INTRODUCTION TO

STATISTICS

R Dh@ker, Lecturer, PCNMS 1

INTRODUCTION

The word statistics conveys a variety

of meaning to people in different walks

of life.

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The word statistics comes from the

Italian words Statista

( Statement).

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CONT…INTRODUCTION

The German word Statistik

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Political state

The word Statistics today refers to

either quantitative information or a

method of delaling with quantitative

or qualitative information.

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DEFINITION “Statistics is defined as collection,

Presentation, analysis and interpretation of

numerical data”. Acc. Croxton & cowden

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statistics is the sciences and art of

dealing with figure and facts.

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Biostatistics Biostatistics is the branch of statistics

applied to biological or medical

sciences.

Biostatistics is the methods used in

dealing with statistics in the field of

health sciences such as biology,

medicine, nursing, public health etc.

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Biostatistics is the branch of statistics

applied to biology or medical sciences.

Biostatistics is also called “Biometry”

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In Greek, Bios Life

Metron

So, it is measurement of life

Measured

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USE & APPLICATION OF STATISTICS

It facilitates comparisons

It simplifies the message of figure

It helps in formulating and testing

hypothesis

It help in prediction

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SCALE OF MEASUREMENT

Measurement is the process of assigning numbers

or labels to objects, persons, states, or events in

accordance with specific rules to represent

quantities or qualities of attributes.

We do not measure specific objects, persons, etc.,

we measure attributes or features that define them.

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Nominal ScalesNominal Scales

Ordinal ScalesOrdinal Scales

Interval ScalesInterval Scales

Ratio ScalesRatio Scales

FOUR BASIC SCALES OF MEASUREMENT

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Types of

Measurement Scales R

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Nominal measurement

There must be distinct classes but these classes have no quantitative properties. Therefore, no comparison can be made in terms of one category being higher than the other.

For example - there are two classes for the variable gender - males and females. There are no quantitative properties for this variable or these classes and, therefore, gender is a nominal variable.

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CONT…NOMINAL SCALE

Sometimes numbers are used to

designate category membership-

Example: Country of Origin

1 = United States 3 = Canada2 = Mexico 4 = Other

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There are distinct classes but these classes have a natural ordering or ranking. The differences can be ordered on the basis of magnitude.

For example - final position of horses in a thoroughbred race is an ordinal variable. The horses finish first, second, third, fourth, and so on. The difference between first and second is not necessarily equivalent to the difference between second and third, or between third and fourth. 13

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Ordinal Scales

CONT…ORDINAL SCALES

Does not assume that the intervals between numbers are equal

Example:

finishing place in a race (first place, second place)

1 hour 2 hours 3 hours 4 hours 5 hours 6 hours 7 hours 8 hours

1st place 2nd place 3rd place 4th place

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INTERVAL SCALES It is possible to compare differences in magnitude,

but importantly the zero point does not have a natural meaning. It captures the properties of nominal and ordinal scales - used by most psychological tests.

Designates an equal-interval ordering - The distance between, for example, a 1 and a 2 is the same as the distance between a 4 and a 5

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We can see that the same difference exists between 10o C ( 50 F) and 20 degree C ( 68 F)

25 C ( 77F) and 35 C ( 95 F)

But we can not say that 20C is twice as hot as a temperature of 10C

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Example - Celsius temperature is an interval

variable. It is meaningful to say that 25 degrees

Celsius is 3 degrees hotter than 22 degrees Celsius,

and that 17 degrees Celsius is the same amount hotter

(3 degrees) than 14 degrees Celsius. Notice,

however, that 0 degrees Celsius does not have a

natural meaning. That is, 0 degrees Celsius does not

mean the absence of heat!

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RATIO SCALESIt is the highest level for measurement

This level has all the three attributes:

Magnitude

Equal interval

Absolute zero point

It represent continuous values

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Example:

Biophysical parameters

Weight

Height

Volume

Blood pressure

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30 Kg is thrice of 10 kg

20 cm is twice of 10 cm

8 hours is four time of 2 hours

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TYPES OF MEASUREMENT SCALES (CONT.)

Each of these scales have different properties

(i.e., difference, magnitude, equal intervals, or

a true zero point) and allows for different

interpretations.

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The scales are listed in hierarchical order.

Nominal scales have the fewest measurement

properties and ratio having the most properties

including the properties of all the scales beneath

it on the hierarchy.

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TYPES OF MEASUREMENT SCALES (CONT.)

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The goal is to be able to identify the type of

measurement scale, and to understand proper

use and interpretation of the scale.

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TYPES OF MEASUREMENT SCALES

(CONT.)

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Bob

Gene

Sam

PRIMARY SCALES OF MEASUREMENT

ScaleNominal Symbols

Assigned to Runners

Ordinal Rank Orderof Winners

Interval PerformanceRating on a

0 to 10 Scale

Ratio Time to Finish, in

Seconds

3rd place 2nd place 1st place

Finish

Finish

3 7 9

15.2 14.1 13.4

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Scale Basic

Characteristics

Common Examples

Marketing Examples

Nominal Numbers identify & classify objects

Social Security nos., numbering of football players

Brand nos., store types

Ordinal Nos. indicate the relative positions of objects but not the magnitude of differences between them

Quality rankings, rankings of teams in a tournament

Preference rankings, market position, social class

Interval Differences between objects can be compared, zero point is arbitrary

Temperature (Fahrenheit) Celsius)

Attitudes, opinions, index nos.

Ratio Zero point is fixed, ratios of scale values can be compared

Length, weight Age, sales, income, costs

Descriptive statistics

Descriptive statistics use to organize and

summarize the data to draw meaningful

interpretations.

Descriptive statistics deal with the

enumeration, organization and graphical

representation of data.

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CONT…DESCRIPTIVE STATISTICS

Descriptive statistics includes-

Measures to condense data

Measures of central tendency

Measures of dispersion

Measures of relationship ( Correlation

coefficient)

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Measures to condense data

Frequency and percentage distribution through

tabulation and graphic presentation.

Table

Graphs and diagrams

Percentages

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Table Type

Frequency distribution

table

Contingency table

Multiple Response table

Miscellaneous table R Dh@ker, Lecturer, PCNMS

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FREQUENCY DISTRIBUTION TABLE

The data may be qualitative or quantitative

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The following are the weight in kg 48 medical students. Construct the frequency distribution table

50, 61, 70 71 63 34 75 80 45

56 57 58 60 62 72 78 48 50 63

64 67 52 52 54 55 56 57 70 71

72 73 64 65 66 67 62 63 65 52

60 54 56 58 57 61 81 82 80

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RELATIVE FREQUENCY

Relative frequency = Class frequency---------------------------Total frequency

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FREQUENCY DENSITY OF A CLASS

Frequency density of a class=frequency of the class------------------------------- width of the class

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105 100 109 106 122 103 122 107

102 105 103 100 119 116 120 122

115 119 118 109 103 108 106 107

104 103 105 102 106 103 109 114

122 114 100 116 115 110 120 100

117 120 107 116 119 122 122 107

106 117

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138 164 150 132 144 125 149 157 146 158 140 109 136 148 152 144 168 126 138 186 163 109 154 165 146 183 105 108 135 153 140 135 161 145 135 142 150 156 145 128

GRAPHS AND DIAGRAMS

Type

Bar diagram

Pie chart

Histogram

Frequency

polygon

Line diagram R Dh@ker, Lecturer, PCNMS

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Cumulative

frequency curve

Scattered diagram

Pictograms

Map diagrams

CONT…GRAPHS AND DIAGRAMS

Presentation of quantitative, continuous or measured data is through graphs. The common graphs in use are:-

Histogram Frequency polygon Frequency curveLine chart or graphCumulative frequency diagram Scatter or dot diagram

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Presentation of qualitative , discrete or

counted data is through diagrams. The

common diagrams in use are:-

Bar diagram

Pie diagram

Pictogram diagram

Map diagram or spot map R Dh@ker, Lecturer, PCNMS

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CONT…Graphs and diagrams

Measures of central tendency

Arithmetic mean

Median

Mode

Geometric mean

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MEASUREMENT OF CENTRAL TENDENCY

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Sl. no Data levelCharacteristics Measurement of central

tendency

1 NominalMeasured on scale of

frequency of categories Mode (Mo)

2 OrdinalMeasured on no scale but

can be ranked Median (Md)

3 IntervalMeasured on a scale with no

true zero Mean (M)

4 RatioMeasured on a scale with

absolute zero Mean (M)

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