Why Statistics ??????

1. Developing project.

2. New protocol or system.

3. Institutional data analysis.

4. Solving a specific problem.

5. Researches.

6. Exams for trainee.

In all this we have :1. Data collected

2. Human error

3. Decision to be taken

Definition of statistics

•It is logic that make use of mathematics in the science of collecting, analyzing and interpreting of data for the purpose of making decision.

•It is the science of making wise decision in the presence of uncertainty= variability. (a decision making tool).

Example of Fields that use statistics:

•Drug development.

•Preclinical and clinical studies.

•Chemical biological labs.

•Quality control.

•Consumer testing.

•Pharmaceutical research.

Steps of research

•Design of experiment.

•Data collection (specific).

•Data analysis.

• Interpretation of results:•Discussion

•Writing conclusion

Why we need to take sample?

• Population : all phenomenon under study. Eg: all hypertensive people.

• Sample : are chosen number from population so

• Sample must be representative to the whole population so that result gained from sample can be extrapolated to the population.

Population and sample

• Getting all phenomenon not possible.

• Time.

• Cost.

• Some tests are destructive.

Variable=المتغير• Is the measurement that exhibits variability.

Variability= تنوع/تغير

• Variability is a source of experimental errors and statistics aim to make decision as correct as possible in presence of error.

• Source of variability either between individuals or from different conditions (day &night, male &female, health &diseased )

Collected variable type 2 main types

Discrete data

Have countable number of possible

outcomes

Continuous data

Have unlimited number of possible

outcomes

Discrete data →Nominal data• Classified into groups in an unordered manner and with no

indication of relative severity.

• e.g:

1. male or female sex

2. mortality [dead or alive]

3. disease presence [yes or no]

4. Race (white, African , Asian)

5. marital status( married, single)

Discrete data →Ordinal data

•Ranked in a specific order but with no consistent level of magnitude of difference between ranks

•e.g:

•NYHA functional class describes the functional status of patients with heart failure.

•Child Pugh score

•Grades

Continuous data

• Continuous variables can take on any value within a given range.

• E.g:

• Weight

• Blood pr

• Blood glucose

• Temp

Probability (of error) • It is the chance that a given result would occur by random

sampling from a specific population.

• Usual = 5% (may be 1%, 10%)

Confidence interval • It is the interval within which we believe true mean lies.

Why???

• Becz. Mean and SD of sample are rarely equal to population parameters.

statistics

Descriptive

Visual Numerical

Central tendency

Variability

statistical inference

Hypothesis testing

For nominal data

frequencies

percentage

For ordinal data

frequencies

percentage

Median and mode

Non – parametric tests

For continuous data

Central tendency

• Mean, median, mode.

variability • SD, variance, SE, Range.

Hypothesis testing

• Statistical tests.

For continuous data (parametric tests)

One sample

• One sample T test

2 samples• Paired t test (dependant)

• 2 independent samples

More than 2 gps

• ANOVA test

SPSS program outline

Data view

Variable view

Output view

Syntax

Central tendency

Mean= average

Median

mode

Mean= average • Advantage : include all data in result

• Disadvantage: sensitive to outliers

Median= middle value or middle observation

• Arrange data

• For odd NO:M=(N+1)/2th

• For even NO:M=average of the 2 middle values

• Advantage :Insensitive to outliers

• EX: 7,8,6,9,5,6,10,→5,6,6,7,8,9,10 →M= (7+1)/2=4th = 7

Mode •Value with the greatest frequency

•Frist mode, second mode,………

N.B:• Use mean if results follow normal distribution• Use median if data is +ve or-ve skewed• Use mode for preference test

variability

Range

• (max-min)

• Depends only on 2 values

variance

• The mean squared deviation of values from their arithmetic mean.

Standard deviation

• Square root of variance.

• The higher the value the greater the variability around mean.

X AVER X-AVER [X-AVER]21 52 38.3 13.7 187.692 48 38.3 9.7 94.093 46 38.3 7.7 59.294 41 38.3 2.7 7.295 40 38.3 1.7 2.896 37 38.3 -1.3 1.697 37 38.3 -1.3 1.698 32 38.3 -6.3 39.699 26 38.3 -12.3 151.2910 24 38.3 -14.3 204.49∑ 383 ∑ 750.1

variance 83.34444444SD 9.129317852

Frequency distribution=التكرار

• For nominal and ordinal data it is easy.

• But for continuous data need manipulation before • We have to divide data by interval

• Calculate max and min values

• Divide max-min/ no of desired interval

Example: transform, visual bininigTraining

Wt of 50 rats

30 32 34 39 34

36 38 41 31 26

47 42 32 33 41

27 28 36 31 29

37 32 33 45 35

28 41 32 35 34

29 30 37 40 32

35 37 30 28 34

38 34 36 35 41

30 34 37 25 33

statistics

Descriptive

Visual Numerical

Central tendency

Variability

statistical inference

Hypothesis testing

Statistical Inference

Null hypothesis=H0

• No difference between study variables

Alternative hypothesis=Ha

• There is a significance difference between variables.

For continuous data (parametric tests)

One sample

• One sample T test

2 samples• Paired t test (dependant)

• 2 independent samples

More than 2 gps

• ANOVA test

Correlation

• It is the measure of association between 2 variables.

• It can answer the question ( can the value of one variable be used to predict the corresponding value of the other variable).

•We calculate → correlation coefficient = R

•R values varies between -1 and 1

•Example: tablet hardness.

Correlation

1. Direction (direct or inversely )

2. Strength•Weak (0<r<0.5)

•Medium(0.5<r<0.75)

•Strong(r>0.75)

3. Significance (H0: R=0)(Ha:R not=0)

Choosing the Appropriate Statistical Test Depends on the Following:

Type of data (nominal, ordinal, or continuous)

Distribution of data (e.g., normal)

Number of groups

Study design (e.g., parallel, crossover)

Presence of confounding variables

Parametric versus nonparametric tests