a full lecture presentation on ANOVA .
areas covered include;
a. definition and purpose of anova
b. one-way anova
c. factorial anova
d. mutiple anova
e MANOVA
f. POST-HOC TESTS - types
f. easy step by step process of calculating post hoc test.
a full lecture presentation on ANOVA .
areas covered include;
a. definition and purpose of anova
b. one-way anova
c. factorial anova
d. mutiple anova
e MANOVA
f. POST-HOC TESTS - types
f. easy step by step process of calculating post hoc test.
Ducan’s multiple range test - - Dr. Manu Melwin Joy - School of Management St...manumelwin
In 1955, Duncan devised a method to compare each treatment mean with every other treatment mean. The procedure is simple and powerful and has become very popular among researchers, especially in the plant science area.
A Study of Some Tests of Uniformity and Their PerformancesIOSRJM
The uniform distribution appears due to natural random events or to the application of methods for transforming samples from any other distribution to samples with uniformly distributed values in the interval (0,1). Thus, in order to test whether a samplecomes from a given distribution, one can test whether its transformed sample is distributed according to the uniform distribution or not. Several test procedures are developed to test the goodness of fit for uniformity. In this paper, we want to study the performance of eleven different tests for uniformity by considering different sample sizes as well as different alternatives. The results so obtained are displayed in various tables and graphs. Finally, conclusions are made on the basis of the results.
Chi square test- a test of association, Pearson's chi square test of independence, Goodness of fit test, chi square test of homogeneity, advantages and disadvantages of chi square test.
Ducan’s multiple range test - - Dr. Manu Melwin Joy - School of Management St...manumelwin
In 1955, Duncan devised a method to compare each treatment mean with every other treatment mean. The procedure is simple and powerful and has become very popular among researchers, especially in the plant science area.
A Study of Some Tests of Uniformity and Their PerformancesIOSRJM
The uniform distribution appears due to natural random events or to the application of methods for transforming samples from any other distribution to samples with uniformly distributed values in the interval (0,1). Thus, in order to test whether a samplecomes from a given distribution, one can test whether its transformed sample is distributed according to the uniform distribution or not. Several test procedures are developed to test the goodness of fit for uniformity. In this paper, we want to study the performance of eleven different tests for uniformity by considering different sample sizes as well as different alternatives. The results so obtained are displayed in various tables and graphs. Finally, conclusions are made on the basis of the results.
Chi square test- a test of association, Pearson's chi square test of independence, Goodness of fit test, chi square test of homogeneity, advantages and disadvantages of chi square test.
Quantitative Analysis for Emperical ResearchAmit Kamble
Overview for Approach Methods for quantitative analysis; which includes
1) Planning of Experiments
2) Data Generation
3) presentation of report
some numerical approach methods; data modeling; hypothesis methods
Chapter 8
Sampling
Sampling
Sampling involves decisions about who or what will be tested, observed, or interviewed in your study (Morse, 2007)
Key questions to address:
Who should and should not be included?
How many should be included?
Probability
Probability is the likelihood that an event or a condition will occur
You can express probability in terms of the chance the event will occur or in percentages
Levels of Significance
Levels of significance are the difference that will be accepted as too large to be attributed to chance
These levels are set by the researcher at the outset of a study
Probability Samples
Probability samples are formed to ensure that each subject has an equal chance of being included so an unbiased sample can be used
Probability Samples
A sampling design explains how the subjects are chosen and should include:
Number of subjects
How they will be assessed, screened, and selected
Inclusion and exclusion criteria
Probability Samples
Random selection is accomplished by having:
Identification of all possible participants
Every potential participant is given an equal chance of being selected
Probability Samples
Variations of random sampling include:
Stratified: randomly select from each stratum
Cluster: sample groups rather than individuals
Multistage: sample from multiple sets of clusters
Nonprobability Sampling
Reasons why researchers use nonprobability samples are:
Limited resources for developing an accurate sampling frame or purchase lists of potential subjects
Information needed to identify all potential subjects is not available
Nonprobability Sampling
Reasons why researchers use nonprobability samples are:
Limited number of subjects
Subjects are difficult to find or difficult to persuade to participate in study
Subjects do not complete study
Experimental mortality
Nonprobability Sampling
Types of nonprobability samples include:
Quota sampling: select a specified number of participants from each group
Convenience sampling: enroll those who are available
Snowball network or referral sampling: begin with known individuals and ask them to refer others who meet selection criteria
Tracking and Reporting
Sample Development
In order to improve the reporting of randomized controlled trials (RCTs), the Consolidated Standards of Reporting Trials (CONSORT) were developed
A flow diagram that can be used for tracking sample development
CONSORT Flow Diagram
Source: Altman, D.G., Schulz, K.F., Moher, D., Egger, M.. Davidoff, F., Elbourne, D., Gøtzsche, P.C., & Lang, T. (2001). The revised CONSORT statement for reporting randomized trials: Explanation and elaboration. Annuals of Internal Medicine; 134(8), 663-694.
Example of Flowchart
Source: Buchbinder, R., Osborne, R.H., Ebeling, P. R., Wark, J.D., Mitchell, P.M., Wriedt, C., Graves, S.D., Staples, M.P., & Murphy, B. (2009). A randomized trial of vertebroplasty for painful osteoporotic vertebral factures. The New England Journal of Medicine, 361 ...
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Delivering Micro-Credentials in Technical and Vocational Education and TrainingAG2 Design
Explore how micro-credentials are transforming Technical and Vocational Education and Training (TVET) with this comprehensive slide deck. Discover what micro-credentials are, their importance in TVET, the advantages they offer, and the insights from industry experts. Additionally, learn about the top software applications available for creating and managing micro-credentials. This presentation also includes valuable resources and a discussion on the future of these specialised certifications.
For more detailed information on delivering micro-credentials in TVET, visit this https://tvettrainer.com/delivering-micro-credentials-in-tvet/
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Normal Labour/ Stages of Labour/ Mechanism of LabourWasim Ak
Normal labor is also termed spontaneous labor, defined as the natural physiological process through which the fetus, placenta, and membranes are expelled from the uterus through the birth canal at term (37 to 42 weeks
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
South African Journal of Science: Writing with integrity workshop (2024)
Unit 4 rm
1. General Classification of variables
1. Qualitative Variables (Categorical variables)
2. Quantitative Variables
(i) Discrete Variable
(ii) Continuous Variable
Prime considerations
(i) Observability
(ii) Count ability
(iii) Measurability
2. Variable
A Variable is a phenomenon that change from time to time,
place to place, and individual to individual etc.
Discrete variable
It can assume value from a limit set of numbers
Example :
(i) Number of flowers in a plant
(ii) Number of students in a class
(iii) Number of Non-defective screws in a box containing screws
(iv) Number of retail outlets
[Observable, countable]
3. Continuous variable [Observable,
Measurable]
Variables that can take any value within a range
Example
i) Leaf length of a particular plant
i) Weight of an apple
i) Distance travelled by a car
Experimental variable
The Variable whose effect is going to be known is called
experimental variable
Controlled variable
The effectiveness of an experimental variable is examined by
comparing with other variable, is called controlled variable
4. Structure of Variables in scientific
Investigations
i) Department Variable(s)
i) Independent Variable(s)
Dependent variable
A Variable is said to be dependent if it changes as a
result of change in the independent variable(s)
Independent Variable
Any variable that can be manipulated by the researcher is
known as independent variable
Example
(i) Leaf weight = f[Leaf length]
(ii) Profit of a company = f[sales]
(iii) Agricultural production = f[Rainfall, Soilfertility, Technology
Adoption]
5. Illustrations for variables
Name of Instrument Variable of study
1. Spectrophotometer (Biomedical
Engineering)
concentration of a given solution
2. Barometer (Electrical Engineering) Atmospheric Pressure
3. Electricity Meter / Energy Meter (Electrical
and Communication Engineering)
Energy dissipated from the circuit
resistance
4. Tensile tester (Mechanical Engineering) Tension testing
5. Hydrometer (Civil Engineering) Density of liquids
6. Packet Broker (Computer Engineering) Bandwidth analysis
NOTE: Clearly spell out the nature of the variable (Discrete/Continuous) with unit)
6. Nominal scale variables
i) These are unordered categorical variables
Nominal variables are often binary:
1-Presence, 0-Absence
Example: Sex of the respondent (Male, Female)
Hair color (Black, White, Grey)
Presence of absence of depression (1. Presence, 0-absence)
Ordinal Scale Variables
They are ranked data where there is an ordering of categories
7. STATISTICAL DISTRIBUTIONS
Discrete distributions: Based on Discrete Variable
1. Binomial Distribution
2. Poisson Distribution
3. Geometric Distribution
Continuous Distributions: Based on Continuous Variable
1. Normal Distribution
2. Exponential Distribution
3. Weibull Distribution
Points to be considered
1. Definition
2. Example
3. Applications
8. BINOMIAL DISTRIBUTION
James Bernoulli
Details Success Failure
Product Manufacturing Confirms to quality standards Not confirming to equality
standards
Plant experiment Seed germinated Seed not germinated
Medical Experiment Medicine cured Medicine Not cured
9. Experiment
A plant biologist wanted to test the quality of the seeds. He has conducted the
experiment is 100 pots. In each pot has kept 5 seeds. The results are
presented in the following table
Number of (x) Seeds Germinated 0 1 2 3 4 5 Total
Number of Pots (f) 15 25 30 20 6 4 100=N
10. Definition
The probability distribution of the random variable ‘x’, the number
of success is ‘n’ Binomial trails, is called binomial distribution and
is given by the formula
Where =0 otherwise
n⇒Number of trails
p⇒Probability of success
q⇒Probability of failure
x⇒Number of successes in ‘n’ trails
n,p ⇒ parameters of the distribution
p+q=1
11. Poisson Distribution
Prof. S.D. Poisson
Occurrence of Rare Event
1. Occurrence of flood in the last century is a country
2. Identification of printing mistakes occured in a dictionary
with large number of pages
3. Occurrence of deaths due to a rare disease
12. DATA
The following data is related to the occurrence of number of
floods in the last century in India
Number of floods occurred (x) 0 1 2 3 4≥ Total
Number of years (f) 85 9 3 2 1 N=100
14. Geometric Distribution
A random variable ‘x’ is said to have geometric distribution if it
assumes non-negative values and it is given by:
Applications
1. Finding inefficiency of a telephone exchange system
during busy periods of time
2. To help managers to reduce the system trails occurring
prior to success to reduce costs.
19. Weibull Distribution
Applications
1) Reliability and software
2) Probability that the drill bit with fail before 10 hours of
usage
3) Determination of Hazard Rate in order to set a service of
wear and strength of a component
A Continuous random variable ‘x’ has a Weibull distribution with parameter α and β
and its probability density function is given by
21. SAMPLING METHODS AND TYPE OF
POPULATION
Method of Sampling Type of Population
1. Simple Random sampling Homogenous population
2. Stratified sampling Heterogeneous population
3. Systematic sampling Homogenous population
4. Cluster sampling Mixed Type!
22. SIMPLE RANDOM SAMPLING (SRS)
SRSWOR : Simple Random sampling Without Replacement
SRSWR : Simple random Sampling With Replacement
23. STRATIFIED SAMPLING : How to Draw
Samples ?
Strata : DIVISIONS (PLURAL)
Stratum : DIVISION (SINGULAR)
27. CLUSTER SAMPLINGS
Clusters
(i) Clusters
(ii)Equal size
Unequal size
•Each cluster will consist of Homogenous units Mostly in practical
situations, we find clusters of unequal size
•We will select the required number of clusters RANDOMLY from the
CLUSTERS
•We survey all the units in the selected clusters
28. EXAMPLE
We observe that there are 7 clusters
The clusters consists of unequal number of units
Selected 3 clusters RANDOMLY out of 7 clusters
Let the selected clusters are c2
, c5
and c7
We collect the required from all the units in clusters 2,5, and 7
This method is called cluster sampling
NOTE : The units from the selected clusters are HOMOGENOUS / Nearly
Homogenous
c1
29. LARGE SAMPLE Sample size ‘n’ ≥ 30
SMALL SAMPLE Sample size ‘n’ <30
Tests based on size of samples
Student’s t-test (n<30)
Chi-square test (n>30)
F-test (n<30)
TESTS BASED ON
SAMPLES
30. BASIC TABLE FOR UNDERSTANDING
STATIC Based on Sample
PARAMETER Based on
Population
50. FACTOR ANALYSIS
Meaning
It is a multivariate statistical technique to identify the
factors underlying the variables by means of clubbing
related variables in the same factor. Variables are
clubbed into different factors on the basis of their
interrelationship.
The number of data set should be at least five per variable
Number of variables = 15
Size of the sample = 75
51. Example
Objective of the study
A market researcher wants to determine the underlying
benefits consumers seek from the purchase of a car
Variables under study
X1: I like a car that has stylish Interior
X2: I like a car that looks great
X3: I prefer a car that gives high mileage
X4: I prefer a car with low maintenance
X5: I prefer a car that provides a good value for money
Rating Scale
0 Strongly Disagreeing
1 Disagreeing
2 Agreeing
3 Agreeing to a great extent
4 Strongly Agreeing
53. Discriminant Analysis
Meaning
Discriminant Analysis is a multivariate statistical technique
used for classifying a set of observations into predefined
groups. The purpose is to determine the predicator
variables on the basis of groups determined. The form of
the discriminate function is given by
Where c => a constant
bi => Discreminant Coefficient
Xi => Predictor Variables
54. Example
Objective of the study
To study the successfulness or not for a new improved digital
camera
Characteristics under the study
X1: Durability of the camera
X2: performance of the camera
X3: Style
Category : Buyer of the Digital camera
Non-Buyer of the Digital camera
Rating Scale
0 Poor
1 Fair
2 Good
3 Better
4 Excellent
56. Cluster Analysis
Meaning
It is a multivariate statistical technique for grouping cases
of data based on SIMILARITY of responses to several
variables / objects. The purpose of cluster analysis is to place
subjects / objects into groups, or clusters, suggested by the
data, such that objects in a cluster are homogeneous in some
sense, and objects in different clusters are dissimilar to a
great extent
57. Example
Objective of the study
A canteen manager wishes to study the clusters of students
preference of 5 brands of carbonated Soft Drinks
Brands of Carbonated Soft Drinks
X1
: Coke
X2
: Pepsi
X3
: Thumps up
X4
: Sprite
X5
: Dew
Rating Scale
0: Very rarely
1: Normally
3: Often
4: Quite often
58. k
Perform cluster Analysis and find the Homogeneous clusters of
the Carbonated Soft Drinks
Example:
Cluster 1: Coke, Pepsi, Thumps Up
Cluster 2: Sprite, Dew
59. ANALYSIS OF VARIANCE / DESIGNS
OF EXPERIMENTS
Meaning
To study the variation is the data set in a systematic manner
using F-test
60. DESIGN
Objective : To study the variation is relief time among the
patients suffering from a particular ailment
The above data structure is called Completely Randomized
Design
61. RANDOMIZED BLOCK DESIGN
Objective
To study the variation in relief time among the patients
suffering from a particular ailment. Variation in Relief Time (2
Factors)
Effect of Drug (Between Drugs)
Effect of Age (Between Age group)
Data Structure
Drugs Administered : A,B,C,D and E
Age group of Patients : < 14, 14 - 35, 35 - 60, 60≥
62.
63. LATIN SQUARE DESIGN (LSD)
Meaning
i) A LSD is an arrangement of n2
observations (objects)
i) An Observation (object) can occur only once in the
row/column
64. LATIN SQUARE DESIGN
Objective :
To study the variation in relief time among the patients suffering
from a particular ailment
Variation in Relief Time (3 Factors)
(1) Effect of drug (Between Drugs) [D1
,D2
,D3
,D4
]
(2) Effect of Age (Between Age Groups)
[ <14, 14-35, 35-60, 60≥ ]
(3) Effect of Administering time [Between Administering
Time]
A: 4 AM
B: 8 AM
C: 2 PM
D: 6 PM
65.
66. SAMPLE PROBLEM-RANDOMIZED BLOCK
DESIGN
Based on the data given below carry out the analysis and
comment on your results
[Given F0.05
=4.76 for (3.6) d.f. and F0.05
=5.14 for (2,6) d.f.]
67.
68.
69.
70. SAMPLE PROBLEM – Latin Square Design
An agricultural experiment was conducted and the
results are given below. The design adopted is a LSD.
Analyze the data and comment on your results.
[Given F0.05
=4.76 for (3.6) d.f]
71.
72.
73. Time Series Analysis
MEANING : A Phenomenon relating to time is called a time series
set up
COMPONENTS OF TIME SERIES
1. Trend
2. Seasonal variation
3. Cyclical variation
4. Irregular Variation
Time series Model
Yt
=T+S+C+I (Additive Model)
or
Yt
=T.S.C.I (Multiplicative Model)