Biostatistics ZMP 602Mathematical tools used to Collect

Organize

Analyse

Present

InterpretTo make Decisions

E_Mail: Atef@Sci.cu.edu.eg

TYPES OF STATISTICS

To Organize, Display, Describe data using

tables, graphs

Use information from descriptive statistics to make decisions or predictions about a population

Descriptive Inferential

Statistical Terms

All sets of individuals, items, or objects whose the characteristics being studied.

A selected portion from the studied population

Population

Sample

Population

Sample

Types Of Variables

CAUSE (Factor)

(Independent Variable) EFFECT (Response)

( Dependent Variable)

According to causal relationship

VariablesThe characteristics (quantities or qualities) that the individuals of a population possess.

TYPES OF VARIABLESA. Quantitative Variables

Can be measured numerically (numeric variable)

Arithmetic operations (+, -, x, /)

Can be applied Are measured in a unit that can be subdivided infinitely

(Continuous Variables)

Ex: Age (in years)

TYPES OF VARIABLES

• Scores are labels that Cannot be ranked

A.1. Nominal Level Variables

A. Qualitative Variables

Gender: male , Female

Race: White , Black

Religion: Muslim, Christian

Scores are labels that Cannot be treated as numbers

Measured in a unit that can not be subdivided infinitely (Discrete Variables)

TYPES OF VARIABLES

• Scores are non-numerical forms and can be ranked

A.2. Ordinal Level VariablesA. Qualitative Variables

Grades: Good, Very good, Excellent

Medals: Gold, Silver, Bronze

Measures of Central Tendency •

 

 

Descriptive Statistics

Variance It is the arithmetic mean of the squared deviations from the mean of a

statistical distribution.

𝛔𝟐=(𝐱𝟏−𝐗 )𝟐+ (𝐱𝟐−𝐗 )𝟐+…+(𝐱𝐧−𝐗 )𝟐

𝐍

Squared Deviation

Sample Size

Standard deviation

It is the square rootof the variance (). 

Standard Error (S.E.) of Mean

It is the standard deviation of the sample mean divided by square root of sample size.

Freq

uen

cy

𝝁63.8%

−𝟏𝝈 −𝟐𝝈 −𝟑𝝈

95.5% 99.7%63.8%95.5%99.7%

+𝟏𝝈+𝟐𝝈+𝟑𝝈

xx

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Population

o Bell shapedo Smootho Symmetrical

Normal (Gaussian) Distribution Curve

PopulationS2S1

SAMPLING

Sample 1

Sample 2

𝝁𝒊𝒔 𝒕𝒉𝒆𝑷𝑶𝑷𝑼𝑳𝑨𝑻𝑰𝑶𝑵𝒎𝒆𝒂𝒏𝝁

𝐗 𝒊𝒔𝒕𝒉𝒆𝑺𝑨𝑴𝑷𝑳𝑬𝒎𝒆𝒂𝒏

Bar Chart

Parameter Value Freq.

A 6B 4

AB 1O 9

A B AB O0

2

4

6

8

10

Frequency

Values of Variable

o It is used to present all types of variables.

PRESENTATION OF DATA

Pie Chartso A pie chart can be used to represent all types of variables, but is more commonly

used for categorical variables.

o The data is represented in a circle and the angle of each circular sector is proportional to the corresponding absolute frequency.

𝜶=𝟑𝟔𝟎∘

𝑵∗ 𝒇 𝒊

EXAMPLEo In a class of 30 students, 12 play basketball, 3 swim, 4 play

football and the rest do not practice any sport.S tud ents Ang le

Basketb a l l 12 144°

S w imming 3 36°

Foo tb a l l 9 108°

No sp o r t 6 72°

To ta l 30 360°

Basketball Swimming Football No sport

HISTOGRAMSo A histogram is a graphic representation of a variable in the

shape of bars (rectangles).o They are used for all types of variables with a large quantity of

data that is grouped into classes.o The base width of the bars (rectangles) are proportional to the

class widths and the height is the absolute frequency of each interval.

o The surface area of every bar is proportional to the frequency of the represented values.

c i f i F i

[50, 60) 55 8 8

[60, 70) 65 10 18

[70, 80) 75 16 34

[80, 90) 85 14 48

[90, 100) 95 10 58

[100, 110) 110 5 63

[110, 120) 115 2 65

65

6050 70 80 90 100 110 120

16

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10

8

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0

2

Freq

uen

cy HISTOGRAM

POLYGON

Class intervals

40 50 60 70 80 90 100 110 1200

10

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X-Y Scatter Chart

BASIC STATISTICAL INFERENCEHYPOTHESIS TESTS ON THE MEAN

𝝁 :

TEST THE NULL HYPOTHESIS 𝑯𝟎 :𝝁=𝝁𝟎

𝝁𝟎 :

𝑯 𝑨 :𝝁>𝝁𝟎 , 𝑯 𝑨 :𝝁<𝝁𝟎 , 𝑯 𝑨 :𝝁≠𝝁𝟎 ,

Inferential Statistics