Transcript Adv Statistics

Sec 3 SMTP Research Module
ADVANCED
STATISTICS
Mrs Goh Cheng Wai
Relation of data
• A correlation tells us whether two
variables vary together
• Correlation coefficient
[X: independent variable, Y: dependent variable]
+1 (perfect correlation) X , Y 
- 1 (perfect negative correlation) X , Y 
0 (no correlation between X and Y)
Correlation  Cause and effect
• Correlations can only be used to estimate
the relationship between two
characteristics.
• Do not use them to establish cause and
effect.
• E.g. A high correlation between intelligence
and exposure to classical music
DOES NOT MEAN
listening to classical music causes one
to become intelligent.
ANOVA (Analysis of variance)
• How many sets of data can each t-test
compare?
• What if you must compare the means of 3
or more groups?
• ANOVA tells you whether there is an
overall difference among the groups.
• However, ANOVA cannot identify where
the difference lies or which pair is
responsible for the difference.
Standard deviation & standard error
Standard deviation
(SD) tells you how
scattered the
measurements are.
Standard error of
the mean (SE)
indicates the
uncertainty around
the estimate of the
mean.
Link between error bars and
statistical significance
Standard error bars
do not overlap.
Difference may be
significant or
insignificant.
Standard error bars
overlap.
Difference is
insignificant (p  0.05)
Hands-on session
3S1 and 3P3 (first seven in the list): Comp Lab 1
3S2 and 3O3: Comp Lab 2
3A3: Comp Lab 3
3I3 + 3P3 (next seven in the list): Comp Lab 4
Deadline to submit 1st draft of proposal to
mentor: Monday 11 April