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Biostatistics ZMP 602Mathematical tools used to Collect
Organize
Analyse
Present
InterpretTo make Decisions
E_Mail: [email protected]
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
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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
14
12
10
8
6
4
0
2
Freq
uen
cy HISTOGRAM
POLYGON
Class intervals
40 50 60 70 80 90 100 110 1200
10
20
30
40
50
60
70
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