees on either scale is an arbitrary number and not a ‘true’ zero. The zero point does not indicate an absence of temperature; it is an arbitrary point on the scale.

Interval scale do not have an absolute zero, ratios of scores are not meaningful. 60° is not twice as hot as 30° ,


4. Ratio scale (Quantitative)

Used when measurements have the properties of the first three scales and the additional property that their ratios are meaningful.

A property of a ratio scale is a true zero, indicating a complete absence of the trait being measured, i.e. in this scale we have a fixed origin or zero point as opposed to an arbitrary origin, e.g. height, weight, length as long as the number zero remains a fixed origin.

This scale represents the highest level of measurement.


Ratio scale examples

Weight and money

A person weighing 80kg is twice as heavy as a person weighing 40kg,

If we have $100 we have twice as much purchasing power as $50. If we have no money in our pockets, we have no ability to purchase anything.

•Most biomedical variables form a ratio

scale

(Pulse rate in beats per minute, blood

press in mm mercury)


• Discrete: - Discrete variables can take only certain values and none in between. ( Number of patients attending dental hospital..)

• Continuous: - Continuous variables may take any value ( patients weight, height,age, blood pressure.. )


Importance of scales of measurement

The reason we stress scales of measurements is because the nature of the data determines which statistical tests are appropriate to use.

Different descriptive techniques and different statistical tests are appropriate to different measurement scales.

Types of statistical tests will be discussed next lecture.


Technology

Ebd1 lecture 3 2010