MEDICAL STATISTICSMEDICAL STATISTICSprof. Amany R. Abo-El-Seoud

DATA

SOURCESRecords, Census

Survey, Research studies(sampling)

PRESENTATIONTables

SummarizationGraphs

Analysis & interpretation

information

Planning for health programs

SamplingSampling

Objectives:

• List the benefits of sampling

• Describe types of sampling

• Enumerate factors affecting sample size

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

Types of samples

Non-probability

Probability

Accessibility

Quota

Simple random

systematic

stratified

cluster

multistage

QUIZQUIZ

How can you select a sample of 100 diabetic How 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 a How 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 females How 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?

SAMPLE SIZESAMPLE SIZE

Determinants :Determinants : Type of studyType of study Relative risk / Odd’s ratio /Prevalence of the Relative risk / Odd’s ratio /Prevalence of the

study problemstudy problem MoneyMoney TimeTime Equipments availableEquipments available

Sample size estimation for tests between Sample size estimation for tests between two independent sample proportions two independent sample proportions

Formula Formula

where where N= the sample size estimate N= the sample size estimate

Zcv=Z critical value for alpha (.05 alpha has a Zcv of 1.96) 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) Zpower=Z value for 1-beta (.80 power has a Z of 0.842) P1=expected proportion for sample 1 P1=expected proportion for sample 1 P2=expected proportion for sample 2 P2=expected proportion for sample 2

Sample size estimation for tests between Sample size estimation for tests between two independent sample means two 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

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 استدالل

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

Tests of significanceTests of significanceComparison 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

(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

(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

(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%

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

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

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

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 70

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Dose (mg/kg)

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Types of correlationTypes of correlation

+ve

-ve

No

• 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 (or by computer)

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

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

Thank you