1. Biostatistics ZMP 602 E_Mail: Atef@Sci.cu.edu.eg
Mathematical tools used to
Collect
Organize
Analyse
Present
To make Decisions
Interpret

2. TYPES OF STATISTICS Descriptive Inferential To Organize,
Display,
Describe data using tables, graphs
Use information from descriptive statistics to make decisions or predictions about a population

3. A selected portion from the studied population
Statistical Terms
Population
All sets of individuals, items, or objects whose the characteristics being studied.
Sample
A selected portion from the studied population
Population
Sample

4. Types Of Variables Variables
The characteristics (quantities or qualities) that the individuals of a population possess.
Types Of Variables
According to causal relationship
CAUSE (Factor)
(Independent Variable)
EFFECT (Response)
( Dependent Variable)

5. Arithmetic operations
TYPES OF VARIABLES
A. Quantitative Variables
Can be measured numerically (numeric variable)
Ex: Age (in years)
Arithmetic operations
(+, -, x, /)
Can be applied
Are measured in a unit that can be subdivided infinitely (Continuous Variables)

6. Religion: Muslim, Christian
TYPES OF VARIABLES
A. Qualitative Variables
Measured in a unit that can not be subdivided infinitely (Discrete Variables)
A.1. Nominal Level Variables
Scores are labels that Cannot be treated as numbers
Scores are labels that Cannot be ranked
Gender: male , Female
Race: White , Black
Religion: Muslim, Christian

7. TYPES OF VARIABLES A. Qualitative Variables
A.2. Ordinal Level Variables
Scores are non-numerical forms and can be ranked
Grades: Good, Very good, Excellent
Medals: Gold, Silver, Bronze

8. Measures of Central Tendency
Descriptive Statistics
Measures of Central Tendency

9. Variance 𝛔 𝟐 𝛔 𝟐 = 𝐱 𝟏 − 𝐗 𝟐 + 𝐱 𝟐 − 𝐗 𝟐 +…+ 𝐱 𝐧 − 𝐗 𝟐 𝐍
It is the arithmetic mean of the squared deviations from the mean of a statistical distribution.
Squared Deviation
𝛔 𝟐 = 𝐱 𝟏 − 𝐗 𝟐 + 𝐱 𝟐 − 𝐗 𝟐 +…+ 𝐱 𝐧 − 𝐗 𝟐 𝐍
Sample Size

10. Standard deviation 𝛔
It is the square rootof the variance ( 𝛔 𝟐 ).

11. Standard Error (S.E.) of Mean
It is the standard deviation of the sample mean divided by square root of sample size.
𝐒.𝐄.= 𝛔 𝐧
𝝈=𝟏.𝟔𝟖, 𝒏=𝟓
𝐒.𝐄.= 𝟏.𝟔𝟖 𝟓 =𝟎.𝟑𝟑𝟔

12. Normal (Gaussian) Distribution Curve
Bell shaped
Smooth
Symmetrical
Frequency 𝝁 x x x x
Population
99.7%
95.5%
63.8%
63.8%
95.5%
99.7%
+𝟑𝝈
+𝟐𝝈
+𝟏𝝈
−𝟏𝝈
−𝟐𝝈
−𝟑𝝈

13. SAMPLING Sample 2 Population Sample 1 𝐗 𝒊𝒔 𝒕𝒉𝒆 𝑺𝑨𝑴𝑷𝑳𝑬 𝒎𝒆𝒂𝒏 𝝁
𝐗 𝒊𝒔 𝒕𝒉𝒆 𝑺𝑨𝑴𝑷𝑳𝑬 𝒎𝒆𝒂𝒏
Sample 2
Population
Sample 1 S2 S1 𝝁
𝝁 𝒊𝒔 𝒕𝒉𝒆 𝑷𝑶𝑷𝑼𝑳𝑨𝑻𝑰𝑶𝑵 𝒎𝒆𝒂𝒏

14. Presentation of data Bar Chart
It is used to present all types of variables.
Parameter Value
Freq. A 6 B 4 AB 1 O 9
Frequency
Values of Variable

15. Pie Charts
A pie chart can be used to represent all types of variables, but is more commonly used for categorical variables.
The data is represented in a circle and the angle of each circular sector is proportional to the corresponding absolute frequency.
EXAMPLE
In a class of 30 students, 12 play basketball, 3 swim, 4 play football and the rest do not practice any sport.
𝜶= 𝟑𝟔𝟎 ∘ 𝑵 ∗ 𝒇 𝒊
Students
Angle
Basketball 12
144°
Swimming 3
36°
Football 9
108°
No sport 6
72°
Total 30
360°

17. HISTOGRAMS
A histogram is a graphic representation of a variable in the shape of bars (rectangles).
They are used for all types of variables with a large quantity of data that is grouped into classes.
The base width of the bars (rectangles) are proportional to the class widths and the height is the absolute frequency of each interval.
The surface area of every bar is proportional to the frequency of the represented values. ci fi Fi
[50, 60) 55 8
[60, 70) 65 10 18
[70, 80) 75 16 34
[80, 90) 85 14 48
[90, 100) 95 58
[100, 110)
110 5 63
[110, 120)
115 2

18. POLYGON Frequency HISTOGRAM Class intervals 16 14 12 10 8 6 4 2 50 602
Frequency
HISTOGRAM 50 60 70 80 90
100
110
120
Class intervals

19. X-Y Scatter Chart

20. Inferential Statistics HYPOTHESIS TESTS ON THE MEAN
BASIC STATISTICAL INFERENCE
HYPOTHESIS TESTS ON THE MEAN
TEST THE NULL HYPOTHESIS 𝑯 𝟎
𝑯 𝟎 : 𝝁= 𝝁 𝟎
𝑯 𝑨 : 𝝁> 𝝁 𝟎 ,
𝑯 𝑨 : 𝝁< 𝝁 𝟎 ,
𝑯 𝑨 : 𝝁≠ 𝝁 𝟎 ,
𝝁: 𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒎𝒆𝒂𝒏,
𝝁 𝟎 : 𝒂 𝒈𝒊𝒗𝒆𝒏 𝒇𝒊𝒙𝒆𝒅 𝒗𝒂𝒍𝒖𝒆