1. 3. Data analysis
SIS

2. Exercise 3.1 Trend consistent change (increase or decrease)
eg atmospheric temperatures
Pattern
Repeated change (increase and decrease)
seasonal variations

3. Exercise 3.2
Which is a more useful graph – join the dots or line of best fit?
they both have uses 
 join the dots shows the variation, LOBF the trend
Can you see any trend?
decrease 
What effect would it have on your certainty if you only had data from 1996, 2000, 2004 and 2008?
still a decrease but less obvious from 2000
What value do you think might occur in 2009? in 2030?

4. Time series
a line graph where a measured variable is plotted against time
can help identify patterns, eg:
a trend,
a repeating cycle,
random fluctuation (not actually a pattern)
a combination of all three
natural (random) variation in the measurements may cause the pattern to be blurred by “noise”

5. Figure 3.1 is there a trend in this data? a small rise(???)
a line of best fit through the data is very dubious
smooth the data
clear some of the noise
the real pattern becomes clear
smoothing means the loss of the raw data
should be clearly shown as smoothed

6. The running means smoothing method
requires that there are no gaps in the data
each time interval between the data is the same
calculate and plot the mean of a number of successive data points
three and five are common
Example 3.1

7. Exercise 3.2 data smoothed

8. Linear regression a fancy name for line of best fit Class Exercise 3.4
The data in Exercise 3.2: slope of –0.1 and a y-intercept of 211.
(a) Use this to calculate the value for the fallout in (i) 2000, (ii) 2009 and (iii) 2030 
2000: : : 8.0
(b) Which do you believe is the (i) most accurate and (ii) least accurate?
Most: Least: 2030

9. Exercise 3.3
What is the difference between interpolation and extrapolation?
interpolation – determining a value within the data range
extrapolation – determining a value outside the data range

10. Extrapolation error

11. 3.1 Outliers
data points in a set that seem to be so different from the rest
they don’t belong (??) and should be deleted (??)
leaving them in changes the mean and standard deviation
unless the measurement process for the suspect point is known to have a problem
you should not simply remove it without testing

12. Example 3.2
9.21
9.13
9.05
9.25
8.95
9.10
8.99
4.28
9.22
With outlier
Without outlier
Mean
8.62
9.11 SD
1.53
0.11

13. The Q-test for outliers
calculate a test-value (Q in this case) from equation based on the data
compare this value to a table of values
make a judgement on the basis of the comparison
Q = | vo – vn | ÷ r
vo is the value of the outlier
vn the value of the nearest data point
r the range (always positive)
compare to table value
if Q > table, the outlier can be deleted

14. Example 3.3
Can the 4.28 point from the DO data in Example 3.4 be eliminated (using medium limits)?
Q = (8.95 – 4.28) ÷ (9.25 – 4.28) = 0.94
table value is 0.48 (10 pts)
0.94 (Q) > 0.48 (table)
can safely delete the 4.28 data point

15. Exercise 3.4 (a) 15, 22, 18, 6, 25, 19 doubtful value is 6
Q = |15 – 6|÷ (25-6) = 0.47
Table value = 0.64 > Q value
Can’t discard
(b) 0.75, 0.83, 0.53, 0.82, 0.76, 0.81, 0.69, 1.03
doubtful values are 0.53 &1.03
Q = 0.32 & 0.42; Table value = 0.54
Can’t discard either
(c) 41.5, 46.2, 41.6, 42.0, 41.1, 42.1
doubtful value is 46.2
Q = 0.80; Table value = 0.54
Can discard