The document discusses various statistical concepts relevant to pharmacology, including types of variables (nominal, ordinal, discrete, continuous), measures of central tendency, and tests of significance (parametric and non-parametric). It outlines different statistical tests like t-tests, ANOVA, and chi-square tests, explaining their applications and relevance in analyzing data in biomedical research. Additionally, it touches on regression analysis and survival analysis techniques applicable in clinical studies.

1. Dr.M.S.Ahil,
Assistant Professor
Institute of Pharmacology
Madurai Medical College

3. Statistics is a science of numbers

5. Variables
Qualitative
1.Nominal ( gender)
2.Categorical (Colour of hair)
Quantitative
1.Ordinal (Worse; Unchanged ; Improved)
2.Discrete (No of children per family)
3.Continuous (Hb%; birth weight)

6. Nominal: Qualitative
Can not be described numerically
There will be only 2 types
Ex: sex; Having cancer or not
Categorical: Like nominal
But more than 2 categories
Ex;Colour of hair; blood groups

7. Ordinal: Worse; Unchanged ; Improved
Discrete: A variable which can take the value of integer alone
Ex:No of children per family
Continuous:It can take any possible value
Ex: Hb%; birth weight
Quantitative

9. Measure of central tendency
Mean
Arithmetic Mean
Geometric Mean
Harmonic Mean
Median
Mode

10. Nth root of the product of N items
For large series log values can be find out added and divided by N
and antilog can be calculated
(Log G.M =log X1+logX2+log X3)/N
Used in dose response curves frequently
Geometric Mean

11. Reciprocals of no of items (replicates) in each sample are
added
Reciprocal of the arithmetic mean of them is found out
HM= N/1/k1+1/k2+…..1/kn)
Harmonic mean of 5,9,4,7
=4/(1/5+1/9+1/4+1/7)
This is used in Dunnets test
Harmonic Mean

12. Why should we measure variation?

13.  Group I
 3
 4
 2
 5
 4
 5
 5
 4
 5
 3
 Mean=40/10=4
 Group II
 1
 13
 2
 10
 2
 3
 2
 0
 6
 7
 Mean=40/10=4

14. Measures of Dispersion
Standard Deviation
Sd2 = Ʃ (x-x) 2 /n-1
= Ʃ x2 - (Ʃ x) 2 /n
n-1
S = √Sd2/ n−1
Standard Error = sd/√N
Significance: SE will decrease if no of samples increase.
Larger sample size is better

16. Normal or Gaussian Distribution
Distribution:
The no of subjects with values in specified short intervals
are plotted against the intervals
Normal Distribution:
It is bell shaped & symmetrical
Mean.mode,median coincide
95% of values fall within 2 sd from median
Eg: pulse rate; birth weight

18. Tests of Significance
Parametric
When there is a parameter
The distribution is normal
Non Parametric
Without mathematical calculations
No assumption is made about the distribution

19. Parametric tests
1.Students t test Unpaired
Paired
2.Analysis of variance (ANOVA) - One way/ Two way
3.Pearson correlation

20. Non Parametric Test
1. Chi square test /Fisher’s exact test
2 Wilcoxon’s test-
Signed Rank test (Paired data)
Two sample rank test (Unpaired data)
(Mann- Whitney test)
3.Kruskal Wallis / Friedman
4. Spearman Rank Test

21. Chi-square
Developed by Karl Pearson
Developed from Greek letter chi (χ)
Pronounced as kye
Used when relation between nominal and categorical variables are
tested
Eg: Smoking and cancer
Social class and filariasis
State of nutrition and intelligence quotient

22. Professor Gosset
Pen name “student”
Quantitative samples
Small samples ≤ 30
Normal distribution

23. t= mean difference/SE of mean difference
Calculate degree of freedom (n1+n2-2)
Refer t table at that degree of freedom
If the value exceed or equals that is considered as significant
P should be significant at 0.05 level or less than that
P< 0.05- the difference occuring by chanceis less than
5% of cases

26. 1. Between subject comparison (unpaired t test)
Testing the difference of effect of acetylcholine in
producing contraction of isolated ileum in normal
and morphine treated mouse
2.Within subject comparison (paired t test)
The difference of weight before and after treatment of
anorectic compound in 10 rats

28. Z test
It is comparing one location test with the mean of the
general population
A comparative study of dalteparin and UFH in patients
with unstable angina
It is used when the sample size is large
And the standard deviation is known

29. Wilcoxon’s Signed Rank Test (Paired data)
Rank the values
Average values given for tied values
The respective signs are attached
Plus and minus ranks are added separately
Smaller total is taken
Referred in the table for paired samples against no of pairs
The changes in Hb% after iron supplementation for 9
hospitalised children

30. Mann-Whitney Test
Two sample Rank Test (unpaired Data)
Same as above
Sample of one from other is distinguished by underlining
Smaller total is referred against no of items in that sample
No of newborns observed in two groups of rat fed with 2 types of protein
rich foods

31. Efficacy and safety of polymyxins in critically ill patients with
renal disease
AKI NonAKI
Sex
CHI square
Age
Students t test
Duration of therapy in days
APACHE
Adjusted Mortality
Mann whitney

32. Rats Control Amnesia
group
Piracetam+
Scopolamine
Modafinil +
scopolamine
R1 12 6 7 8
R2 11 7 8 7
R3 13 6 9 9
R4 11 5 9 7
R5 12 6 6 9
R6 12 7 8 8

33. ANOVA
Compares variance of two or more samples
Compare variations between the groups with those within groups
F =MSGr/MSEr
MSGr mean square between groups
MSEr mean square within groups
Eg: Neuroprotective effect of 3 doses of gossypin against
global cerebral ischemia model in rats

34. Posthoc analysis
Tukeys correction: For equal sample size
Newman Keuls test: If the means are very different
Fisher’s exact test: It is multiple t test
Bonferroni post test

35. Dunnett’s
ANOVA says there are differences between the groups but not
which group differ from the other
Dunnett is a post hoc analysis for that purpose
td= Mi-Mc/√(2MSE/HM)
Mi mean of ith experimental group
Mc mean of the control group
MSE Mean square error from anova
HM is the harmonic mean

36. Two Way Anova
 When there is need to study the effect of two factors on
variations in a specific variable
 Eg: The effect of age and sex on the height of the individual
 The effects of body build and age on variations of serum
cholesterol

38. Memory restorative effect of riluzole in mice
jun12
 Five groups employed
 Control
 Low dose riluzole & sodium nitrite
 High dose riluzole & sodium nitrite
 Low dose streptozotocin & sodium nitrite
 High dose streptozotocin & sodium nitrite
 Escape latency time is analysed
 Anova and posthoc Dunnett

39. Kruskal wallis & Friedman’s
 One way anova
 Kruskal wallis
 Eg: 4 groups of individuals studied
for the Hb% after different
treatments
Two way anova
 Friedmans
 Eg:24 subjects under different
vitamins and minerals on
weight gain

40. Cohran Q test
 Non parametric test
 Find out the differance between different types of test
 performed by same individuals
 Outcome is nominal
 That is success or failure
 Equivalent to Friedman’s

41. Effect of aegle marmelos on IBD oct 12
 5 groups
1.control
 2.Prednisolone;
 3 different doses of extract
 Melonaldehyde level
 Superoxide dismutase
Anova
 Disease activity score
Kruskal walls
 Macroscopic score

42. Withania somnifera ameliorates lead induced
augmentation of adrenergic response in rats dec 13
 3 groups
 1.control
 2.lead acetate
 3.lead acetate and plant extract
 Level of adrenaline in blood and plasma
 One way anova
 Concentration response curve of portal vein for nifedpine,
phenylephrine
 Two way anova

43. Colistin versus non colistin in multi drug resistant
Acinetobacter spp. Blood stream infections may
13
 Uni variate analysis of 14 day mortality between two groups
 Gender
 Operation last month
 Concomittant infection
 chi square
 Age
 Pitt bacteremia score
 APACHE II
 students t test
 Kaplan meiyer
 Log rank
 Cox Multiple regression

45. Correlation
 Mutual relationship between two variables
 Positive or negative
 Not necessarily a cause effect relationship
 Rabbits with atropinase has green streak on their coat
 Correlation coefficient varies from 1 to -1
 If 0 no correlation at all

47. Tests for correlation
 Pearson (parametric)
 Spearman rank correlation (non parametric)
 Eg:any relation between age and the bioavailability of a drug

48. Regression
 The value of dependant variable (y) changes with independent variable
(x)
 Linear
 Logistic
 Cox regression

49.  Linear regression
 Represented by an equation y=a+bx
 This equation is derived by least square method
 b is known as slope; a is known as intercept
 Hb1 AC= 1.61+ 0.017X serum fructosamine
 Creatinine clearance = (140- age) x weight in kg
72 x serum creatinine

50.  Multiple regression
 When there are multiple factors affect the outcome
 Extensions of linear regression
 y=a+b1x1+b2x2+b3x3
 Mortality rate between two type of treatment in acinetobactor
infection
 It also depend on
 Age at admission;
 Co morbid conditions
 Bacterial load at the time of admission

51.  Logistic regression
 Eg:5 year survival rate after a cancer treatment
 Er-ve patient has 10% less survival rate than +ve patients in Ca
breast
 When the basic test used was Chi’s square test

52. Variable Statistical unit Team compare Regression model
Numerical Mean T-test/anova Linear
Categorical Percentage Chi square Logistic
Person time KM estimates Log rank Cox regression

53. Pharmacokinetics of a new drug in young healthy
adult Indians june 12
 Volume of distribution of 2 doses of propofol versus
 Age
 Height
 Weight
 Body surface area
 Intergroup analysis t test
 Pearson correlation
 Multiple regression

54. ASV use and mortality in snake bite
 Mortality Yes No
 Age
 Gender
 Chi
 Time gap
 Mechanical ventillation
 Type of snake
 Fishers exact rank
 Total dose
 Use of ASV and risk actors from snake bite for mortality
 Logistic regression

55. Correlation versus regression
 Correlation tell about the association
 Regression predict the value of dependant variable if independent
variable is known
 Correlation applied when both the variables are random
 Regression is applied only one variable is random

56. Kaplan-meier test
 Nonparametric
 Survival function from lifetime data
 It is a statistical unit
 When you want to compare teams use log rank test
 eg:In the analysis of kaurenic acid in the antitumour activity

58. Output variable
Input
variable
Nominal Categorical Ordinal Quantitative
Discrete
Non
Normal
Normal
Nominal Chi s or
Fischer’s
Chi square Chi’s/
Mann
whtney
Mann
whitney
Mann w/
log rank
Students t
Categorical Chi ‘s Chi’ s Kruskal
wallis
Kruskal
Wallis
Kruskal
wallis
ANOVA
Ordinal Chi’s /
Mann
whtney
e Spearm
an rank
Spearman
rank
Spearman
rank
Spearma/
Linear reg
Quantitative
Discrete
Logistic
reg
e e Spearman
rank
Spearman
rank
Spearma/
Linear reg
Non normal Logistic
reg
e e e Spearman
/Pearson
Spear/Pear/
Linear
Normal Logistic
reg
e e e Linear
regression
Pearson/
Linear reg

60. SPSS MENU
Statistical test SPSS Menu
Incidences;prevalence;
95% confidence intervals
Descriptive Statistics; Frequencies
Chi’s Square Descriptive Statistics; cross tabs
Student’s t test Compare means/one sample test/ paired t test
ANOVA General linear model
One way ANOVA
Spearmans/ Pearson’s
correlation
Correlate; Bivariate
Linear regression Regression; Linear
Logistic regression Regression; Binary Logistic
Survival Analysis Survival; Kaplan Meier

62. Workshop

63. Effect of melatonin and gabapentin on pain and
anxiety dec 13
 Thee are three groups
 1.placebo
 2.melatonin
 3. gabapentin
 What test will you apply to compare
 1. Difference in BP and heart rate

 2. VAS score & VPS score

64. Single intramuscular injecton of diclofenac sodium in
paediatric patients may june 2015
Two groups ≤24 months ≥ 60 months
 What test can be applied for comparing ?
 3.Temperature at presentation
 4.Onset of antipyresis
 5.Which type of analysis to be done to find out association of antipyresis
 with differant variables

65. Comparitve study of effcacy of intrathecal clondine and
midazolam on postoperative analgesia jun 12
2 groups clonidine midazolam
What test to be applied to compare
 6.Additional analgesic requirements (yes or no)
 7.Side effects (present or absent)
 8.Pulse rate
 9.BP
 10.Pain score

66. Protective effect of aegle marmelos of chronic fatigue in
rats jun 12
 Five groups
 1.Control
 2.Stress control
 3.Low dose extract
 4. High dose extract
 5.Imipramine group
 11. Name the test to compare the latency in entering open arm
 12.Name the test to compare time spent in open arm

67. Negative prognostic factors in colorectal
carcinoma retrospective study surgery may 10

 Age
 Co morbidity
 Serum CEA
 Adjacent organ invasion are recorded
 13.What parameter should be measured to know the survival chances?
 14.What model should be utilised to investigate the contribution of
individual variables