Statistical tools in research 1

Statistical Tools
in
Research
Dr. Ashish Suttee
M.Pharm., MBAHCS., Ph.D.
Statistician
6/2/2021 1
ashish7sattee@gmail.com

Always be ready to walk the
unexplored path
Dr. APJ ABDUL KALAM
6/2/2021 2

Statistics
Is
easy
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Outlines
Basics of Statistics
Hypothesis
Statistical tools (Student t test and ANOVA)
What you need to know about MS Excel ?
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Basics of Statistics
 Introduction to Statistics
 Hierarchy of statistics (Descriptive and inferential)
 Statistical tests ( Parametric and non parametric)
 Softwares available for statistics
 Variables and its types
 Quiz
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Introduction
 Statistics is a branch of science that deals with the collection,
organisation, analysis of data and drawing of inferences from
the samples to the whole population.
 This requires a proper design of the study, an appropriate
selection of the study sample and choice of a suitable statistical
test.
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Introduction
 An adequate knowledge of statistics is necessary for proper
designing of a research or an epidemiological study or a
clinical trial.
 Improper statistical methods may result in erroneous
conclusions which may lead to unethical practice.
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Introduction
 Statistical methods involved in carrying out a study include
planning, designing, collecting data, analysing, drawing
meaningful interpretation and reporting of the research
findings.
 The statistical analysis gives meaning to the meaningless
numbers, thereby breathing life into a lifeless data.
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Introduction
 The results and inferences are precise only if proper statistical
tests are used.
 In this presentation, I will try to acquaint the researcher with
the basic research tools that are utilised while conducting
various research studies.
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Hierarchy of Statistics
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Statistics
Descriptive
Inferential

Descriptive
 Descriptive statistics try to describe the relationship between
variables in a sample or population.
 Descriptive statistics provide a summary of data in the form of
mean, median and mode.
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Descriptive Statistics example
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QUIZ.1
Inferential statistics provide a summary of data in the form
of mean, median and mode.
a. True
b. False
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QUIZ.1
Answer
b. False

AV aids: https://m.youtube.com/watch?v=SFPGVTThJNk

Inferential Statistics
 Inferential statistics use a random sample of data taken from a
population to describe and make inferences about the whole
population.
 It is valuable when it is not possible to examine each member
of an entire population.
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 In inferential statistics, data are analysed from a sample to
make inferences in the larger collection of the population.
 The purpose is to answer or test the hypotheses. A hypothesis
(plural hypotheses) is a proposed explanation for a
phenomenon.
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 Hypothesis tests are thus procedures for making rational
decisions about the reality of observed effects.
 Probability is the measure of the likelihood that an event will
occur. Probability is quantified as a number between 0 and 1
(where 0 indicates impossibility and 1 indicates certainty).
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 In inferential statistics, the term ‘null hypothesis’ (H0) denotes
that there is no relationship (difference) between the population
variables in question.
 Alternative hypothesis (Ha ) denotes that a statement between
the variables is expected to be true.
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QUIZ.2
In inferential statistics, the term ‘null hypothesis’ (H0)
denotes that there is no relationship (difference) between
the population variables in question.
a. True
b. False

QUIZ.2
Answer
a. True

 The P value (or the calculated probability) is the probability of
the event occurring by chance if the null hypothesis is true.
 The P value is a numerical between 0 and 1 and is interpreted
by researchers in deciding whether to reject or retain the null
hypothesis .
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 If P value is less than the arbitrarily chosen value (known as α
or the significance level), the null hypothesis (H0) is rejected .
 However, if null hypotheses (H0) is incorrectly rejected, this is
known as a Type I error.
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Inferential Statistics- Example
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Statistical tests
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Statistical
tests
Parametric
Non-
parametric

Parametric and non-parametric tests
 Numerical data (quantitative variables) that are normally
distributed are analysed with parametric tests.
 The most basic prerequisites for parametric statistical analysis
is:
 The assumption of normality which specifies that the means of
the sample group are normally distributed
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Parametric and non-parametric tests
 However, if the distribution of the sample is skewed towards
one side or the distribution is unknown due to the small sample
size, nonparametric statistical techniques are used.
 Non-parametric tests are used to analyse ordinal and
categorical data.
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Parametric test
 The parametric tests assume that the data are on a quantitative
(numerical) scale, with a normal distribution of the underlying
population.
 The samples have the same variance (homogeneity of
variances). The samples are randomly drawn from the
population, and--
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Parametric test
the observations within a group are independent of each other.
 The commonly used parametric tests are the Student's t-test,
and analysis of variance (ANOVA).
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Parametric test- Normal distribution Pic.
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Parametric tests
 When the assumptions of normality are not met, and the
sample means are not normally, distributed parametric tests can
lead to erroneous results.
 Non-parametric tests (distribution-free test) are used in such
situation as they do not require the normality assumption.
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QUIZ.3
The non- parametric tests assume that the data are on a
quantitative (numerical) scale, with a normal distribution of
the underlying population.
a. True
b. False

QUIZ.3
Answer
b. False

Non-Parametric tests
 Nonparametric tests may fail to detect a significant difference
when compared with a parametric test.
 That is, they usually have less power.
 As is done for the parametric tests, the test statistic is
compared with known values for the sampling distribution of
that statistic and the null hypothesis is accepted or rejected.
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 The types of non-parametric analysis techniques and the
corresponding parametric analysis techniques are delineated in
given Table .
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Softwares Available For Statistics,
Sample Size Calculation And Power
Analysis

 Numerous statistical software systems are available currently.
The commonly used software systems are Statistical Package
for the Social
 Sciences (SPSS – manufactured by IBM corporation),
Statistical Analysis System ((SAS – developed by SAS
Institute North Carolina, United States of America), --
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 -R (designed by Ross Ihaka and Robert Gentleman from R
core team), Minitab (developed by Minitab Inc), Stata
(developed by StataCorp) and the MS Excel (developed by
Microsoft).
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 There are a number of web resources which are related to
statistical power analyses. A few are:
 StatPages.net – provides links to a number of online power
calculators
 G-Power – provides a downloadable power analysis program
that runs under DOS
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 Power analysis for ANOVA designs an interactive site that
calculates power or sample size needed to attain a given power
for one effect in a factorial ANOVA design
 SPSS makes a program called Sample Power. It gives an
output of a complete report on the computer screen which can
be cut and paste into another document.
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General awareness about the types of variables before
selecting the statistical tools for researchers
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Variables
 Variable is a characteristic that varies from one individual member
of population to another individual.
 Variables such as height and weight are measured by some type of
scale, convey quantitative information and are called as quantitative
variables.
 Sex and eye colour give qualitative information and are called as
qualitative variables.
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Types of variable
Variable
Qualitative
Categorical
Nominal
Ordinal
Quantitative
Discrete Continuous
Interval
Ratio
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A Hierarchy of variable

Quantitative variables
 Quantitative or numerical data are subdivided into discrete and
continuous measurements.
 Discrete numerical data are recorded as a whole number such as
0, 1, 2, 3,… (integer), whereas continuous data can assume any
value.
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QUIZ.4
Which type of information is given by data
if it contains Sex and eye colour ?
a. Qualitative
b. Quantitative
c. Mean
d. All of the above

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QUIZ.4
Answer
a. Qualitative

 Observations that can be counted constitute the discrete data and
observations that can be measured constitute the continuous
data.
 Examples of discrete data are number of episodes of respiratory
arrests or the number of re-intubations in an intensive care unit.
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Hierarchy of quantitative variable
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Quantitative
variable
Discrete Continuous
Interval Ratio

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Discrete variables
 Examples
 In a survey with 14 children on their favourite ice-cream flavour,
it was found that 4 children like butterscotch flavour, 5 children
like chocolate flavour, 3 children like vanilla flavour and 2
children like strawberry flavour of ice-cream.
 It is an example of discrete data as we can count the number of-
children who like a particular flavour of ice-cream.
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Discrete variables (graphical representation)
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Bar graph

Discrete variables ( Numerical representation)
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 Similarly, examples of continuous data are the serial serum
glucose levels, partial pressure of oxygen in arterial blood and
the oesophageal temperature.
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Continuous data ( Graphical representation)
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Histogram

Continuous data ( Numerical representation)
When data is given based on ranges along with their frequencies.
Following is an example of continuous data:
Items 0-5 5-10 10-20 20-30 30-40
Frequency 2 5 1 3 12
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Continuous data ( Interval data)
 Interval values represent ordered units that have the same difference.
Therefore we speak of interval data when we have a variable that
contains numeric values that are ordered and where we know the exact
differences between the values.
 An example would be a feature that contains temperature of a given
place like you can see below:
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QUIZ.5
When data is given based on ranges (10-20)
along with their frequencies ?
a. Discrete data
b. Continuous data
c. Individual data
d. Raw data

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QUIZ.5
Answer
b. Continuous data

Continuous data ( Interval data- graphical rep.)
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Continuous data ( Interval data- numerical rep.)
Interval data example
You collect the SAT scores of a group of 59 graduating students
from City A. Test-takers can score anywhere between 400–1600
on the SAT.
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Continuous data ( Interval data- numerical rep.)
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Continuous data ( Ratio data)
 Ratio Data is defined as quantitative data, having the same properties
as interval data, with an equal and definitive ratio between each data
and absolute “zero” being treated as a point of origin.
 In other words, there can be no negative numerical value in ratio
data.
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 For example
 Four people are randomly selected and asked how much money
they have with them. Here are the results : $20, $40, $60, and
$80.
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Continuous data ( Ratio data-numerical rep.)
 Is there an order to this data? Yes, $20 < $40 < $60 < $80.
 Are the differences between the data values meaningful?
 Sure, the person who has $40 has $20 more than the person
with $20.
 Can we calculate ratios based on this data? Yes,
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Continuous data ( Ratio data- numerical rep.)
because $0 is the absolute minimum amount of money a
person could have with them.
 The person with $80 has four times as much as the person with
$20.
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QUIZ.6
Five people are randomly selected and asked
how much money they have with them. Here are
the results : $200, $400, $600, and $800.
Identify the data.
a. Continuous interval data
b. Continuous ordinal data
c. Continuous ratio data
d. Continuous categorical data

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QUIZ.6
Answer
c. Continuous ratio data

 You collect data on the commute duration of employees in a large city.
The data is continuous and in minutes.
 To organize your data, enter it into a grouped frequency distribution
table. Create groups with equal intervals on the left hand column and
enter the number of scores that fall within each interval into the right
hand column.
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
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Continuous data ( Ratio data-graphical rep)
 To visualize your data, plot it on a frequency distribution
polygon. Plot the groupings on the x-axis and the frequencies on
the y-axis, and join the midpoint of each grouping using lines.
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Continuous data ( Ratio data-graphical rep)
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Qualitative variables
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 Variables that are not measurement variables. Their values
do not result from measuring or counting.
 Examples: hair color, religion, political party, profession

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QUIZ.7
Qualitative Variables are the measurement
variables. Their values can be measured or
counted from results..
a. True
b. False

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QUIZ.7
Answer
b. False

Hierarchy of Qualitative variable
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Categorical Variable
 Categorical variables are qualitative data in which the values are
assigned to a set of distinct groups or categories.
 These groups may consist of alphabetic (e.g., male, female) or
numeric labels (e.g., male = 0, female = 1) that do not contain
mathematical information beyond the frequency counts related to
group membership.
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Categorical Variable
 Instead, categorical variables often provide valuable social-
oriented information that is not quantitative by nature (e.g., hair
color, religion, ethnic group).
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Categorical Variable ( Graphical rep.)
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Categorical Variable ( Numerical rep.)
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Categorical Variable ( Numerical rep.)
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Nominal Variable
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 A nominal variable is a type of variable that is used to
name, label or categorize particular attributes that are
being measured.
 It takes qualitative values representing different
categories, and there is no intrinsic ordering of these
categories.

Nominal Variable
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 You can code nominal variables with numbers, but the
order is arbitrary and arithmetic operations cannot be
performed on the numbers.
 This is the case when a person’s phone number, National
Identification Number postal code, etc. are being
collected.

Nominal Variable ( Example)
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Personal Biodata: The variables included in a personal
biodata is a nominal variable. This includes the name, date
of birth, gender, etc. E.g
 Full Name _____
 Gender
 Email address_____
 Customer Feedback: Organizations use this to get
feedback about their product or service from customers.
E.g.

Nominal Variable ( Example)
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Organizations use this to get feedback about their product or
service from customers. E.g.
How long have you been using our product?
 Less than 6 months
 6 months
 7 months+
 What do you think about our mobile app?_____

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QUIZ.8
The variables included in a personal biodata
is a nominal variable.
a. True
b. False

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QUIZ.8
Answer
a. True

Ordinal Variable
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 Ordinal variable is a type of measurement variable that
takes values with an order or rank.
 It is the 2nd level of measurement and is an extension of
the nominal variable.
 They are built upon nominal scales by assigning numbers
to objects to reflect a rank or ordering on an attribute.
Also, there is no standard ordering in the ordinal variable
scale.

Ordinal Variable
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 In another sense, we could say the difference in the rank
of an ordinal variable is not equal.
 It is mostly classified as one of the 2 types of categorical
variables, while in some cases it is said to be a midpoint
between categorical and numerical variables.

Ordinal Variable
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Ordinal Variable ( Example)
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 Likert Scale: A Likert scale is a psychometric scale used
by researchers to prepare questionnaires and get people's
opinions.

Ordinal Variable ( Example-Likert scale)
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How satisfied are you with our service tonight?
1.Very satisfied
2.Satisfied
3.Indifferent
4.Dissatisfied
5.Very dissatisfied

Ordinal Variable ( Example-Likert scale)
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Interval Scale: each response in an interval scale is an interval
on its own.
How old are you?
 13-19 years
 20-30 years
 31-50 years

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QUIZ.9
Which of the following scale is used by
researchers to prepare questionnaires and get
people's opinions?
a. Nominal
b. Ratio
c. Likert
d. Interval

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QUIZ.9
Answer
c. Likert

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AV aids
https://m.youtube.com/watch?v=hZxnzfnt5v8

Hypothesis
 Introduction to hypothesis
 Types of hypothesis (Null and alternate)
 Acceptance and rejection criteria of null and alternate
hypothesis
 Common errors in hypothesis ( type I and type II)
 Quiz
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Hypothesis
A supposition or proposed explanation made on the
basis of limited evidence as a starting point for
further investigation .
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What is meant by hypothesis in research?
A hypothesis is a precise, testable statement of what the
researcher(s) predict will be the outcome of the study.
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Few instances of Hypothesis
1. If I replace the battery in my car, then my car will
get better gas mileage.
2. If I eat more vegetables, then I will lose weight
faster.
3. If I add fertilizer to my garden, then my plants will
grow faster.
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Few instances of Hypothesis
4. If I brush my teeth every day, then I will not develop
cavities.
5. If I take my vitamins every day, then I will not feel
tired.
6. If 50 ml of water are added to my plants each day and
they grow, then adding 100 ml of water each day will
make them grow even more.
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Research hypothesis example?
A study designed to look at the relationship between sleep
deprivation and test performance might have a hypothesis
that states, "This study is designed to assess the
hypothesis that sleep-deprived people will perform
worse on a test than individuals who are not sleep-
deprived."
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How to formulate an effective hypothesis?
a. State the problem that you are trying to solve.
b. Make sure that the hypothesis clearly defines the topic
and the focus of the experiment.
c. Try to write the hypothesis as an if-then statement.
d. Define the variables.
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Few examples of formulating effective hypothesis?
1. If you get at least 6 hours of sleep, you will do better on
tests than if you get less sleep.
2. If you drop a ball, it will fall toward the ground.
3. If you drink coffee before going to bed, then it will take
longer to fall asleep.
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References: https://medium.com/swlh/hypothesis-testing-c8c408a62cb2

Types
1. Null hypothesis (H0)
2. Alternate hypothesis (Ha)
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a. A null hypothesis is a type of hypothesis used in
statistics that proposes no statistical significance
exists in a set of given observations. The null
hypothesis attempts to show that no observations.
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Reference: https://www.thoughtco.com/null-hypothesis-examples-609097

b. The null hypothesis attempts to show that no variation
exists between variables or that a single variable is
different than its mean. It is presumed to be true until
statistical evidence nullifies it for an alternative
hypothesis.
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c. A null hypothesis is a hypothesis that says there is no
statistical significance between the two variables in the
hypothesis. In the example, Amayra's null hypothesis would
be something like this: There is no statistically significant
relationship between the type of water I feed the flowers
and growth of the flowers.
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QUIZ.10
A null hypothesis is a hypothesis that says
there is no statistical significance between
the two variables in the hypothesis.
a. True
b. False

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QUIZ.10
Answer
a. True

Null hypothesis (H0)
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There is no statistically significant relationship between the type of
water I feed the flowers and growth of the flowers.

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In general, the null hypothesis is usually constructed to be
that of the status quo; that is, it is the hypothesis requiring
no action to be taken, no money to be spent, or in general
nothing changed. This is the reason for denoting this as
the null or nothing hypothesis.
AV aids:
https://m.youtube.com/watch?v=UgYc08Wr8io

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QUIZ 11
If my experimental hypothesis were ‘Eating potato chips before
bed affects the number of nightmares you have’, what would the
null hypothesis be?
a. Eating potato chips before bed gives you more nightmares.
b. Eating potato chips before bed gives you fewer nightmares.
c. Eating potato chips is linearly related to the number of
nightmares you have.
d. The number of nightmares you have is not affected by eating
potato chips before bed.

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QUIZ 11
ANSWER
d. The number of nightmares you have is not
affected by eating potato chips before bed

2. Alternate hypothesis (Ha)
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a. The alternative hypothesis is the hypothesis used in
hypothesis testing that is contrary to the null
hypothesis.
b. It is usually taken to be that the observations are the
result of a real effect (with some amount of chance
variation superposed).

Alternate hypothesis (Ha)
c. The alternate hypothesis is just an alternative to the null.
For example, if your null is “I'm going to win up to
$700” then your alternate is “I'm going to win more than
$700.” Basically, you're looking at whether there's enough
change (with the alternate hypothesis) to be able to reject
the null hypothesis.
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Effect of bio-fertilizer ‘A’ on plant growth
Alternate hypothesis (Ha) :
Application of bio-fertilizer ‘A’ increases
plant growth
Null hypothesis (H0):
• Application of bio-fertilizer ‘A’ do not
increase plant growth
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AV aid: https://m.youtube.com/watch?v=WtdiMUwWX0k

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Reference: https://www.thoughtco.com/scientific-method-p2-373335

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Reference: https://www.thoughtco.com/steps-of-the-scientific-method-p2-606045

ACCEPTANCE AND REJECTION CRITERIA OF
NULLAND ALTERNATE HYPOTHESIS IN
RESEARCH ( AT L.O.S. 5% OR 0.05 TABLE VALUE)
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Instance
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How to formulate nice hypothesis?
1. Null hypothesis H0 : All formulations are being shown the
same antitussive effect.
2. Alternate hypothesis Ha : All formulations are not being
shown the antitussive effect.
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When the null hypothesis is rejected?
When the calculated value is more than the critical value or
table value, in this case null hypothesis is rejected.
For instance
In One way ANOVA,
If calculated F value of the given data is MORE THAN the F-
table value (F critical value), then null hypothesis is rejected
and the test is highly significant. (Calculated F value 5 > 3.19
F table value)
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When the null hypothesis is accepted?
When the calculated value is less than the critical value or table
value, in this case null hypothesis is accepted.
For instance
In Student t test,
If calculated t value of the given data is LESS THAN the t- table
value (t- critical value), then null hypothesis is accepted and the
test is not significant. (Calculated t value 2.09 < 3.19 t table value)
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Common errors in Hypothesis
QUIZ 12
If calculated t value of the given data is more than the t-
table value (t- critical value), then null hypothesis is
accepted and the test is not significant. (Calculated t
value 5.09 > 3.19 t table value)
a. True
b. False
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QUIZ 12
ANSWER
b. False
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a. Type I error: = (Reject H0 /H0 is true)
b. Type II error: = (Accept H0 / Ha is true)
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a. Instance of type I error
Consider we are testing two brands of paracetamol to
evaluate if Brand 1 is better in curing subject's suffering
from fever as compared to Brand 2. As both brands
contain paracetamol, it is expected that the effect of both
brands is similar.
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Let us try to built a statistical hypothesis around this
Null Hypothesis (H0) : Brand 1 is equal to Brand 2
Alternate Hypothesis (Ha) : Brand 1 is better than Brand 2 Let us
try to evaluate error that can occur.
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Error 1:
Based on analysis it is concluded that Brand 1 is better than
Brand 2, basically we reject H0 . Knowing that Brand 1 is
equal to Brand 2 (H0 ), we are making an error here by
rejecting H0 . This is called as Type I error. Statistically it
is defined as Type I error = (Reject H0 /H0 is true)
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a. Instance of type II error
Consider we are testing paracetamol against placebo to
evaluate if paracetamol is better in curing subject's
suffering from fever as compared to placebo. (It is
expected that the effect of paracetamol is better than
placebo).
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Let us try to built a statistical hypothesis around this
Null Hypothesis (H0) : Paracetamol is equal to placebo
Alternate Hypothesis (Ha) : Paracetamol is better than
placebo
Let us try to evaluate error that can occur.
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Error 2:
If analysis concludes that paracetamol is equal to placebo,
we accept H0 . Knowing that paracetamol is better than
placebo (Ha ) we are making an error here by accepting H0 .
This is called as Type II error. Statistically it is defined as
Type II error = (accept H0 / H0 is false)
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QUIZ 13
Which of the following is common error in
testing a Hypothesis ?
a. Type II and III
b. Type I
c. Type III
d. Type I and II
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QUIZ 13
ANSWER
d. Type I and II
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Exercise 1
 Formulate the null and alternative hypothesis statement of the given illustration
 Fifteen students undergoing training are randomly assigned to three different types
of instruction modules. At the end of training period their test score are as follows:

Instruction modules-
---------
A B C
Test 1 86 90 82
Test 2 79 76 68
Test 3 81 88 73
Test 4 70 82 71
Test 5 84 89 81
Is there any significant difference in the mean scores of the
three instruction modules.

Exercise 1
 Solution
 Null hypothesis : The null hypothesis assumes no difference in the mean scores of
the three instruction modules.
 Alternate hypothesis: The alternate hypothesis assumes significant difference in
the mean scores of the three instruction modules.

Exercise 2
 In order to test the significance of variation of the retail prices of a commodity in
three cities, four shops were chosen at random from each cities and prices
observed in rupees were as follows

City A City B City C
16 14 4
8 10 10
12 10 8
12 6 10
Does the data indicate that the prices n three cities are
significantly different?

Exercise 2
 Solution
 Null hypothesis : The null hypothesis assumes no significant difference in the
mean prices in three cities.
 Alternate hypothesis: The alternate hypothesis assumes significant difference in
the mean prices in three cities.

Statistical tools
(Student t test and ANOVA)

Student t test and ANOVA
 Importance of Statistical Tools
 Introduction to student t test and ANOVA
 Requirement
 Types
 Applications
 Table (Student t test and ANOVA or F- table)
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Few instances of Statistical Tools
1. Student t test
2. Analysis of variance (ANOVA)
3. Chi-square test.
4. Correlation.
5. Multiple correlation
6. Wilcoxan rank tests
7. Regression analysis.
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Importance of Statistical Tools
 Statistics is a wide subject useful l in almost all disciplines
especially in Research studies.
 Each and every researcher should have some knowledge in
Statistics and must use statistical tools in his or her research,
one should know about the importance of statistical tools and
how to use them in their research or survey.
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 The quality assurance of the work must be dealt with: the
statistical operations necessary to control and verify the
analytical procedures as well as the resulting data making
mistakes in analytical work is unavoidable.
 This is the reason why a multitude of different statistical tools
is, required some of them simple, some complicated, and often
very specific for certain purposes.
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 In analytical work, the most important common operation is the
comparison of data, or sets of data, to quantify accuracy (bias)
and precision. Fortunately, with a few simple convenient
statistical tools most of the information needed in regular
laboratory work can be obtained: the "t-test, the "F-test“
(ANOVA), and regression analysis. Clearly, statistics are a tool,
not an aim. Simple inspection of data, without statistical
treatment, by an experienced and dedicated analyst may be just
as useful as statistical figures on the desk of the disinterested.
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 The value of statistics lies with organizing and simplifying data,
to permit some objective estimate showing that an analysis is
under control or that a change has occurred.
 Equally important is that the results of these statistical
procedures are recorded and can be retrieved.
 The key is to sift through the overwhelming volume of data
available to organizations and businesses and correctly interpret
its implications.
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 But to sort through all this information, you need the right
statistical data analysis tools.
Hence in this presentation, i have made an attempt to give a
brief study on Statistical tools, "t-test, the "F-test“ (ANOVA),
used in research studies.
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Student t test
Introduction
a. Student t-test was given by W. S. Gossett. He published his
test anonymously as “Student‟ because he was working for
the brewer‟s Guinness and had to keep the fact they were
suing statistics a secret.
b. The test is used to compare samples from two different
batches. It is usually used with small (<30) samples that are
normally distributed.
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Student t test
Requirements/ Assumptions
 Data should be normally distributed
 Sample size should be <30 (overall)
 Group required: one or two only ( not more than two)
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Types of Student t test
1. An Independent Student t-test compares the means for
two groups ( also known as unpaired sample t test)
2. A Dependent Student t-test compares means from the
same group at different times (say, one year apart, also
known as Paired sample t-test )
3. A One sample t-test tests the mean of a single group
against a known mean
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1.An Independent Student t-test compares
the means for two groups
An independent samples t-test is used when you want to
compare the means of a normally distributed interval
dependent variable for two independent groups.
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For instance,
if you wanted to conduct an experiment to see how drinking
an energy drink increases heart rate, you could do it by
unpaired way.
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The "unpaired" way would be to measure the heart rate of
10 people before drinking an energy drink and then measure
the heart rate of some other group of people who have
drank energy drinks.
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These two samples consist of different test subjects, so
you would perform an unpaired t-test on the means of
both samples.
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Applications
Numerical instance 1
To observe the precision of analytical method, the
experiment may be performed by two analysts with two UV
spectrophotometers at different laboratories
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S. NO .1 UV 1 UV 2
1 0.342 0.344
2 0.346 0.347
3 0.350 0.352
4 0.352 0.354
5 0.357 0.358
6 0.360 0.361
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The observed absorbance values of a drug solution from two
spectrophotometers at different laboratories are given below. Whether the
difference in absorbance values observed in instruments is significant or
not

An crude extract formulation of a plant was administered
to one group of animals and the other group of animals
received marketed formulation. The percentage glucose
level reduction values observed at 4th hour of post
administration are given in the following table. The
difference in the blood glucose levels is significant or not.
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S. NO .1 Crude extract
formulation
Marketed formulation
1 32 42
2 28 44
3 30 40
4 31 38
5 28 39
6 29 42
6/2/2021 166
%age Blood glucose Reduction

QUIZ 14
How many groups are present in an independent
Samples t-test?
a. 3
b. 4
c. 2
d. 1
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QUIZ 14
ANSWER
c. 2
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2. A Dependent Student t-test compares
means from the same group at different times
a. A Dependent samples t test (also called a paired
samples t test is where you run a t test on dependent
samples.
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b. Dependent samples are essentially connected — they are
tests on the same person or thing.
For instances
1. Knee MRI costs at two different hospitals,
2. Two tests on the same person before and after training,
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3. Two blood pressure measurements on the same person
using different equipment.
4. If you wanted to conduct an experiment to see how
drinking an energy drink increases heart rate, you
could do it by paired way.
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QUIZ 15
A Dependent samples t-test compares means from the
same group at different times is also known as
a. Unpaired
b. Paired
c. One sample
d. None of the above
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QUIZ 15
ANSWER
a. Paired
6/2/2021 173

The "paired" way would be to measure the heart rate of
10 people before they drink the energy drink and then
measure the heart rate of the same 10 people after
drinking the energy drink. These two samples consist of
the same test subjects, so you would perform a paired t-test
on the means of both samples.
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Applications
The systolic blood pressure levels of a hypertensive
patient observed before and after new drug entity are
given below. To observe the statistical differences in blood
pressure with new drug entity treatment, the data is as
follows
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Patient
No
Before Treatment After Treatment
1 142 122
2 144 124
3 146 120
4 140 118
5 148 121
6 145 124
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Systolic blood pressure (mmHg)

Applications
The disintegration time observed from tablets before and
after incorporation of disintegrating agents (without
changing the others factor) is showed in the following
table. Test the statistical differences in disintegration time
observed due to the presence of disintegrant.
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Tablet
No.
Without
disintegrant
With disintegrant
1 22 14
2 24 12
3 23 10
4 25 12
5 23 13
6 26 15
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Disintegration time (min)

3. A One sample Student t-test tests the mean
of a single group against a known mean
A Pharmaceutical company claims that the average
dissolution rate of company’s tablet is 365 unit. You
randomly select 12 tablets from a batch and test their
dissolution rate under similar conditions.
You get the following data:
Dissolution: 361, 363, 366, 359, 358, 366, 359, 367,
rate 364, 365, 363, 365.
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3. A One Student t-test tests the mean of a
single group against a known mean
Does the actual dissolution rate for these tablets deviate
significantly from 365 (α = 0.05)?
The goal of your analysis is to test for a significant
deviation between your sample mean and the proposed
population mean.
6/2/2021 180

Applications of Student-t test
 The T-test is used to compare the mean of two samples,
dependent or independent.
 It can also be used to determine if the sample mean is
different from the assumed mean.
 T-test has an application in determining the confidence
interval for a sample mean.
6/2/2021 181

Student t test table
6/2/2021 182

ANOVA (Analysis of variance)
Introduction
1. It is statistical technique specially designed to test whether
the means of more than quantitative populations are equal
2. The analysis of variance technique, developed by R.A. Fisher
in 1920’s, is capable of fruitful application to diversity of
practical problems
3. It is applied to conclude that whether the results are differ
significantly.
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Assumption of F test
1. Normality
2. Homogeneity
3. Randomness
4. Independence of error
5. Sample size should be < 10 ( each group)
6. Group required: at least 3 or more
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Terminology used in ANOVA test
1. CF : Correction factor
2. TSS : Total sum of square
3. BSSC : Between sum of square (Columns wise)
4. BSSR : Between sum of square (Rows wise)
5. WSS : Within sum of square TSS- BSSC
6. df : Degree of freedom (n-1)
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c. Computing of ANOVA by using MS Excel
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d. ANOVA- F table
6/2/2021 189

Interpretation and applications
Will discuss with live example
If calculated F value is MORE THAN the F- table value (F-
critical value), then null hypothesis is rejected and the test is
highly significant. ( F value 5> 3.19 F table value) and vice versa
Application: It is intended to analyse variability in data in
order to infer the inequality among population means.
• Note: When conducting an ANOVA, FDATA will always fall within between 0 and
infinity range. As variability due to chance decreases, the value of F will Increase
6/2/2021 190

ANOVA
QUIZ 16
How many groups are required for applying the
ANOVA?
a. 1
b. 2
c. 3
d. All of the above
6/2/2021 191

ANOVA
QUIZ 16
ANSWER
c. 3
6/2/2021 192

MS Excel
What you need to know about MS Excel ?
 Data analysis activation
 How to apply student t test and ANONA ( one way or single
 factor) on given data
 Finally , interpretation and conclusion
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MS Excel
Data analysis activation----> Open MS Excel
6/2/2021 194

MS Excel
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MS Excel
6/2/2021 196

MS Excel
 Data analysis activation----> Open MS Excel----- It will take 1-2 minutes for activation.
 Then close the MS Excel
 Again reopen it .
 Now the Data Analysis toolpak is activated.
 AV aid: https://m.youtube.com/watch?v=0zZYBALbZgg
6/2/2021 197

Computing of ANOVA by using MS Excel
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Computing of ANOVA by using MS Excel
6/2/2021 200

 It is important that a researcher knows the concepts of the basic
statistical methods used for conduct of a research study.
 This will help to conduct an appropriately well-designed study
leading to valid and reliable results.
 Inappropriate use of statistical techniques may lead to faulty
conclusions, inducing errors and undermining the significance of the
article.
6/2/2021 201

 Bad statistics may lead to bad research, and bad research may leadto unethical
practice.
 Hence, an adequate knowledge of statistics and the appropriate use of statistical
tests are important.
 An appropriate knowledge about the basic statistical methods will go a long way
in improving the research designs and producing quality medical research
 which can be utilised for formulating the evidence-based guidelines.
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References
1. Bhatt, S., Mahesh, R., Devadoss, T. & Jindal, A. K. Anxiolytic-like
effect of (4-benzylpiperazin-1-yl)(3-methoxyquinoxalin-2-
yl)methanone (6g) in experimental mouse models of anxiety. Indian
J. Pharmacol. 45, 248–251 (2013).
2. Choudhary, N., Khatik, G. L., Choudhary, S., Singh, G. & Suttee,
A. In vitro anthelmintic activity of Chenopodium album and in-silico
prediction of mechanistic role on Eisenia foetida. Heliyon 7, e05917
(2021).

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References
3. Mishra, P., Singh, U., Pandey, C., Mishra, P. & Pandey, G.
Application of student’s t-test, analysis of variance, and covariance.
Ann. Card. Anaesth. 22, 407 (2019).
4. Rahman, S. N. R. et al. Application of Design of Experiments®
Approach-Driven Artificial Intelligence and Machine Learning for
Systematic Optimization of Reverse Phase High Performance Liquid
Chromatography Method to Analyze Simultaneously Two Drugs
(Cyclosporin A and Etodolac) in Solution, Human Plasma,
Nanocapsules, and Emulsions. AAPS PharmSciTech 22, (2021).

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References
5. Shunmugaperumal, T. & Kaur, V. In Vitro Anti-inflammatory and
Antimicrobial Activities of Azithromycin After Loaded in Chitosan- and
Tween 20-Based Oil-in-Water Macroemulsion for Acne Management.
AAPS PharmSciTech 17, 700–709 (2016).
6.Singh, S. Testing in Statistics — Part One. 933, (2020).
7. Blog, B. F. Nominal , Ordinal , Interval & Ratio Variable + [ Examples ]
What is a Measurement Variable ? Types of Measurement Variables
Nominal Variable.
8. Now, C. Categorical Data : De nition + [ Examples , Variables &
Analysis ] Categorical Data De nition Types of Categorical Data.
9. Lavrakas, P. J. Looks like you do not have access to this content. 2–3
(2008).

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10. Blog, S. et al. Statistics How To. 1–11 (2021).
11. Najat, A. The importance of statistical tools for data evaloutions
Prepared by : Abdulla Najat Tawfiq. 0–16 (2021).
doi:10.13140/RG.2.2.34553.19042
12. Ali, Z. & Bhaskar, S. B. Basic statistical tools in research and data
analysis. Indian J. Anaesth. 60, 662–669 (2016).
13. Begum, K. J. & Ahmed, A. The Importance of Statistical Tools in
Research Work. Int. J. Sci. Innov. Math. Res. 3, 50–58 (2015).
14. Of, T. & Most, D. 1 ) Nominal Data : (2019).

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15. Rennemeyer, A. Types of Data in Statistics - Nominal, Ordinal,
Interval, and Ratio Data Types Explained with Examples. Freecodecamp
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You may catch me via ashish7sattee@gmail.com
Contact no. 9814778316

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