This document provides an overview of reliability analysis and factor analysis. It discusses the concepts of validity, reliability, and their importance in scientific research. Reliability is defined as the consistency or dependability of measurement, and is assessed using reliability analysis techniques like Cronbach's alpha. Factor analysis is introduced as a technique to simplify complex constructs into underlying dimensions or factors. The key steps of factor analysis include examining the correlation matrix, extracting initial factors using methods like principal component analysis, and rotating factors to arrive at the final factor solution. Decisions on the number of factors are based on statistical criteria like eigenvalues and scree plots, as well as conceptual grounds.
Ragui Assaad- University of Minnesota
Caroline Krafft- ST. Catherine University
ERF Training on Applied Micro-Econometrics and Public Policy Evaluation
Cairo, Egypt July 25-27, 2016
www.erf.org.eg
Ragui Assaad- University of Minnesota
Caroline Krafft- ST. Catherine University
ERF Training on Applied Micro-Econometrics and Public Policy Evaluation
Cairo, Egypt July 25-27, 2016
www.erf.org.eg
Ragui Assaad- University of Minnesota
Caroline Krafft- ST. Catherine University
ERF Training on Applied Micro-Econometrics and Public Policy Evaluation
Cairo, Egypt July 25-27, 2016
www.erf.org.eg
Ragui Assaad- University of Minnesota
Caroline Krafft- ST. Catherine University
ERF Training on Applied Micro-Econometrics and Public Policy Evaluation
Cairo, Egypt July 25-27, 2016
www.erf.org.eg
A chapter describing the use and application of exploratory factor analysis using principal axis factoring with oblique rotation.
Provides a step by step guide to exploratory factor analysis using SPSS.
Explains use of statistical power, inferential decision making, effect sizes, confidence intervals in applied social science research, and addresses the issue of publication bias and academic integrity.
Potential Solutions to the Fundamental Problem of Causal Inference: An OverviewEconomic Research Forum
Ragui Assaad- University of Minnesota
Caroline Krafft- ST. Catherine University
ERF Training on Applied Micro-Econometrics and Public Policy Evaluation
Cairo, Egypt July 25-27, 2016
www.erf.org.eg
This presentation deals with the basics of design of experiments and discusses all the three basic statistical designs i.e. CRD, RBD and LSD. Further it explains the guidelines for developing experimental research.
For more classes visit
www.snaptutorial.com
Exam 1 Psych 355
3. A p level of 0.05 corresponds to a confidence level of __________%
4. In a within-groups design where one group is measured twice over time, the appropriate hypothesis test is an:
7. Why do we divide by N-1 rather than by N when estimating a population standard deviation from the sample standard deviation?
Presenting "Making Use of Reliability Statistics" 6:30pm May 7th at the local IEEE Reliability Society meeting - join us if you can.
In general we need to master the use of statistics to make better decisions. Let the data talk, explore it to learn it's secrets, and conduct experiments with a purpose.
A chapter describing the use and application of exploratory factor analysis using principal axis factoring with oblique rotation.
Provides a step by step guide to exploratory factor analysis using SPSS.
Explains use of statistical power, inferential decision making, effect sizes, confidence intervals in applied social science research, and addresses the issue of publication bias and academic integrity.
Potential Solutions to the Fundamental Problem of Causal Inference: An OverviewEconomic Research Forum
Ragui Assaad- University of Minnesota
Caroline Krafft- ST. Catherine University
ERF Training on Applied Micro-Econometrics and Public Policy Evaluation
Cairo, Egypt July 25-27, 2016
www.erf.org.eg
This presentation deals with the basics of design of experiments and discusses all the three basic statistical designs i.e. CRD, RBD and LSD. Further it explains the guidelines for developing experimental research.
For more classes visit
www.snaptutorial.com
Exam 1 Psych 355
3. A p level of 0.05 corresponds to a confidence level of __________%
4. In a within-groups design where one group is measured twice over time, the appropriate hypothesis test is an:
7. Why do we divide by N-1 rather than by N when estimating a population standard deviation from the sample standard deviation?
Presenting "Making Use of Reliability Statistics" 6:30pm May 7th at the local IEEE Reliability Society meeting - join us if you can.
In general we need to master the use of statistics to make better decisions. Let the data talk, explore it to learn it's secrets, and conduct experiments with a purpose.
Lifting and handling solutions for heavy wind turbine components - Fyns Kran ...Fyns Kran Udstyr A/S
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Determining the right sample size for a reliability test is always challenging. If the sample size is too small, not enough failure information can be generated. If the sample is too large, cost and time probably will be wasted. In this presentation, we will discuss several commonly used methods on determining the right sample size for 1) reliability demonstration tests, 2) operational life tests under use condition, 3) accelerated life tests under elevated stresses. The theory behind these methods will be discussed first, and then examples of applying these methods will be provided using commercial software tools.
Data Analysis & Interpretation and Report WritingSOMASUNDARAM T
Statistical Methods for Data Analysis (Only Theory), Meaning of Interpretation, Technique of Interpretation, Significance of Report Writing, Steps, Layout of Research Report, Types of Research Reports, Precautions while writing research reports
CRM 101: What is CRM?
This is a simple definition of CRM.
Customer relationship management (CRM) is a technology for managing all your company’s relationships and interactions with customers and potential customers. The goal is simple: Improve business relationships to grow your business. A CRM system helps companies stay connected to customers, streamline processes, and improve profitability.
When people talk about CRM, they are usually referring to a CRM system, a tool that helps with contact management, sales management, agent productivity, and more. CRM tools can now be used to manage customer relationships across the entire customer lifecycle, spanning marketing, sales, digital commerce, and customer service interactions.
A CRM solution helps you focus on your organization’s relationships with individual people — including customers, service users, colleagues, or suppliers — throughout your lifecycle with them, including finding new customers, winning their business, and providing support and additional services throughout the relationship.
Who is CRM for?
A CRM system gives everyone — from sales, customer service, business development, recruiting, marketing, or any other line of business — a better way to manage the external interactions and relationships that drive success. A CRM tool lets you store customer and prospect contact information, identify sales opportunities, record service issues, and manage marketing campaigns, all in one central location — and make information about every customer interaction available to anyone at your company who might need it.
With visibility and easy access to data, it's easier to collaborate and increase productivity. Everyone in your company can see how customers have been communicated with, what they’ve bought, when they last purchased, what they paid, and so much more. CRM can help companies of all sizes drive business growth, and it can be especially beneficial to a small business, where teams often need to find ways to do more with less.
Here’s why CRM matters to your business.
CRM is the largest and fastest-growing enterprise application software category, and worldwide spending on CRM is expected to reach USD $114.4 billion by the year 2027. If your business is going to last, you need a strategy for the future that’s centered around your customers, and enabled by the right technology. You have targets for sales, business objectives, and profitability. But getting up-to-date, reliable information on your progress can be tricky. How do you translate the many streams of data coming in from sales, customer service, marketing, and social media monitoring into useful business information?
A CRM system can give you a clear overview of your customers. You can see everything in one place — a simple, customizable dashboard that can tell you a customer’s previous history with you, the status of their orders, any outstanding customer service issues, and more. You can even choose to include information
Research is a systematic and scientific method of finding solutions by obtaining various types of data and systematic analysis of the multiple aspects of the issues related.
The techniques or the specific procedure which helps to identify, choose, process, and analyze information about a subject is called Research Methodology
Experimental design is a statistical tool for improving product design and solving production problems.
INTRODUCTION
DEFINITION
HYPOTSIS
ANALYSIS OF QUANTITATIVE DATA
STEPS OF QUANTITATIVE DATA ANALYSIS.
STEPS OF QUANTITATIVE DATA ANALYSIS.
INTERPRETATION OF DATA
PARAMETRIC TESTS
Commonly Used Parametric Tests.
• Quantitative research
It is for cases where statistical conclusions to collect actionable insights are essential. Numbers provide a better perspective for making critical business decisions. Quantitative research methods are necessary for the growth of any organization. Insights drawn from complex numerical data and analysis prove to be highly effective when making decisions about the business’s future.
Why limit ourselves to traditional quantitative metrics like visitor count, page weight, conversion, and revenue when there is so much valuable qualitative data available? We can turn qualitative data into quantitative data and use the same rigorous analysis techniques to help lead us to better designs, products, services, and experiences.
Factor analysis is a technique that is used to reduce a large number of variables into fewer numbers of factors. The basic assumption of factor analysis is that for a collection of observed variables there are a set of underlying variables called factors (smaller than the observed variables), that can explain the interrelationships among those variables.
1. 1
Introduction to applied statistics
& applied statistical methods
Prof. Dr. Chang Zhu1
Overview
•Reliability analysis
•Factor analysis
2. 2
Validity and Reliability
• The principles of validity and reliability are
fundamental cornerstones of the scientific
method.
Reliability
• The degree of consistency between two
measures of the same thing (Mehrens and
Lehman, 1987).
• The measure of how stable, dependable,
trustworthy, and consistent a test is in
measuring the same thing each time
(Worthen et al., 1993)
3. 3
Reliability
Intrinsic
motivation
• Extrinsic
motivation
Reliability
• In science, theoretical constructs are often unobservable
things.
• Even when things are observable, measurement error
means often there is a need to calculate “summary”
variables.
• Reliability analysis tests whether the different
measurements are reliable/consistent
4. 4
Reliability
Reliability is used to measure the extent to
which an item, scale, or instrument will
yield the same score when administered in
different times, locations, or populations,
when the two administrations do not differ
in relevant variables.
Reliability analysis
• Reliability analysis allows you to study the
properties of measurement scales and the items
that make them up.
• Test the extent to which the items in your
questionnaire are related to each other
• Cronbach’s alpha is the most common used
measure of reliability.
• In SPSS: choose Analyze > Scale > Reliability
6. 6
Reliability analysis results
• The commonly accepted value of α is .7
Brief report:
• The reliability of the scale of xxx was
satisfactory (Cronbach’s alpha=xx).
Or
• The reliability of the scale of xxx was not
satisfactory (Cronbach’s alpha=xx).
Factor Analysis: constructs
• Constructs are usually defined as unobservable latent
variables.
• Example: the construct of teaching effectiveness. Several
variables are used to allow the measurement of such construct
(usually several scale items are used) because the construct
may include several dimensions.
• Unlike variables directly measured such as speed, height,
weight, etc., some variables such as egoism, creativity,
happiness, satisfaction, learning conceptions, learning styles,
teaching styles, self-regulation…. are not a single measurable
entity.12
8. 8
Factor Analysis
• A major goal of factor analysis is to represent
relationships among sets of variables parsimoniously
yet keeping factors meaningful.
• A good factor solution is both simple and
interpretable.
• When factors can be interpreted, new insights are
possible.
15
Understanding Factor Analysis
• Factor analysis is commonly used in:
–Data reduction
–Scale development
–The evaluation of the psychometric
quality of a measure, and
–The assessment of the dimensionality
of a set of variables.
16
9. 9
An example, a questionnaire of 30 items
5 factors are identified for the 30 item questionnaire
10. 10
Application of Factor Analysis
• Examine three common applications of factor analysis:
– Defining indicators of constructs (1)
– Defining dimensions for an existing measure (2)
– Selecting items or scales to be included in a measure (3)
19
Application of Factor Analysis (1)
Defining indicators of constructs:
Ideally 4 or more measures should be chosen to
represent each construct of interest.
The choice of measures should, as much as possible,
be guided by theory, previous research, and logic.
20
13. 13
Factor analysis
Step 1: The Correlation Matrix
– Generate a correlation matrix for all variables
– Identify variables not related to other variables
– If the correlation between variables are small, it is unlikely
that they share common factors (variables must be related
to each other for the factor model to be appropriate).
– Think of correlations in absolute value.
– Correlation coefficients greater than 0.3 in absolute value
are indicative of acceptable correlations.
– Examine visually the appropriateness of the factor model.
25
Factor analysis
Step 1: The Correlation Matrix
In SPSS:
• The Kaiser-Meyer-Olkin of sampling adequacy
(KMO) should be greater than .5 to be acceptable.
• Barlett’s test should be significant to indicate
variables are relatively independent from one another.
26
14. 14
The primary objective of this stage is to determine
the factors.
Initial decisions can be made here about the number
of factors underlying a set of measured variables.
Estimates of initial factors are obtained using
Principal components analysis.
The principal components analysis is the most
commonly used extraction method.
27
Factor analysis
Step 2: Factor extraction
• In principal components analysis, linear combinations of the
observed variables are formed.
• The 1st principal component is the combination that accounts
for the largest amount of variance in the sample (1st extracted
factor).
• The 2nd principle component accounts for the next largest
amount of variance and is uncorrelated with the first (2nd
extracted factor).
• Successive components explain progressively smaller portions
of the total sample variance, and all are uncorrelated with each
other.
28
Factor analysis
Step 2: Factor extraction
15. 15
• To decide on how many factors we need to represent
the data, we use 2 statistical criteria:
– Eigen Values, and
– The Scree Plot
29
Factor analysis
Step 2: Factor extraction
• The determination of the number
of factors is usually done by
considering only factors with
Eigen values greater than 1.
• Factors with a variance less than 1
are no better than a single variable,
since each variable is expected to
have a variance of 1.
30
Total Variance Explained
Comp
onent
Initial Eigenvalues
Extraction Sums of Squared
Loadings
Total
% of
Variance
Cumulativ
e % Total
% of
Variance
Cumulativ
e %
1 3.046 30.465 30.465 3.046 30.465 30.465
2 1.801 18.011 48.476 1.801 18.011 48.476
3 1.009 10.091 58.566 1.009 10.091 58.566
4 .934 9.336 67.902
5 .840 8.404 76.307
6 .711 7.107 83.414
7 .574 5.737 89.151
8 .440 4.396 93.547
9 .337 3.368 96.915
10 .308 3.085 100.000
Extraction Method: Principal Component Analysis.
Factor analysis
Step 2: Factor extraction
16. 16
• The examination of the Scree plot provides a
visual of the total variance associated with
each factor.
• The steep slope shows the large factors.
• The gradual trailing off (scree) shows the
rest of the factors usually lower than an
Eigen value of 1.
• In choosing the number of factors, in
addition to the statistical criteria, one should
make initial decisions based on conceptual
and theoretical grounds.
• At this stage, the decision about the number
of factors is not final.
31
Factor analysis
Step 2: Factor extraction
32
Component Matrixa
Component
1 2 3
I discussed my frustrations and feelings with person(s) in school .771 -.271 .121
I tried to develop a step-by-step plan of action to remedy the problems .545 .530 .264
I expressed my emotions to my family and close friends .580 -.311 .265
I read, attended workshops, or sought someother educational approach to correct the
problem
.398 .356 -.374
I tried to be emotionally honest with my self about the problems .436 .441 -.368
I sought advice from others on how I should solve the problems .705 -.362 .117
I explored the emotions caused by the problems .594 .184 -.537
I took direct action to try to correct the problems .074 .640 .443
I told someone I could trust about how I felt about the problems .752 -.351 .081
I put aside other activities so that I could work to solve the problems .225 .576 .272
Extraction Method: Principal Component Analysis.
a. 3 components extracted.
Component Matrix using Principle Component Analysis
Factor analysis
Step 2: Factor extraction
18. 18
• 4th Step: Making final decisions
– The final decision about the number of factors to choose is the
number of factors for the rotated solution that is most interpretable.
– To identify factors, group variables that have large loadings for the
same factor.
– Plots of loadings provide a visual for variable clusters.
– Interpret factors according to the meaning of the variables
• This decision should be guided by:
– A priori conceptual beliefs about the number of factors from past
research or theory
– Eigen values computed in step 2.
– The relative interpretability of rotated solutions computed in step 3.
35
Factor analysis
Step 4: Making final decisions
Factor Analysis
• What can be included in factor analysis?
19. 19
Practice
Practice: conduct factor and
reliability analyses
• A researcher has generated a new questionnaire which
is designed to measure happiness. The questionnaire
that she has generated has 10 items on it and she has
collected responses from 200 respondents.
• The questionnaire is measured on a five point scale
where 1 = strongly disagree and 5 = strongly agree.
• The data file is named Happy_measure.sav
• This example is taken from:
http://wps.pearsoned.co.uk/ema_uk_he_dancey_statsmath_4/84/21627/55366
53.cw/content/index.html
20. 20
In SPSS: Factor analysis
• Analyze > Dimension Reduction > Factor
• Move all the variables to the Items list
In SPSS: Descriptives options
• Select all the options in the Descriptives dialog box
21. 21
In SPSS: Extraction method
• Method: Principal components
• Analyze: correlation matrix and Scree plot
• Eigenvalues greater than 1
In SPSS: Rotation method
• Choose Varimax as the rotation method
22. 22
In SPSS: Factor scores
• Choose Anderson-Rubin as method of calculating
In SPSS: Options
• Choose Exclude case listwise for missing values
• Absolute value below: .4
23. 23
Preliminary analysis
• The first table we should look at is labeled
KMO and Barlett’s Test. The KMO value is
.79 (above .05) and the Barlett’s test is
significant (p < .001), which indicates that
the sample is adequate for factor analysis.
KMO and Bartlett's Test
Kaiser-Meyer-Olkin Measure of Sampling Adequacy. .790
Bartlett's Test of Sphericity Approx. Chi-Square 819.746
df 45
Sig. .000
How many factors to extract?
• eigenvalues
scree plot
Total Variance Explained
Component
Initial Eigenvalues Extraction Sums of Squared Loadings Rotation Sums of Squared Loadings
Total % of Variance Cumulative % Total % of Variance Cumulative % Total % of Variance Cumulative %
1 3.186 31.862 31.862 3.186 31.862 31.862 3.170 31.699 31.699
2 2.928 29.279 61.140 2.928 29.279 61.140 2.944 29.442 61.140
3 .757 7.569 68.710
4 .658 6.583 75.293
5 .637 6.369 81.662
6 .522 5.220 86.882
7 .429 4.290 91.171
8 .380 3.801 94.973
9 .316 3.155 98.128
10 .187 1.872 100.000
Extraction Method: Principal Component Analysis.
24. 24
interpretation
• Examine the underlying theme
Rotated Component Matrixa
Component
1 2
Q8_I want to go out and party .892
Q7_I want to contact friends & family .837
Q9_The people at work inspire me .779
Q2_I have lots of friends .754
Q3_I love meeting people .694
Q6_I have a lot to look forward to .825
Q10_I feel excited at the start of each day .802
Q4_I feel full of energy .801
Q1_I feel enthusiastic .748
Q5_I have lots of interesting things to do .647
In SPSS: Reliability analysis
Based on the factor analysis, we have 2 factors
extracted or 2 sub-scales and the respective items as
below:
• Sub-scale 1 (sociability): Q2, 3, 7, 8, and 9
• Sub-scale 2 (positive feeling): Q1, 4, 5, 6, 10
We will calculate the Cronbach’s α for sub-scale 1 first.
25. 25
In SPSS: Factor analysis
• Analyze > Scale > Reliability
• Move the variables Q2, 3, 7, 8, and 9 to the Items list
• In the output, the table Reliability Statistics tells us that
the internal consistency of the 5 items is measured with
α = .851 (which is high).
Reporting the results
• Description of the analysis
• Table of factor loadings
(practical guideline page 8 and 9)
26. 26
Reporting the results
• A principal component analysis (PCA) was conducted on the 10
items with orthogonal rotation (varimax). The Kaiser-Meyer-Olkin
measure verified the sampling adequacy for the analysis: KMO = .79
which is good according to Field (2009). All KMO values for
individual items are well above the acceptable limit of .50 (Field,
2009). Bartlett’s test of spherity χ² (45) = 819.746, p < .001,
indicated that correlations between items were sufficiently large for
PCA. Two components had eigenvalues over Kaiser’s criterion of 1
and in combination explained 61.14% of the variance. The scree plot
also supports a two-factor structure. Table 1 shows the factor
loadings after rotation. The items that cluster on the same factors
suggest that factor 1 represents sociability and factor 2 positive
feeling.
Analysis description
Assignment
• Reliability analysis
• Factor analysis