3. • Correlation refers to any of a broad class
of statistical relationships involving
dependence.
4.
5. Why is correlation important?
•
•
•
•
One of the most frequently used statistics – Important to be able to
interpret it correctly
Fundamental to theory building
Basis of many meta-analyses
Building block for more sophisticated methods – e.g., Multiple
Regression, Factor Analysis, Structural Equation Modelling
12. BIVARIATE CORRELATIONS
• In Bivariate Correlations, the relationship
between two variables is measured. The
degree of relationship (how closely they
are related) could be either positive or
negative.
• The maximum number could be either +1
(positive) or -1 (negative). This number is
the correlation coefficient. A zero
correlation indicates no relationship.
• Examples. Are a student’s grade and the
amount of studying done correlated? You
might find that these variables are
positively correlated.
13. PARTIAL CORRELATIONS
•
The Partial Correlations procedure computes partial
correlation coefficients that describe the linear
relationship between two variables while controlling for
the effects of one or more additional variables.
Correlations are measures of linear association.
•
Example. Is there a relationship between healthcare
funding and disease rates? Although you might expect
any such relationship to be a negative one, a study
reports a significant positive correlation: as healthcare
funding increases, disease rates appear to increase.
Controlling for the rate of visits to healthcare providers,
however, virtually eliminates the observed positive
correlation.
14. DISTANCES
• This procedure calculates any of a wide
variety of statistics measuring either
similarities or dissimilarities (distances),
either between pairs of variables or
between pairs of cases. These similarity or
distance measures can then be used with
other procedures, such as factor analysis,
cluster analysis, or multidimensional
scaling, to help analyze complex data sets.
• Example: Is it possible to measure
similarities between pairs of automobiles
based on certain characteristics, such as
engine size, MPG, and horsepower? By
computing similarities between autos, you
can gain a sense of which autos are
similar to each other and which are
different from each other.
15. Other Forms of correlations
• Spearman correlation coefficient – Less
influenced by outliers
• – Converts data to ranks before correlating
• Point-Biserial correlation
– One binary and one metric variable
• Let see :
16.
17. • When a quantitative factor is used, trend
analysis is very useful
18. Why Trend Analysis Studies Used
1.
Allows us to describe a historical pattern
2.
Able to make projections on past patterns, past or
future trends
3.
In most instances, it allows us to eliminate trend
component of the series
19. • Standard form of ANOVA could be
applied but would not capitalize on
the quantitative information
available
• By assuming a linear model, the
following fit is obtained
20. • In statistics, trend analysis often refers to
techniques for extracting an underlying pattern
of behaviour in a time series which would
otherwise be partly or nearly completely hidden
by noise.
• A simple description of these techniques is
trend estimation, which can be undertaken
within a formal regression analysis.
21. • The independent variable is a continuous
variable representing the amount of weekly
reading hours, while the dependent variable is a
continuous variable representing reading
achievement scores.
22. • Research question: Is there a
linear trend between the
amount of weekly reading
hours and reading
achievement?
23. • We usually plot the entire set of treatment means on a graph,
connect the points, and examine the display for any underling
shape or trend.
24. • Trend analysis is a specialized form of
single-df comparisons when a quantitative
independent variable is manipulated.
• Analyze…Compare Means…One-Way
ANOVA
• See :
