- A sample is a small group selected from a population to represent that population. Sampling provides benefits like being less time-consuming, less expensive, and allowing results to be repeated. - There are two main types of samples: probability and non-probability. Probability samples include simple random, systematic, stratified, and cluster samples. Sample size is determined based on factors like the type of study, expected results, costs, and available resources. - Inferential statistics allow generalization from a sample to a population through hypothesis testing and significance tests. Tests include t-tests, F-tests, chi-squared tests, and correlation/regression to analyze relationships between variables. Significant results suggest differences are likely not due to chance

1. MEDICAL STATISTICSMEDICAL STATISTICS
prof. Amany R. Abo-El-Seoud

2. DATA
SOURCES
Records, Census
Survey, Research studies
(sampling)
PRESENTATION
Tables
Summarization
Graphs
Analysis &
interpretation
information
Planning for health programs

3. SamplingSampling
Objectives:
• List the benefits of sampling
• Describe types of sampling
• Enumerate factors affecting sample size

4. Definition:
• A sample is a small group of population
(people or things) selected carefully to be
representative for that population
Benefits :
Less time, less effort, less expensive
Can be repeated

5. Types of samples
Non-
probability
Probability
Accessibility
Quota
Simple random
systematic
stratified
cluster
multistage

6. QUIZQUIZ
 How can you select a sample of 100 diabeticHow can you select a sample of 100 diabetic
patient from the outpatient clinic?patient from the outpatient clinic?
 How can you select 200 student from aHow can you select 200 student from a
primary school (all students are 4000)?primary school (all students are 4000)?
 How can you select 50 males and 50 femalesHow can you select 50 males and 50 females
from faculty employee (their number is 2000)from faculty employee (their number is 2000)
 How can you select a village from sharkia?How can you select a village from sharkia?

7. SAMPLE SIZESAMPLE SIZE
Determinants :Determinants :
 Type of studyType of study
 Relative risk / Odd’s ratio /Prevalence of theRelative risk / Odd’s ratio /Prevalence of the
study problemstudy problem
 MoneyMoney
 TimeTime
 Equipments availableEquipments available

8. Sample size estimation for tests betweenSample size estimation for tests between
two independent sample proportionstwo independent sample proportions
 FormulaFormula

wherewhere
 N= the sample size estimateN= the sample size estimate
Zcv=Z critical value for alpha (.05 alpha has a Zcv ofZcv=Z critical value for alpha (.05 alpha has a Zcv of
1.96)1.96)
Zpower=Z value for 1-beta (.80 power has a Z ofZpower=Z value for 1-beta (.80 power has a Z of
0.842)0.842)
P1=expected proportion for sample 1P1=expected proportion for sample 1
P2=expected proportion for sample 2P2=expected proportion for sample 2

9. Sample size estimation for tests betweenSample size estimation for tests between
two independent sample meanstwo independent sample means
where
N= the sample size estimate
Zcv=Z critical value for alpha (.05 alpha has a Zcv of
1.96)
Zpower=Z value for 1-beta (.80 power has a Z of
0.842)
s=standard deviation
D=the expected difference between the two means

10. INFERENTIAL STATISTICSINFERENTIAL STATISTICS
Objectives:
• Understand the meaning of inference,
hypothesis testing
• Identify different types of statistical tests
Inference = generalization of results
obtained from sample -‫استنتاج‬ ‫استدلل‬

11. Inferential StatisticsInferential Statistics
• Put a hypothesis
X = Y H0 or X >Y H1 or Y>X H2
• Collect, analyze data
• Test ur hypothesis using tests of significance:
Comparison of mean values : t , F tests
(used for numeric continuous data)
Comparing qualitative values: chi square test (for
discrete, ordinal and categorical data)
• Finding relations between different variables
using Correlation & regression tests

12. Tests of significanceTests of significance
Comparison of mean valuesComparison of mean values
(1) Z test: for normally distributed data and
the sample size >60
z= mean of popul- mean of sample /SD
If z>2 ( outside the C.I.) then the sample
differs from population and lies in 5% out
the normal distribution curve

13. (2) student’s t test
Comparing 2 sample means
For small sample size (6 – <60)
Degree of freedom= n1 + n2 - 2
Search for the difference in t tables
under d.f at 0.05 level

14. (3) Paired t test: comparing paired data or
data for the same person before and
after intervention
pt= 1st
reading – 2nd
reading/sq r of SD2 of
difference/number of sample
d.f=n - 1

15. (4) F or ANOVA test: to compare more than
two sample means.
Significant test means that there is real
difference between groups not because of
chance. i.e the probability of chance in this
difference < 5%

16. For qualitative data
(1) Chi squared test : to find significant
relation between 2 variables or order
distributions or categorical data.
(2) Difference between proportions
as t test but use percentage instead of
mean values

17. Correlation testCorrelation test
To find a relation between 2/more variables in
direction & strength (one is dependent =
response. It is plotted on the y axis) &(the
other/s is independent = explanatory or risk.
It is plotted on the x axis)
• Correlation does not mean causation.
• Spurious correlation: significant statistically
but insignificant clinically

18. Steps for simple correlation test:Steps for simple correlation test:
1- choose the 2 variables from your data
that you think they make a relationship
that support the aim of study.
2- do a scatter diagram from the drawing
window for the selected 2 variables.
3- if the scatter diagram shows an
association so you can do correlation test
to get level of significance of that
relationship

19.  In studying the relationship between two variables it is
advisable to plot the data on a graph as a first step. This allows
visual examination of the extent of association between the
variables.
 The chart used for this purpose is known as a scatter diagram
which is a graph on which each plotted points represents an
observed pair of values of the dependent (Y) and independent
(X) variables.
Scatter diagram:
Regression and correlation analysis
0 1 2 3 4 5 6 7
0
1
2
3
4
5
6
7
Dose (mg/kg)
Numberofdeadanimals

20. Types of correlationTypes of correlation
+ve
-ve
No

22. • Significant correlation means that there is
association between the studied variables.
As wt with age, BP with Na, cortisone level
with blood sugar.
• Significant correlation is calculated by
T= r * √ n-2 / 1-r2 (orbycomputer)

23. Coefficient of correlation “r” ranges from 0 to 1 It is
either +ve or -ve in direction
(r=0.5 p=0.02), (r=- 0.6,p=0.01) (r= 0.1,p=0.98)
Coefficient of determination R 2
: to quantify the variation of
one variable that is contributed to the other variable.
Types of correlation: I) single (simple) & multiple
II) Pearson : numeric, normally distributed,linear
Spearman : ordinal, non linear,not normally distributed

24. Regression analysis:Regression analysis:
To predict a dependent variable from another
known variable (s).
• Linear: dependent = intercept +/- b coefficient x
independent variable
e.g. birth wt = y +/- b x gestational age
= 2000 + 5 x 36
• Multiple
e.g. Birth wt= y +/- b1*gest+/- B2*HC

25. Thank you