Statistics- by Dr.Asma Rahim and Dr.Bindu Vasudevan

1. Interpretation of statistical values
&
fundamentals of epidemiology
Dr.Asma Rahim
Dr.Bindhu vasudevan
Dept. of Community Medicine

2. What you are expected to Know?
• Mean
• What is SD ?
• What is SE?
• What is Confidence limits as noted
in many journals?

3. • What is P value ?How to interpret it?
• Which are the different statistical tests to be
applied on different situations?
• Study designs in Medical research.
• Measurements of risk in clinical research
• What is sensitivity ,Specificity, Predictive
value of a test?

4. Dilemma of a PG Student!!!
•DNB exams more stress on Original work.
•Methodology of your work is important.
•Look ahead for statistical queries.
•Examiners familiar with research designs
•OSCE stations have questions on
Statistics.

5. Types of variables
• Qualitative
– Dichotomous
– Nominal
– Ordinal
• Quantitative
– Discrete
– Continuous

6. 1. Which is a qualitative variable
• a) BMI
• b) S. bilirubin
• c) Name of residing place
• d) Blood urea

7. 2. Which is a quantitative variable
• Causes of deaths
• Religious distribution
• Age group distribution
• Age distribution

8. 4. Which is an ordinal variable
• A)Blood pressure
• B)Name of residing place
• C)Grading of carcinoma
• D) temperature

9. 5. Which is not a nominal scale
variable
• A)Causes of death
• B) religion
• C)diagnosis
• D)visual analogue scale

10. Quantitative data Qualitative data
Hb in gm% Anemic/non anemic
Height in cm Tall/short
B.P in mm of Hg Hypo/normo/
hypertensives

11. In a group of 100 under five children
attending IMCH O.P the mean weight is
15kg. The standard deviation is 2.
1.In what range 95% of children’s weight
will lie in the sample?
2. In what range the mean weight of all
children who are attending IMCH OP
will lie?

12. Range in which 95% children’s weight in the
sample will lie:
95% reference range =
mean +/- 2SD = 13-17Kg
Range in which 95% children’s weight
attending IMCH O.P will lie:
95% Confidence interval =
mean +/- 2SE( Standard error)-

13. Standard Error
17
19
16
17kg
18
15

14. Central limit Theorem
• Central limit theorem states that
• The random sampling distribution of
sample means will be normal distribution
• Means of random sample means will be
equal to population mean
• The standard deviation of sample means
from population mean is the standard error

15. • The PEFR of 100, 11 year old girls follow a
normal distribution with a mean of 300 1/min,
standard deviation 20 l/min and standrd error of
2 l/min
• What will be the range in which 95% of the girl’s
PEFR will lie in the sample?
• What will be the range in which mean of the
population will lie from which the sample was
taken?

16. Range in which 95% of girls PEFR in the
sample will lie:
mean +/- 2SD = 260 - 340
Range in which mean PEFR Value will lie:
mean +/- 2SE( Standard error)- 95%
Confidence interval = 298-304

17. Normal distribution curve
•

18. Sample size
• Calculate the sample size to find out the
prevalence of a disease after implementing
a control programme with 10% allowable
error. Prevalence of the disease before
implementing the programme was 80 %

19. Sample size
• Qualitative data N = 4pq/L2
• P = positive factor /prevalence/proportion
• Q = 100 – p
• L = allowable error or precision or
variability
• Quantitative data N = 4SD2/L2

20. • N= 4 x 80 x 20/8 x 8 = 100

21. • Determine the sample size to find out the Vitamin A
requirement in the under five children of Calicut
district . From the existing literature the mean daily
requirement of the same was documented as 930 I.U
with a SD of 90 I.U. Consider the precision as 9.

22. • N = 4SD2/L2
• 4 x 90 x 90 /9 x9 = 400

23. • Determine the sample size to prove that
drug A is better than drug B in reducing the
S.Cholesterol. The findings from a previous
study is given
Drug Mean SD
A 215 20
B 240 30

24. • Quantitative data N =
(Zα + Zβ )2 x S2 x 2 /d2
Zα = Z value for α level = 1.96 at α 0.05
Zβ = Z value for β level =1.28 for β at 10%
S = average SD
d = difference between the two means

25. • Qualitative data N =
(Zα + Zβ )2 p x q /d2
Zα = Z value for α level = 1.96 at α 0.5
Zβ = Z value for β level =1.28 for β at 10%
P = average prevalence
d = difference between the prevalence

26. Reject Accept
Null hypothesis Null hypothesis
Null hypothesis Type 1 error Correct
true (alpha error) decision
Null hypothesis Correct Type 2 error
false decision (Beta error)

27. • Alpha = 1.96.
• Beta = 0.1 to 0.2 or 10 to 20%.
• Power of the study = 1- beta error
• Strength at which we conclude there is no
difference between the two groups.

28. Statistical test chosen depends on----
• Whether comparison is between
independent or related groups.
• Whether proportions or means are being
compared.
• Whether more than 2 groups are compared.

29. Deciding statistical tests?
• In a clinical trial of a micronutrient on
growth, the weight was measured before
and after giving the micronutrient.. Which
test will you use for comparison?
• paired t test
• F test
• T test
• Chi square test

30. Parametric and Nonparametric tests
Parametric: When the data is normally
distributed.
Nonparametric : When data is not normally
distributed,usually with small sample size.

31. Common statistical tests
Design Nature of variable Statistical test Statistic derived
Two independent Qualitative (nominal) Chi square Chi square
Groups Quantitative (continous) Student t test t
Two related
groups Qualitative (nominal) Chi square Chi square
Quantitative (continous) Paired t test t
More than 2 Qualitative (nominal Chi square Chi square
Independent Quantitative (continous) Anova F
groups

32. Difference in proportion Chi-square test, Z test,
Difference in mean(Before Paired t test
and after comparison-same
group)
Difference in mean (two Unpaired t test, If sample
independent groups) > 30-Z test
More than 2 means(> 2 Anova
groups)
Association Spearman correlation
Prediction regression

33. Non parametric tests
Chi-square test
Fishers test,
Mc Nemar test
Wilcoxon Signed rank test Paired t test
Wilcoxon test , Mann- independent t test
Whitney U , Kolmogrov
Kruskal-wallis test Anova

34. The most appropriate test for
comparing Hb values in the adult
women in two different population of
size 150 and 200 is
• A) t test
• B) Anova
• C) Z test
• D) Chi square test

35. Answer
• C
– Two groups
– >30
– Continuous variable
– Comparing mean

36. The most appropriate test to
compare birth weight in 3
different regions is
• A) t test
• B) Anova
• C) Z test
• D) Chi square test

37. Answer
• B
– Continuous variable
– Compare means
– > 2 groups

38. The most appropriate test to
compare BMI in two different
adult population of size 24 and
30 is
• A) Two sampled t test
• B) Paired t test
• C) Z test
• D) Chi square test

39. Answer
• A
– Two different groups
– Continuous variable
– Size <30

40. The association between smoking
status and MI is tested by
• A) t test
• B) Anova
• C) F test
• D) Chi square test

41. Standard drug used 40% of patients responded
and a new drug when used 60% of patients
responded. Which of the following tests of
parametric significance is most useful in this
study?
• A) Fishers t Test
• B) Independent sample t test
• C) Paired t test
• D) Chi square test.

42. • A consumer group would like to evaluate
the success of three different commercial
weight loss programmes. Subjects are
assigned to one of three programmes
(Group A , Group B ,GROUP C) . Each
group follows different diet regimen. At
first time and at the end of 6 weeks subjects
are weighed an their BP measurements
recorded.

43. Test to detect mean difference in
body weight between Group A &
Group B
• T-TEST
• Difference between means of two samples

44. Is there a significant difference in body
weight in Group A at Time 1 and Time
2?
• Paired T Test
• Same people sampled on two Occasions.

45. Is the difference in body weight of subjects in
Group A,GROUP b ,group C significantly
different at Time 2
• Analysis of variance

46. Is there any relation between blood pressure
and body weight of these subjects?
• Correlation

47. Correlation coefficient
• Shows the relation between two quantitative
variable
• Shows the rate of change of one variable as
the other variable change
• The value lies between –1 to + 1
• Correlation coefficient of zero means that
there is no relationship

49. No.of deaths in 8 villages due to
water borne diseases before &
after installation of water supply
system
• Villages: 1 2 3 4 5 6 7 8
• Before :13 6 12 13 4 13 9 10
• After :15 4 10 9 1 11 8 13

50. Did the Installation of water
supply system significantly
reduce deaths
• Small sample size
• Distribution is not normal
• Non parametric test
• Wilcoxon signed rank test

51. For treatment of Hepatitis A 7
patients treated with herbal
medicines& 7 patients treated with
Allopathic symptomatic management.
S.Br values after 10 days of treatment
is given below
• Herbal :9 6 10 3 6 3 2
• Allopathy: 6 3 5 6 2 4 8

52. Is herbal treatment is better than
allopathic treatment?
• Small sample size
• Distribution is not normal
• Non parametric test
• Mann- Whitney test

53. After applying a statistical test an
investigator get the p value as
0.01. It means that
• A)The probability of finding a significant
difference is 1%
• B) The probability of finding a significant
difference when there is no difference is 1%
• C) The difference is not significant 1%
times and significant 99% times
• D) The power of the test used is 99%

54. Answer
• B
• Null hypothesis states there is no difference,If
there is any difference it is due to chance
• P value = If the null hypothesis is true the
probability of the sample variation to occur by
chance
• P value 0.05= probability of the sample variation
by chance is only 5% if null hypothesis was true
• 95% the sample variation is not due to chance,&
there is a difference. So we will reject NH

55. • P = 0.01 - probability of the sample
variation by chance is only 1% if null
hypothesis was true
• 99 % the sample variation is not due to
chance,& there is a difference. So we will
reject NH
• As p value decreases the difference become
more significant
• For practical purpose p value < 0.05 ; the
difference is significant

56. In assessing the association between
maternal nutritional status and Birth
weight of the newborns two investigators
A and B studied separately and found
significant results with p values 0.02 &
0.04 respectively. From this what can you
infer about the magnitude of association
found by the
two investigators

57. Type of study Alternative Unit of study
name
Descriptive Case series Prevalence
Cross sectional study Individual
Longitudinal Incidence study
Correlational
Analytical Ecological Case reference Populations
studies Case control Follow up Individuals
(observational Cohort Individuals
Analytical studies Randomised Clinical trial Patients
(interventional) controlled trial Community Healthy people
Field trial intervention
Community Community Healthy people
trials

58. Study questions and appropriate designs
Type of question Appropriate study design
Burden of illness Cross sectional survey
Longitudinal survey
Causation, risk and Case control study, Cohort study
prognosis
Occupational risk, Ecological studies
environmental risk
Treatment efficacy RCT
Diagnostic test Paired comparative study
evaluation
Cost effectiveness RCT

59. Odd’s ratio
• In a study conducted by Gireesh G N etal
about the ‘Prevalence of Worm infestation
in children”,50 children in anganwadi were
examined. Out of this 5 had worm
infestation. 2 out of this 5 have a history of
pet animals at home while 21 out of the 45
non infested has a history of pet animals at
home. Is there any association between pet
animals and worm infestations?

60. Study design –Case control
• Measure of risk –Odd’s ratio

61. • Set up a 2x2 table Worm infestation
+ -
a b
+ 2 21
Pet animals
- c d
3 24

62. • Odd’s ratio = ad /bc
• 2 x 24 = 0.76
21 x3

63. Interpretation
• OR =1,RISK FACTOR NOT RELATED
TO DISEASE
• OR <1 ,RISK FACTOR PROTECTIVE
• OR >1 RISK FACTOR POSITIVELY
ASSOCIATED WITH DISEASE

64. Relative risk
• In a study to find the effect of Birth weight
on subsequent growth of children , 300
children with birth weight 2kg to 2.5 kg
were followed till age 1 . A similar number
of children with birth weight greater 2.5 kg
were followed up too. Anthropometric
measurements done in both groups. Results
are shown below

65. Low birth weight Normal
No.children studied 300 300
No.malnourished
At age one 102 51

66. Study design –Cohort study
• Measure of risk –Relative risk ,Attributable
risk.
• Relative risk –Incidence among exposed
Incidence among nonexposed
= 102/300 = 0.34 = 2
51/ 300 0.17
Inference ?

67. • An out break of Pediculosis capitis being
investigated in a girls school with 291
pupils.Of 130 Children who live in a nearby
housing estate 18 were infested and of 161
who live elsewhere 37 were infested. The
Chi square value was found to be 3.93 .
• P value = 0.04
• Is there a significant difference in the
infestation rates between the two groups?

68. Results of a screening test
Disease
Positive Negative
Positive TP(a) FP(b)
Test
Negative FN© TN(d)

69. Features of a screening test
Sensitivity = a/ a+c
Specificity = d/b+d
Positive predictive value = a/a+b
Negative predictive value = d/c+d
False positive rate = bb+d
False negative rate = c/a+c

70. In a group of patients presenting to a hospital emergency
with abdominal pain, 30% of patients have acute
appendicitis, 70% of patients with appendicitis have a
temperature greater than 37.50c and 40% of patients
without appendictis have a temperature greater than
37.50c. Considering these findings which of the
following statement is correct ?
a) Sensitivity of temperature greater than 37.50c as a
marker for appendicitis is 21/49
b) Specificity of temperature grater than 37.50c as a
marker for appendicitis is 42/70
c) The positive predictive value of temperature greater
than 37.50c as marker for appendicitis is 21/30
d) Specificity of the test will depend upon the
prevalence of appendicitis in the population to which it
is applied.

71. Sensitivity and Specificity
+
Appendicitis -
21a 28b
Fever > 37.50c +
- 9c 42d
30a+c 70b+d

72. • Sensitivity = a/a+c - 21/30=70%
• Specificity = d/b+d = 42/70=60%
• Positive predictive value = a/a+b =
21/49=43%
• Negative predictive value = d/c+d = 42/51

73. Exercise 11
Disease prevalence in a population of
10,000 was 5%. A urine sugar test with
sensitivity of 70% and specificity of 80%
was done on the population. The positive
predictive value will be :
a)15.55% b) 70.08% c) 84.4%
d)98.06%

74. • Total population = 10,000
• Disease prevalence = 5%
• No diseased = 500
• Applying this to a 2x2 table :

75. 2x2 table
+ -
+ TEST 350 a 1900 b 2250
- 150c 7600d 7750
500 9500 10000

77. All the Best!!1