This presentation will clarify all basic concepts and terms of hypothesis testing. It will also help you to decide correct Parametric & Non-Parametric test for your data

1. Basics
of
HYPOTHESIS TESTING
for
PHARMACY
Dr Parag Shah | M.Sc., M.Phil., Ph.D. ( Statistics)
pbshah@hlcollege.edu
www.paragstatistics.wordpress.com

2. Basic Concept
of
HYPOTHESIS
TESTING

3. Types
of
Analysis

4. Descriptive
&
Inferential
Statistics
Descriptive Statistics uses the data to provide
descriptions of the population / sample, either
through numerical calculations or graphs or tables.
Inferential Statistics makes inferences and
predictions about a population based on a sample
of data taken from the population.

5. Inferential
Statistics
The methods of inferential statistics are
• the estimation of parameter(s)
• testing of Statistical hypothesis

6. Parameter
and
Statistics
A measure calculated from population data is
called Parameter.
A measure calculated from sample data is called
Statistic.
Parameter Statistic
Mean μ x̄
Standard deviation σ s
Proportion P p
Correlation coefficient ρ r

7. Estimation
Estimation is a process whereby we select a random sample from a
population and use a sample statistic to estimate a population
parameter.
There are two ways for estimation:
• Point Estimation
• Interval Estimation

8. Point Estimate
Point Estimate – A sample statistic used to estimate
the exact value of a population parameter.
• A point estimate is a single value and has the
advantage of being very precise but there is no
information about its reliability.
• The probability that a single sample statistic actually
equal to the parameter value is extremely small. For
this reason point estimation is rarely used.

9. Interval
Estimate
Confidence interval (Interval Estimate)
A range of values defined by the confidence level
within which the population parameter is
estimated to fall.
• The interval estimate is less precise, but gives
more confidence.

10. TESTING OF
HYPOTHESIS

11. Statistical Hypothesis
A Statistical hypothesis is an assumption or any logical statement about the
parameter of the population.
E.g.
• Patients suffering from Chikungunya takes on an average more time to fully
recover than patients suffering from Dengue
• The average annual income of Indian farmer in 2018 is 78000 Rs.
• Proportion of diabetic patients in Gujarat is not more than 15 %

12. Null
hypothesis
A Null hypothesis is a general statement about population
parameter or about relation between two population
parameters.
It is denoted by H0.
• In Null hypothesis if the parameter assumes specific
value then it is called Simple hypothesis.
E.g. 𝜇 = 280, P=0.10
• In Null hypothesis if the parameter assumes set of
values then it is called Composite hypothesis.
E.g. 𝜇 ≥ 280, P ≤ 0.10

13. Alternative
Hypothesis
A statistical hypothesis which is complementary to the
Null hypothesis is called Alternative hypothesis. It is
denoted by H1.

14. Testing of
Hypothesis
The procedure to decide whether to accept or
reject the null hypothesis is called Testing of
hypothesis.

15. Type I
and
Type II Error
The error of rejecting the true null hypothesis is called
Type I error. Similar to False Positive.
The probability of type I error is denoted by 𝛼.
𝛼 = Prob [ Reject H0 / H0 is true]
The error of accepting the false null hypothesis is
called Type II error. Similar to False Negative.
The probability of type II error is denoted by 𝛽.
𝛽 = Prob [ Accept H0 / H0 is false]

16. Type I
and
Type II Error
DECISION
Null Hypothesis
TRUE FALSE
REJECT
Type I Error
False Positive
Probability = α
No Error
True Positive
Probability =1- β
NOT
REJECTED
No Error
True Negative
Probability = 1- α
Type II Error
False negative
Probability = β

17. Level of
Significance
The predetermined value of probability of type I
error is called level of significance.
It is denoted by 𝛼.
The most commonly used level of significance are
1% or 5%.
Interpretation: 5% level of significance means in 5
out of 100 cases, it is likely to reject a true null
hypothesis.

18. Critical Region
The area of the probability curve corresponding to 𝛼 is
called critical region. i.e. the area under normal curve
at which a true null hypothesis is rejected is called
area of rejection or critical region.

19. Power of Test
The probability of rejecting the false null
hypothesis is called the Power of the test.
It is denoted by 1- 𝛽.
i.e. 1- 𝛽 = Prob [ Reject H0 / H0 is false]

20. P value
• P-value ≡ the probability the test statistic would take a
value as extreme or more extreme than observed test
statistic, when H0 is true.
• Smaller-and-smaller P-values → stronger-and-stronger
evidence against H0
• For typical analysis, using the standard α = 0.05 cutoff,
the null hypothesis is
- rejected when p < = .05 and
- not rejected when p > .05.

21. Steps of
Testing of
Hypothesis
Step 1: Setting up Null hypothesis
Step 2: Setting up Alternative hypothesis
Step3: Check assumptions of the test
Step 4: Determining the p value
Step 5: Conclusion
• If p ≤ Level of significance (∝), We Reject Null
hypothesis
• If p > Level of significance (∝), We fail to Reject Null
hypothesis

22. Some of the
tests
• Testing single mean
• Testing significant difference between two means
• Testing single proportion
• Testing significant difference between two proportions
• Testing single standard deviation
• Testing two standard deviations
• Testing means for more than two samples
• Testing standard deviations for more than two samples
• Testing proportion for more than two samples
• Testing for non-normal populations
• Testing correlation and regression coefficients

23. Deciding Test
Parameter
Categorical
(Binary)

24. t test
for
single mean
Step 1: Null hypothesis H0: 𝜇 = 𝜇0
Step 2: Alternative hypothesis H1: 𝜇 ≠ 𝜇0 or 𝜇 > 𝜇0 or 𝜇 < 𝜇0
Step 3: Check Assumptions
Step 4: Test statistic – t and p value
Step 5: Conclusion
• If p ≤ Level of significance (∝), We Reject Null hypothesis
• If p > Level of significance (∝), We fail to Reject Null hypothesis
Assumptions Tests
The population from which the sample
drawn is assumed as Normal distribution
Shapiro-Wilks
/ qq plot
The population variance 𝜎2 is unknown ____

25. t test
for
means of two
independent
samples
Step 1: Null hypothesis H0: 𝜇1= 𝜇2
Step 2: Alternative hypothesis H1: 𝜇1 ≠ 𝜇2 or 𝜇1 > 𝜇2 or 𝜇1 < 𝜇2
Step 3: Check Assumptions
Step 4: Test statistic – t and p value
Step 5: Conclusion
• If p ≤ Level of significance (∝), We Reject Null hypothesis
• If p > Level of significance (∝), We fail to Reject Null hypothesis
Assumptions Tests
The population from which two samples drawn are
assumed as Normal distribution
Shapiro-Wilks
/ qq plot
Two population variance are unknown
(Equal / Unequal)
F test
The two samples are independently distributed ____

26. t test for Equal Variances t test for Unequal Variances
(Welch t test)
d.f. =
where

27. t test
for
means of two
dependent
samples
(Paired t test)
Step 1: Null hypothesis H0: 𝑑 = 0
Step 2: Alternative hypothesis H1: 𝑑 ≠ 0
Step 3: Check Assumptions
Step 4: Test statistic – t and p value
Step 5: Conclusion
• If p ≤ Level of significance (∝), We Reject Null hypothesis
• If p > Level of significance (∝), We fail to Reject Null hypothesis
Assumptions Tests
The difference between the two samples
are normally distributed.
Two-sample Kolmogorov-
Smirnov test / qq plot
The difference between the two samples
are independently distributed
____
The two samples are independently
distributed
____

28. Effect Size
Effect size is a statistical concept that measures the
strength of the relationship between two variables on
a numeric scale.
Statistic effect size helps us in determining if the
difference is real or if it is due to a change of factors.

29. Effect Size
In Meta-analysis, effect size is concerned with
different studies and then combines all the studies
into single analysis.
In statistics analysis, the effect size is usually
measured in three ways:
• standardized mean difference
• odd ratio
• correlation coefficient.

30. Effect Size
Cohen’s 𝑑 is the measure of the difference between two means
divided by the pooled standard deviation.
𝑑 =
𝑥1−𝑥2
𝑆𝑝
where
𝑛1−1 𝑆1
2
+ 𝑛2−1 𝑆2
2
𝑛1+𝑛2−2
It is important to note that Cohen’s 𝑑 does not provide a level of
confidence as to the magnitude of the size of the effect comparable
to the other tests of hypothesis. The sizes of the effects are simply
indicative.
Size of effect 𝒅
Small 0.2
Medium 0.5
Large 0.8

31. Example
𝑑 =
𝑥1 − 𝑥2
𝑆𝑝
where
𝑛1−1 𝑆1
2
+ 𝑛2−1 𝑆2
2
𝑛1+𝑛2−2
If 𝑥1 = 4, 𝑥2 = 3.5, 𝑆1 = 1.5, 𝑆2 = 1, 𝑛1=11, 𝑛2 = 9
Calculate Cohen’s 𝑑 and interpret the difference.
Solution:
Cohen’s 𝑑 = 0.384
The effect is small because 0.384 is between Cohen’s
value of 0.2 for small effect size and 0.5 for medium effect
size. The size of the differences of the means for the two
samples is small indicating that there is not a significant
difference between them.
Size of effect 𝒅
Small 0.2
Medium 0.5
Large 0.8