SPM Seminar

A presentation by Dr. Ritesh Malik Theni Govt. Medical College Tamil Nadu India For Community Medicine Department

Health Informational & Basic Medical Statistics TESTS OF SIGNIFICANCE

Distinction between data and information

Data

• Consists of discrete observation of attributes or events.

• It carries little meaning meaning when considered alone.

Information

• Data needs to be transformed into information by reducing them , summarizing them and adjusting them for variations .

Intelligence

• Information is transformed into intelligence which guides the decision makers , policy makers , planners and administrators .

To obtain the mean, the observations are first added together, and then divided by the number of observations.

Formula : =∑n

Mean is summation of all the observations and division by number of observations.

CONCEPT OF MEAN

CONCEPT OF MEDIAN Average of a different kind , which does not

depend upon the total and number if items , the data is first arranged in an ascending or descending order of magnitude, and then the value of the middle observation

is located , which is called the median. 79 is the median. This is for odd

number cases. 71

77

83

75

79

84

75

81

95

Median for even sets

71 75

77 79

75

81 83

90 95

84

80

The Mode The mode is the commonly occurring value in a

distribution of data. The mode or the most frequently occurring value

is 75. The advantage of mode are that it is easy to understand.

It is not affected by the extreme items. The mode in the case below is 85.

85 78

85 81

91

85 79

89 98

79

HEALTH INFORMATION AND BASIC MEDICAL STATISTICS

AS A GENERAL RULE THE MOST SUCCESSFUL MAN IN LIFE IS THE ONE WHO HAS THE BEST INFORMATION

STANDARD DEVIATIONIt is defined as the “ root –

means-square-deviation”. It is denoted by the greek letters sigma or by initials SD .

Formula :

S.D. = √∑ ( x - )

√n

this is the case when the sample size is more than 30.

when the sample size is less than 30 n-1 is used in the denominator.

2

The standard error of measurement or estimation is the standard deviation of the sampling distribution associated with estimation method.

It is given by the formula : stan. error =standard deviation √n

STANDARD ERROR

Significance of standard error

Since the distribution of the means follows the pattern of a normal distribution , thus it is taken that 95% of the sample means within the limits of 2 standard errors of

mean +or- 2 ( standard deviation ) √nOn either side of the true population or

mean. Therefore, standard error is a measure which enables us to judge whether the mean of a given sample is within the set confidence limits or not .

Normal distribution The area between one standard deviation

on either side of the mean ( x + - 1×S.D ) will cover 68% of the distribution approximately.

The area between 2 standard deviations on either side with a mean ( x + - 2×S.D ) will cover 95% of the distribution.

The area between ( x + - 3×S.D ) will cover 99.7 % of the values.

Thus the confidence limits increase with the multiple of the standard deviation.

Graphs for normal distribution

TESTS OF SIGNIFICANCE

STANDARD ERROR OF THE MEAN

STANDARD ERROR OF

PROPORTION

STANDARD ERROR OF

DIFFERENCE

STANDARD EROR OF

DIFFERENCE BETWEEN 2

PROPORTIONS

STANDARD ERROR OF THE MEAN

In order to set up the confidence limits within which the mean of the population is likely to lie , standard error of mean is taken.

Example: random sample of body temperature of 25 males is taken. The mean is 98.14degree F with a S.D. of 0.6.

Thus the standard error as the yardstick would be :

S.E. = standard deviation √n

Continuation of the example

Thus S.E. = 0.6 √25 = 0.12 if the limits are set out at twice the standard

error from the mean ( 95 % confidence limits ) the range of the population would be

98.14+ - (2×0.12) thus range in which most of the population will

lie is 97.90-98.38 degree F . The chances will be that only 1 in 20 people will be outside this range ( 95%).

Thus when we come across the word significant , it means that the difference is significant or it is unlikely to be merely due to chance.

STANDARD ERROR OF PROPORTION

• Let us suppose that the proportion of males in a certain village is 52%. A random sample of 100 people was taken and the proportion of males was found to be only 40%.

• Thus for checking the confidence limits of the survey the standard error of proportion is done.

• Formula : S.E. ( proportion ) = √ pq n

Standard error of proportion continued p – proportion of males. q – proportion of females. n – size of sample. S.E. = √ 52 × 48 = 5.0 √ 100 we take 2 standard errors on either side of 52 as our

criterion, i.e. if the sample is a truly representative one , we might get by chance a value in the range 52+2(5) = 62 or 52-2(5)= 42 .

Thus the range in confidence limits is 62-42. Since the observed proportion was only 40% and well

outside the confidence limits thus there is a significant error.

This significant test is valid when only 2 classes or proportions are compared.eg. Males n females , sick n healthy etc.

STANDARD ERROR OF DIFFERENCE BETWEEN TWO

MEANS Very often in biological work the investigator is faced with

the problem of comparing results between 2 groups specially when the control experiment is performed along with the other experiment.

it is performed to analyze whether the difference between the 2 mentioned groups is significant or not.

Example : a pharmacological experiment is carried on 24 mice, these were divided into 2 groups. Group A was control group with no treatment , group B was exposed to the drug. At the end of the experiment the mice were sacrificed and their kidney weighs were tabulated. Number mean Standard

deviation

CONTROL group

12 318 10.2

EXPERIMENT group

12 370 24.1

SE BETWEEN THE MEANS FORMULA

S.E. = √ S.D1 n1 + S.D 2 n2 Putting the values from the

experimentation ; =√8.67 + 48.4 = √57.07 = 7.5 The standard error of difference between the two

means is 7.5/ the actual difference between the two means ( 370-318) = 52 , which is more than twice the standard error of difference between the 2 means and therefore is significant. We conclude that treatment has affected the kidney weighs.

STANDARD ERROR OF DIFFERENCE BETWEEN

PROPORTIONS In this instead of means we test

the significance of difference between 2 proportions or ratios to find out if the difference between the 2 proportions or ratios is by chance or not.

Example : trial of 2 whooping cough vaccines data are tabulated below , we have to find the standard error of difference.

Continued ( mathematical expression ) : From the data below it appears that

vaccine B is superior to vaccine A . S.E. ( difference between two

proportions) formula

= √p1q1 n1 + p2q2 n2

Substituting the above values we get the standard error as 6.02. whereas the observed

Continuation of calculation of S.E. of difference between proportion : Difference ( 24.4-16.2 ) was 8.2.

the observed difference between the 2 groups is less than twice the S.E. of difference i.e 2 × 6 = 12 .

Thus the observed difference might be due to chance and not significant.

Alternatively we can use the chi square test for this method of test of significance.

Chi square test Chi square test is an alternative method of

testing the significance of difference of 2 proportion. It has the advantage that it can be used when more than 2 groups are compared.

The previous example of the whooping cough vaccine is taken and the following procedure is followed :

1. TEST THE NULL HYPOTHESIS : this hypothesis assumes that there was no

difference between the effect of 2 vaccines, and then proceed to test the hypothesis in quantitative terms.

O ( observed ) , E ( expected ) is tabulated.

Continued chi square test 2. Applying the chi square test : chi = ∑ ( O – E )

E

3. Finding the degree of freedom : d.f. = ( c-1) ( r-1 ) c – number of columns in the table. d – number of rows in the chart. 4. Probability tables : we then turn to the

probability tables for the analysis of the standard error of difference between the proportions.

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A PRESENTATION BY

Ritesh Malik