Statistics

• STATISTICS

• INTRODUCTION AND DEFINITIONS

• STATISTICS

• A field of study concerned with methods and procedures of:
• Collection, Organization, Classification & Summarization of data.
• (Descriptive Statistics)
• Analysis, and Drawing of inferences about a body of data when only a part of data are observed. ( Analytic Statistics)

• BIOSTATISTICS

• When the data being analyzed are derived from biological and medical sciences, the term “ Biostatistics” is used.

• ADVANTAGES

• 1. Carrying out a research
• Statistical analysis should be considered in the planning phase of the study
• 2. Evaluating published articles
• Statistical errors are common in clinical researches that may invalidate the conclusion.


• ADVANTAGES
• 3. Ethical consideration
• It is unethical to use erroneous statistics especially in scientific publications. Using harmful or ineffective treatment or avoidance of useful treatment can occur if the statistics is wrong.
• 4. Professional and personal satisfaction

• PURPOSES

• 1. Data reduction
• By condensing data to manageable proportions thus facilitating interpretation
• 2. Evaluate role of chance
• To see if the effect of a certain event is a real one
• 3. Sampling and generalization
• What proportion of discharged patients required readmission? What are their characteristics? The answer required generalization of the sample's result.

• APPLICATIONS

• Are the differences between groups significant?
• Are these two measures related or associated?
• Can one predict the value of one variable from knowledge of the values of other variables؟

Variables

A characteristic that takes on different values
things.eg.


• Variables

• Quantitative Variables

• Qualitative Variables

The variable

• that can be measured in the usual sense
of measurement
as age , weight, height,…

• It is the variable that can not be measured in the usual sense

• but can be described or categorized ..Socio-economic

• QUALITATIVE VARIABLE

• . eg.;
• - socio-economic groups.
• ill person with medical diagnosis
• In this case we count the number of individuals falling into each category as the socioeconomic status, diagnostic category,…

• Quantitative

• Variables


DISCRETE VARIABLE
• It is characterized by gaps or interruptions
• in the values
• that it can assume.

• CONTINOUS VARIABLE

• It does not posses the gaps or interruption, It can assume any value within a
• specified interval of values
• assumed by any variable

• - The number of daily

• admissions
• -The number of decayed, missing or filled teeth
• per child

• -Weight,

• -Height,
• -Mid-arm circumference

• VARIABLES SCALE

• 1. NOMINAL SCALE
• It uses names, numbers or other symbols. Each measurement assigned to a limited number of unordered categories and fall in only one category.
• eg. males & females


• 2. ORDINAL SCALE
• to assigned Each measurement
• a
• limited number of categories that are ranked in a graded order. ( 1st, 2nd, 3rd..)
• .

• VARIABLES SCALE

• 3. INTERVAL SCALE
• Each measurement is assigned to one of unlimited categories that are equally spaced with NO true zero point.

• 4. RATIO SCALE

• Measurement begins at a true zero point and the scale has equal intervals

• POPULATION

• POPULATION OF ENTITIES
• Largest collection of entities that had common characteristics for which we have an interest at a particular time.

• POPULATION OF VARIABLES

• It is the largest collection of values of a random variable for which we have an interest at a particular time.

• SAMPLE

• It is part or subset of the population
• Sample of entities:
• which is a subset of population of entities
• Sample of variables:
• which is subset of population of variables


• GROUPED DATA
• To group a set of observations, we select a set of contiguous, non overlapping intervals, such that each value in the set of observation can be placed in one, and only one, of the interval, and no single observation should be missed.
• The interval is called:
• CLASS INTEVAL.

• NUMBER OF CLASS INTERVALS

• The number of class intervals :
• Should not be too few because of the loss of important information. and
• Not too many because of the loss of the needed summarization .
• When there
• is a priori classification
• of that
• particular observation we can follow that classification ( annual tabulations), but when there is no such classification we can follow the
Sturge's Rule

• NUMBER OF CLASS INTERVALS

• Sturge's Rule:
• k=1+3.322 log n

• k= number of class intervals

• n= number of observations in the set


• The result should not be regarded as final, modification is possible

• WIDTH OF CLASS INTERVAL

• The width of the class intervals should be the same, if possible.

• R W = --------

• K

• W= Width of the class interval

• R= Range (largest value – smallest value) K= Number of class intervals

• FREQUENCY DISTRIBUTION

• It determines the number of observations falling into each class interval

• Frequency

• 10
• 23
• 33
• Fasting blood glucoselevels
• < 60
• 60-62
• 63-65
• 22
• 66-68
• 34
• 69-71
• 33
• 72+
• 155


• RELATIVE FREQUENCY
• DISTRIBUTION
• It determines the
• proportion of observation in the particular class interval relative to
• the
• total observations
• in the set.

• Frequency

• Fasting blood glucoselevels
• < 60
Relative frequency
%
6.45
14.84
• 10
• 23
• 60-62
• 21.29
• 33
• 63-65
• 14.19
• 22
• 66-68
• 21.94
• 34
• 69-71
• 21.29
• 33
• 72+
• 100
• 155


• CUMULATIVE FREQUENCY
• DISTRIBUTION
• This is calculated by adding the number of observation in each class interval to the number of
• observations in the
• class interval above,
• starting from the
• second class interval
• onward.

• Frequency

• Cumulative frequency distribution
• 10
• 33
• 10
• 23
• Fasting blood glucose levels
• < 60
• 60-62
• 66
• 33
• 63-65
• 88
• 22
• 66-68
• 122
• 34
• 69-71
• 155
• 33
• 72+
• 155


• S

• EXERCI

• E

• The followings

76
• 86
70
• 85
66

are the weights

55
• 73
49
79
56

(Kg) of 45 adult

62
• 65
77
78
71


• male individuals
• attending a
73
• 69
72
77
47

• primary health

88
• 58
• 68
59
73

• care centers:

90
• 99
55
• 64
85


41
• 63
54
• 68
66

52
• 63
48
90
85

72
• 65
• 83
• 80
71

1
76
• 10
86
19
70
• 28
• 85
37
• 66


2
55
11
73
20
49
• 29
• 79
38
• 56

3
62
• 12
65
21
77
• 30
• 78
39
• 71


4
73
• 13
69
22
72
• 31
• 77
40
• 47

5
88
• 14
58
23
68
• 32
• 59
41
• 73


6
90
• 15
99
24
55
• 33
• 64
42
• 85

7
41
• 16
63
25
54
• 34
• 68
43
• 66


8
52
• 17
63
26
48
• 35
• 90
44
• 85

9
72
• 18
65
27
83
• 36
• 80
45
• 71


• EXERCISE
• Construct a table showing:
• Frequency
• Relative frequency
• Cumulative frequency
• Cumulative relative frequency distribution.

• Number of class intervals:

• K=1+3.322 log n
• =1+3.322 log45
• =1+3.322 X 1.653
• =6.4
• =6
Width of class interval:

• R 99-41

• W= ------ = ------- = 9.7 = 10
• K 6

• CLASS INTERVAL (Kg)

• 40-49
FREQUENCY

4
• RELATIVE FREQUENCY
• %

8.9
• CUMULATIVE FREQUENCY

4
• CUM.REL. FREQUENCY
• %

8.9

• 50-59

7
• 15.6
11
24.5


• 60-69
• 11
• 24.4
22
48.9

70-79

• 13
• 28.9
35
77.8

• 80-89

7
• 15.6
42
93.4

• 90-99

3
• 6.7
45
100.1


Total
• 45
• 100.1

• Thanks