powerpoint

1. CORRELATION ANALYSIS
Jan Niño G. Tinio, MSc
Department of Mathematics
Caraga State University

2. Correlation Analysis
Correlation is a statistical technique
that can show how strongly related
a pair of variables are.
Examples:
(1) score and the no. of hours studying
(2) extent of experience and
competence at work

3. Correlation Analysis
❑ The correlation coefficient, r describes the
extent of correlation between the variables.
❑ One can have idea on the direction, and
strength of the relationship
Ranges from -1.0 to +1.0
Extent: -1.0 or +1.0, strong; close 0, weak;
❑ The p-value shows the extent of practical
significance; that is, as to data provide
sufficient evidence that correlation between
the variables is significant.
Rule of the thumb: p-value < α

5. What test should be used?
Relationship
❑ Pearson Correlation (Pearson Product-Moment
Correlation)
❑ Kendall’s Tau-b Correlation
❑ Spearman’s Rank-Order Correlation
Association
❑ Chi-square

6. Hypotheses
Null Hypothesis: There is no significant
relationship/association between variable 1 and
variable 2.
Alternative Hypothesis: There is a significant
relationship/association between variable 1 and
variable 2.

7. ASSUMPTIONS
❑ The two variables considered should be
measured at the interval or ratio level.
❑ There is linear relationship between the two
variables (ex. use scatterplot to check the
linearity)
❑ There should be no significant outliers.
❑ The variables should be approximately normally
distributed.
PARAMETRIC
STAT

8. ASSUMPTIONS
❑ The two variables considered should be
measured at the interval or ratio level.
PARAMETRIC
STAT

9. ASSUMPTIONS
❑ There is linear relationship between the two
variables (ex. use scatterplot to check the
linearity)
PARAMETRIC
STAT

10. ASSUMPTIONS
❑ There is linear relationship between the two
variables (ex. use scatterplot to check the
linearity)
PARAMETRIC
STAT

11. ASSUMPTIONS
❑ There should be no significant outliers.
PARAMETRIC
STAT

12. ASSUMPTION
❑ The
variables
should be
approxi-
mately
normally
distributed.
PARAMETRIC
STAT
Case 1: Normal
Case 2: Non-normal

13. Kendall’s Correlation
ASSUMPTIONS
❑ The two variables should be measured on
an at least ordinal scale.
(Preferably used for small sample size non-
normal quantitative data)
Non-PARAMETRIC STAT

14. Spearman’s Correlation
Assumptions:
The two variables considered should
be measured on an ordinal, or interval
or ratio level.
Non-PARAMETRIC
STAT

15. Chi-square Test for Association
This test is used to determine whether there is
significant association between two categorical
variables.
Significant value (p-value): We want to compare
this value to the default value of α (level of
significance), which is set to 0.05 or 5%. The
decision rule is: If p-value is lesser than α, then
there is significant association between the two
variables. Otherwise, association is not significant.
Non-PARAMETRIC
STAT

16. Correlation Analysis Statistical Training for MSCRC Study Consultants
What to do?
1) Determine
assumptions.
2) Select
appropriate
correlation
tools.
3) Analyze data.
4) Interpret
outputs.
Test of Significant

17. Data Cleaning and Processing Statistical Training for MSCRC Study Consultants
Exploration with
SPSS
What to explore?
Check normality of
data…
ANALYZE…NON-
PARAMETRIC…ONE-
SAMPLE TEST…RUN
Test of Significant

18. Data Cleaning and Processing Statistical Training for MSCRC Study Consultants
Exploration with
SPSS What to explore?
Analyze data using
selected tools…
ANALYZE…CORRELATI
ON…BIVARIATE…
CHECK chosen tools...
RUN
Test of Significant