This document provides an overview of parametric statistical tests used in pharmacology research. It introduces biostatistics and common statistical terms. It describes different types of data and measures of central tendency like mean, median, and mode. Parametric tests discussed include the z-test, t-test, and ANOVA. The z-test is used for large samples to compare proportions or means. The t-test is similar but for small samples and includes one-sample, two-sample, and paired t-tests. ANOVA compares multiple group means and includes one-way and two-way ANOVA. Examples are provided to demonstrate how to perform and interpret each test.

1. Dr. Yash N. Panchal
Resident Doctor
Pharmacology Department
AMC MET Medical College
Date: 24/12/2021
PARAMETRIC TESTS

2. PRESENTATION LAYOUT
• Introduction of Biostatistics
• Types of Data
• Measures of Central tendency
• Parametric tests
• Z test
• t test

3. WHAT IS BIOSTATISTICS ?
• It is the term used when tools
of statistics (means measured or
counted fact) are applied to the
data that is derived from biological
science such as medicine
• Statistics = Datum = measured or
Counted fact

4. Use of Biostatistics in Pharmacology
• After administration of any drug to human or animals in research, to find
whether effect is due to drug or by chance ?
• To compare actions of 2 different drugs
• To find relative potency of new drug with respect to old standard drug

5. COMMON STATISTICAL TERMS
VARIABLE:
Is a characteristic that can
vary; i.e.- height
CONSTANT:
Quantities that do not vary,
such as π = 3.14
DATA:
A collective set of values
recorded on one or more
observational units
PARAMETER:
It is summary value or
constant of a variable that
describes population, such
as its Mean

6. Types of data
Qualitative
Nominal/
Categorical
Ordinal/
Ranked scale
Quantitative
Discrete
Continuous

7. Primary & Secondary Data
• Primary data – Individual researcher
or research agency collect
data by themselves.
E.g – Experiment, Survey
• Secondary data – Individual researcher
or research agency uses data
that is already available
E.g – Past records

8. Data Compilation & Presentation
• Raw data need to be compiled to make it more understandable one.
• This is done by Master chart
• Parameters entered in Column heading and Finding in raw
• After compilation, it need to be presented by various methods like
1- Tabulation
2- Graphs - For quantitative data – Histogram, Frequency Polygon, Scatter
diagram, Line chart
- For qualitative data – Bar diagram, Pie diagram, Pictogram

9. Measures of Central tendency
• In statistics, a central tendency is a central value that represents
entire data set, and around it all other values gather
• It is called as an average or the center of the distribution
• Most common measures of central tendency are :
1- Arithmetic Mean
2- Median
3- Mode

10. Cont.…
• Importance of Central tendency:
1 - To find representative value
2 – To make more concise data
3 – To make comparisons
4 – Helpful in further statistical analysis

11. Mean
• The mean of set of values is the sum of the all measurements divided by the
number of measurements
• Is most popular and widely used central tendency
• Overall most reliable central tendency is Mean, as it takes all the observations into
consideration
• In Skewed data, the central tendency used is Median

12. Contd..

13. Mean for Grouped data

14. Median
• Is middle value of the sample when data is arranged in the
ascending or descending order
• Median= [(n + 1) / 2]th value
where, n = number of odd observations

15. Median Contd..
• For even number of distribution :
• Median is used as central tendency value for :
1 - Skewed data
2 - Ordinal qualitative data

16. Mode
• Is the value, which occurs most frequently in a set of
measurements
• Is commonly used central tendency for Nominal qualitative data

17. Normal Distribution and Curve
• The commonest and most useful continuous distribution
• It is distribution where most results are located in the middle and
few are spread on both sides
• It has the shape of bell
• Can entirely be described by its mean and standard deviation

18. Normal Distribution and Curve

19. Normal Distribution Characteristics
• Represents features of distribution of observations around
the mean value
• Also known as Gaussian distribution/
Standard distribution
• As most values are clustered around central value, hence
termed as normal distribution

20. Contd..
• Has shape of bell, it is bilaterally symmetrical, if we draw perpendicular line from
apex, curve is divided into 2 symmetrical halves
• Point of Coincide is where Mean = Median = Mode
• AUC is 100 %
• Mean ± 1 SD Cover 68.26% values
Mean ± 2 SD Cover 95.4% values
Mean ± 3 SD Cover 99.7% values

21. Statistical Tests
• Statistical tests are
intended to decide
whether a hypothesis
about distribution of
one or more populations
or samples should be
rejected or accepted
Statistical
tests
Parametric
Non-
Parametric

22. Hypothesis
• Hypo = Hypothetical; sis = statement = just assuming the thing =
statement yet to be verified.
• Is described in the terms of specific cause, specific outcome, time, place
and person
• Example of complete hypothesis – Smoking of 30-40 cigarette daily for 20
years can cause lung cancer in 10% population
• Given by – Observational study
Tested by – Analytical study
Confirmed by – Experimental study

23. Ha & H0
• Null Hypothesis - It states that there is no association
between exposure and outcome
Represented by H0
• Alternative Hypothesis – A statement that directly contradicts
the null hypothesis
Represented by Ha

24. Parametric tests
• This are statistical test that make assumptions about the
parameters of the population distribution(s) from which one’s data
is drown
• It is based on the Parameters ( Mean, Median, Standard deviation,
Standard error)

25. Parametric tests Characteristics
• Always applied in normally distributed data (Bell shaped curve)
• Scale – when data is in interval or ratio (Non-parametric – Nominal
or Ordinal )
• Used for Quantitative and qualitative data
• Measure of central tendency – Mean
• Information about population - Known

26. Tests of Statistical Significance
• Is a formal procedure for comparing observed data with a claim
(Hypothesis)
• Helps researcher to confirm the Hypothesis
• Before initiation of any research study :
Framing of research question
Hypothesis is generated

27. Contd..
Results are obtained and compared with base to check
significance
• E.g – If researcher want to compare heights of boys and girls
H0 = Heights of boy and Ha = The heights of boys is higher
girls are similar and Than girls, and so observed
any difference difference in heights is real
observed is by chance

28. Z test
• Z test is used for dealing with issues relating to large samples when the
frequency is greater than or equal to 30
• It is used when population standard deviation is known
• Assumptions : Population is normally distributed
: The sample is drawn at random
• Conditions : Population standard deviation, Mean (Parameter) is known
: Size of sample is large

29. Contd…
Z test
For Qualitative data For quantitative data
1 - Z test for single proportion 1- Z test for single mean
2 - Z test for difference 2- Z test for difference in mean
in proportion

30. Z test For Single Proportion
• To find significant difference between sample proportion and
population proportion and to check whether sample is
representative or not

31. Contd…
• H0 = Population proportion P is equal to Sample
proportion Po (P=Po)
• Ha : Two tailed : P ≠ Po
: Left tailed : P < Po
: Right tailed : P > P0

32. Example
• A survey claimed that 9 out of 10 doctors
recommend Aspirin for their patients with
headaches. To test this claim, a random sample of
100 doctors is obtained. Of these 100 doctors, 82
indicate that they recommend aspirin. Is this claim
accurate ? Use alfa = 0.05

33. Z table

34. Contd..
• If Zc > Zt, then
H0 = null hypothesis is rejected = there is difference in
proportion between population data and sample data
• If Zt > Zc, then
Null hypothesis accepted
• There is no difference between sample proportion and
population proportion at 5% level of α

35. Z test – Difference between two proportion

36. Z test – Difference between two proportion
Suppose we want to know if there is difference in the
proportion of residents who supports a certain law in
country A compared to the proportion who support the
law in country B. To test, perform a two proportion z
test at significance level 0f 0.05

37. Z test – Difference between two proportion
1 – The collected data:
Sample 1 – Sample size n1 = 50
Proportion in favor of law P1 = 0.67
Sample 2 – Sample size n2 = 50
Proportion in favor of law P2 = 0.57
2- Define the Hypothesis ;
H0: P1 = P2
Ha: P1 ≠ P2

38. P value for Z score

39. Z test For Significance of Mean

40. Z test For Significance of Mean
• Are the IQ scores of students at one school of the
Ahmedabad above the national average ?
Scores of national IQ test are normed to have a mean
of 100 and standard deviation of 15. in simple random
sample of 25 students of one of the school of
Ahmedabad the mean IQ was 110. Use default
Confidence interval of 95

41. Z test For Difference between two mean

42. t test

43. Student’s t test
• Developed by the W.S Gosset in 1908 and he had to
use a pen name “ STUDENT’’ because of his
employer’s policy in publishing research results at
that time
• It compares the difference between means of
different groups to determine whether the difference
is statistically significant

44. One sample t test
• Assumptions : Population is normally distributed
: Sample is drown from the population
and it should be random
: We should know the population mean
• Conditions : Size of the sample is small (< 30)
: Population standard deviation is not
known

45. Contd..
• In one sample t-test, we know the population mean
• We draw a random sample from the population,
measure the sample mean and compare sample
mean with population mean and make a statistical
decision as to whether or not the sample mean is
different from the population

46. Contd..

47. Contd..

48. T table

49. Two sample t test
• Used when two independent random sample come
from the normal population having unknown or
same variance
• We test the null hypothesis that the two population
means are same
μ 1 = μ 2

50. Two sample t test

51. Paired t-test
• Used when measurements are taken from the same
subject before and after some manipulation or
treatment
• E.g- To determine the significance of difference in
blood pressure before and after the administration of
the experimental substance

52. Paired t-test Contd..
• Assumptions : Population is normally distributed
: Sample is drown from the population
and it should be random
• Conditions : Sample are related with each other
: Size of the sample are small and equal
: Standard deviation in population are
equal or not known

53. Paired t-test Contd..

54. Paired t-test Contd..

55. Paired t-test Contd..

56. ANOVA
• Is Analysis of variance
• It is collection of statistical models used to analyze
the difference between GROUP means or variance
• Compares multiple groups at one time
• Was developed by R.A Fischer
• Also called ad F test

57. ANOVA Contd..

58. One Way ANOVA
• Compares two or more unmatched groups when
data are categorized in one factor
• E.g – Comparing control group with three different
doses of the aspirin
- Comparing the productivity of three or more
employee based on working hours in company

59. Two Way ANOVA
• Used to determine the effects of two nominal
variables on a continuous outcome variable
• Analyzes the effect of independent variable on the
expected outcome along with their relationship to
the outcome itself
• E.g – Comparing the productivity of the employee
based on the working hours and working conditions

60. REFERENCES
 Methods in Biostatistics: For Medical Students and Research Workers by
B.K.Mahajan; Jaypee Brothers Medical Publishers Pvt. Limited, 01-Dec-2020.
 Fagerland, M.W., 2012. t-tests, non-parametric tests, and large studies—a paradox of
statistical practice?. BMC medical research methodology, 12(1), pp.1-7.
 Kitchen, C.M., 2009. Nonparametric vs parametric tests of location in biomedical
research. American journal of ophthalmology, 147(4), pp.571-572.
 Postgraduate Pharmacology 1st Edition 2020 by Sougata Sarkar