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Types of errors in testing hypothesis.

There are two types of error in testing of hypothesis: Type I & Type II. Which error is more
dangerous? Discuss with examples. (Refer Chapter-14/ Module-12)
Embed course material concepts, principles, and theories (which require supporting citations), along
with two scholarly peer-reviewed references in support of your answer. Keep in mind that these
scholarly references can be found in the Saudi Digital Library by conducting an advanced search
specific to scholarly references.
Be sure to support your statements with logic and argument, citing all sources referenced. Post your
initial response early and check back often to continue the discussion. Be sure to respond to your peersÃ¢â‚¬â„¢
posts as well.
Chapter 15
STAGE 4: MEASURES OF ASSOCIATION
15-1
Learning Objectives
Understand . . .
Ã¯â€šâ€” How correlation analysis may be applied to study relationships
between two or more variables.
Ã¯â€šâ€” The uses, requirements, and interpretation of the product
moment correlation coefficient.
Ã¯â€šâ€” How predictions are made with regression analysis using the
method of least squares to minimize errors in drawing a line of
best fit.
Ã¯â€šâ€” How to test regression models for linearity and whether the
equation is effective in fitting the data.
Ã¯â€šâ€” The nonparametric measures of association and the
alternatives they offer when key assumptions and
requirements for parametric techniques cannot be met.
15-2
Measures of Association:
Interval/Ratio Data
Pearson correlation
coefficient
For continuous linearly related
variables
Correlation ratio (eta)
For nonlinear data or relating a
main effect to a continuous
dependent variable
Biserial
One continuous and one
dichotomous variable with an
underlying normal distribution
Partial correlation
Three variables; relating two with
the thirdÃ¢â‚¬â„¢s effect taken out
Multiple correlation
Three variables; relating one
variable with two others
Bivariate linear regression
Predicting one variable from
anotherÃ¢â‚¬â„¢s scores
15-3
Measures of Association:
Ordinal Data
Gamma
Based on concordant-discordant
pairs; proportional reduction in
error (PRE) interpretation
KendallÃ¢â‚¬â„¢s tau b
ranks
KendallÃ¢â‚¬â„¢s tau c
dimensions
SomersÃ¢â‚¬â„¢s d
P-Q based; asymmetrical
extension of gamma
SpearmanÃ¢â‚¬â„¢s rho
Product moment correlation for
ranked data
15-4
Measures of Association:
Nominal Data
Phi
Chi-square based for 2*2 tables
CramerÃ¢â‚¬â„¢s V
CS based; adjustment when one table
dimension >2
Contingency coefficient C
CS based; flexible data and distribution
assumptions
Lambda
PRE based interpretation
Goodman & KruskalÃ¢â‚¬â„¢s tau
PRE based with table marginals
emphasis
Uncertainty coefficient
Useful for multidimensional tables
Kappa
Agreement measure
15-5
Researchers Search for Insights
Burke, one of the worldÃ¢â‚¬â„¢s
most value to a project when
they look beyond the raw
grayÃ¢â‚¬Â¦discovering what the
data really mean.
15-6
PearsonÃ¢â‚¬â„¢s Product Moment Correlation r
Is there a relationship between X and Y?
What is the magnitude of the relationship?
What is the direction of the relationship?
15-7
Connections and Disconnections
Ã¢â‚¬Å“To truly understand consumersÃ¢â‚¬â„¢ motives
and actions, you must determine
relationships between what they think
and feel and what they actually do.Ã¢â‚¬Â
David Singleton, vp of insights
Zyman Marketing Group
15-8
Scatterplots of
Relationships
15-9
Scatterplots
15-10
Plot of Forbes 500 Net Profits with Cash
Flow
15-11
Diagram
of
Common
Variance
15-12
Interpretation of Correlations
X causes Y
Y causes X
X and Y are activated by
one or more other variables
X and Y influence each
other reciprocally
15-13
Artifact
Correlations
15-14
Interpretation of Coefficients

A coefficient is not remarkable simply
because it is statistically significant!
It must be practically meaningful.
15-15
Comparison of
Bivariate
Linear
Correlation
and
Regression
15-16
Examples of Different Slopes
15-17
Concept Application
X
Average Temperature (Celsius)
Y
Price per Case
(FF)
12
2,000
16
3,000
20
4,000
24
5,000
Mean =18
Mean = 3,500
15-18
Plot of Wine Price by Average
Temperature
15-19
Distribution of
Y for
Observation of
X
15-20
Wine Price
Study
Example
15-21
Least Squares
Line:
Wine Price
Study
15-22
Plot of Standardized Residuals
15-23
Prediction and Confidence Bands
15-24
Testing Goodness of Fit
Y is completely unrelated to X
and no systematic pattern is evident
There are constant values of
Y for every value of X
The data are related but
represented by a nonlinear function
15-25
Components of Variation
15-26
F Ratio in Regression
15-27
F Ratio in Regression
15-28
Coefficient of Determination: r2
Total proportion of
variance in Y explained by X
Desired r2: 80% or more
15-29
Chi-Square
Based
Measures
15-30
Proportional
Reduction of
Error
Measures
15-31
Statistical Alternatives for Ordinal
Measures
15-32
Calculation of
Concordant (P),
Discordant (Q),
Tied (Tx,Ty), and
Total Paired
Observations:
KeyDesign
Example
15-33
Calculation of
Concordant (P),
Discordant (Q),
Tied (Tx,Ty), and
Total Paired
Observations:
KeyDesign
Example
15-34
Commonly Used
Measures of
Association
15-35
KDL Data for SpearmanÃ¢â‚¬â„¢s Rho
_______ _____ Rank By_____ _____
_____
Applicant
Panel x
Psychologist y
d
d2
1
2
3
4
5
6
7
8
9
10
3.5
10.0
6.5
2.0
1.0
9.0
3.5
6.5
8.0
5.0
6.0
5.0
8.0
1.5
3.0
7.0
1.5
9.0
10.0
4.0
-2.5
5.0
-1.5
.05
-2
2.0
2.0
-2.5
-2
1.0
6.25
25.00
2.52
0.25
4.00
4.00
4.00
6.25
4.00
_1.00_
57.00
.
15-36
Key Terms
1837
Ã¯â€šâ€” Artifact correlations
Ã¯â€šâ€” Concordant
Ã¯â€šâ€” Bivariate correlation
Ã¯â€šâ€” Correlation matrix
analysis
Ã¯â€šâ€” Bivariate normal
distribution
Ã¯â€šâ€” Chi-square-based measures
Ã¯â€šÂ§ Contingency coefficient C
Ã¯â€šÂ§ CramerÃ¢â‚¬â„¢s V
Ã¯â€šÂ§ Phi
Ã¯â€šâ€” Coefficient of determination
(r2)
Ã¯â€šâ€” Discordant
Ã¯â€šâ€” Error term
Ã¯â€šâ€” Goodness of fit
Ã¯â€šâ€” Lambda
Ã¯â€šâ€” Linearity
Ã¯â€šâ€” Method of least squares
15-37
Key Terms
1838
Ã¯â€šâ€” Ordinal measures
Ã¯â€šâ€” Regression coefficients
Ã¯â€šÂ§ Gamma
Ã¯â€šÂ§ Intercept
Ã¯â€šÂ§ SomersÃ¢â‚¬â„¢s d
Ã¯â€šÂ§ Slope
Ã¯â€šÂ§ SpearmanÃ¢â‚¬â„¢s rho
Ã¯â€šÂ§ Residual
Ã¯â€šâ€” Pearson correlation
Ã¯â€šâ€” Scatterplot
coefficient
Ã¯â€šâ€” Prediction and
confidence bands
Ã¯â€šâ€” Proportional reduction in
error (PRE)
Ã¯â€šâ€” Regression analysis
Ã¯â€šâ€” Simple prediction