Provides an overview of statistical & decision science techniques, their application and benefits in agile software projects.

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Statistics & Decision Science for Agile
A Guided Tour
Provides an overview of statistical & decision science
techniques, their application and benefits in agile software
projects.
Agile Convention 2013
1st Agile & Scrum Event in Noida www.agilenoida.wordpress.com

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I am @sanjayaksaxena
cofounder of graype.in
with @R4CHN4
Pursuing Quantitative Analysis & Decision Sciences (QUADS)

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Agenda
Estimation
Prioritization
Application of AHP, SAW and Boxplot in
3

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Estimation

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Estimate Accurately.

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Estimate Accurately.
seems like an oxymoron!

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the only thing we know about an estimate is
that it is not exact!

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An Interlude

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A 5’8” tall statistician drowned while
crossing a river which had an average
depth of barely 4’2” feet!
why?

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If you toss a fair coin 20 times, how many
heads (or tails) do you expect?

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1 2 4 7 9 10 12 17 18 19 20
count of heads
frequency

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Never use average velocity computed
from past data to estimate number of
story points that you can cover in next
iteration.
Moral of the story!
And if you do then you can only be about
50% sure of meeting your commitment!

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key is to understand variation

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How to be 95% sure?

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1 61
2 61
3 62
4 64
5 64
6 64
7 64
8 65
9 65
10 65
11 65
12 66
13 66
14 66
15 67
16 67
17 68
18 68
19 68
20 68
21 69
22 72
23 84
1. start with past velocity data

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1 61
2 61
3 62
4 64
5 64
6 64
7 64
8 65
9 65
10 65
11 65
12 66
13 66
14 66
15 67
16 67
17 68
18 68
19 68
20 68
21 69
22 72
23 84
1st Quartile (Q1): QUARTILE(array, 1)
Median (Q2): QUARTILE(array, 2)
3rd Quartile (Q3): QUARTILE(array, 3)
2. use XL to find quartiles

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1 61
2 61
3 62
4 64
5 64
6 64
7 64
8 65
9 65
10 65
11 65
12 66
13 66
14 66
15 67
16 67
17 68
18 68
19 68
20 68
21 69
22 72
23 84
1st Quartile (Q1)
Median (Q2)
3rd Quartile (Q3)
3. determine IQR
IQR = Q3 - Q1
= 68 - 64
= 4
** IQR is Inter Quartile Range

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1 61
2 61
3 62
4 64
5 64
6 64
7 64
8 65
9 65
10 65
11 65
12 66
13 66
14 66
15 67
16 67
17 68
18 68
19 68
20 68
21 69
22 72
23 84
1st Quartile (Q1)
Median (Q2)
3rd Quartile (Q3)
4. determine outliers , if any
Velocity values smaller than Q1 - 3 x IQR
Velocity values greater than Q3 + 3 x IQR
> Q3 + 3 x IQR = 68 + 3 x 4 = 68 + 12 = 80; therefore a potential outlier

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1 61
2 61
3 62
4 64
5 64
6 64
7 64
8 65
9 65
10 65
11 65
12 66
13 66
14 66
15 67
16 67
17 68
18 68
19 68
20 68
21 69
22 72
23 84
1st Quartile (Q1)
Median (Q2)
3rd Quartile (Q3)
5. review outliers, if any
Exclude them from the data if you
determine that there were extraordinary
reasons causing such a high (or low)
value; and are not likely to reoccur.
Let us assume, we retain the outlier value.
> Q3 + 3 x IQR = 68 + 3 x 4 = 68 + 12 = 80; therefore an potential outlier

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1 61
2 61
3 62
4 64
5 64
6 64
7 64
8 65
9 65
10 65
11 65
12 66
13 66
14 66
15 67
16 67
17 68
18 68
19 68
20 68
21 69
22 72
23 84
ROUND(n/2 - 0.98 x (n)0.5 + 0.5, 0) = 7th row
Median (Q2)
6. determine 95% confidence interval
ROUND(n/2 + 0.98 x (n)0.5 + 0.5, 0) = 17th row
n = 23

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Median velocity is 66 and there is a 95%
chance that this median velocity will fall
between 64 and 68.
With 95% confidence, you can expect to
complete minimum 64 story points worth
of work in next iteration; the maximum
can be 68 story points.
Meaningful Estimate
Alternatively, all of the previous steps could have been done using box plot
tool in a standard statistical analysis software.

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About Story Points

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Always remember the law of
diminishing returns!

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Triangulation - surveying
Image Credit: http://en.wikipedia.org/wiki/File:Distance_by_triangulation.svg

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Triangulation - surveying
Image Credit: http://en.wikipedia.org/wiki/File:Distance_by_triangulation.svg
works very well as it involves measurements & not judgements!

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It is a process of judging the size of a user
story relative to, two other known user
stories with the purpose of increasing the
reliability.
Triangulation - Agile

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Analytical Hierarchical Process

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Analytical Hierarchical Process
its about relative measurement based on judgement
to derive a scale of priorities
for a set of items

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let’s explore a simplified view in our context

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AHP Basics
‣ Relative measurements based on judgement
‣ Uses pairwise comparisons
‣ For “n” items, n x (n - 1)/2 comparisons are required
‣ Uses a scale of 1 to 9 or the reciprocals for comparisons
‣ Items in question should be of same “order of magnitude” **
We say two numbers have the same order of magnitude of a
number if the big one divided by the little one is less than 10.
source: http://en.wikipedia.org/wiki/Order_of_magnitude
**

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AHP thru Example
s1 s2 s3
Derive a scale in terms of areas of squares
3 Items: 3 x (3 -1)/2 = 3 comparisons will
be required

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1 S1/S2 S1/S3
S2/S1 1 S2/S3
S3/S1 S3/S1 1
s1 s2 s3
s1
s2
s3
Each cell (r, c) to contain ratio of itemr/itemc
Only “white cells” need to be filled with
judgement values
Diagonal cells will always have a value “1”
“Dark gray” cell values can be derived from
“white” cell values (reciprocal)
AHP thru Example
**
** r: row & c: column of the matrix

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1 2 5
1/2 1 3
1/5 1/3 1
Step I - Make judgements
AHP thru Example

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Step II - Compute Geometric Mean for each row (contd.)
AHP thru Example
Geometric mean for a1, a2, ... an is computed as
(a1 x a2 ... x an)1/n

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1 2 5
1/2 1 3
1/5 1/3 1
2.1544
1.1447
0.4055
Geometric Mean
AHP thru Example
Step II - Compute Geometric Mean for each row

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3.7046SUM =
0.58
0.31
0.11
Geometric Mean Normalized
AHP thru Example
Step III - Normalize geometric means to arrive at results (contd.)
2.1544
1.1447
0.4055
1 2 5
1/2 1 3
1/5 1/3 1

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AHP thru Example
Step III - Normalize geometric means to arrive at results
If the area [read story points] of one square
[read story] was known, others can be easily
estimated from the resultant “scale of
priorities”.
Similarly, the scale of priorities could have been
applied to themes (instead of squares!) by
judging their relative importance (instead of
areas!!).

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AHP thru Example
Step IV - Review inconsistency (contd.)
1. AVERAGE((r11 x w1 + r12 x w2 + r13 x w3)/w1,
(r21 x w1 + r22 x w2 + r23 x w3)/w2,
(r31 x w1 + r32 x w2 + r33 x w3)/w3)
average must be greater than 3 (or n)
2. compute (average - n)/(n - 2), where n = 3
3. divide the result by random index (see table
below) for n = 3 to obtain Consistency Ratio
4. Consistency Ratio (CR) must be less than 0.1
n 3 4 5 6 7 8 9
Random Index 0.52 0.89 1.11 1.25 1.35 1.40 1.45

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0.58
0.31
0.11
Geometric Mean Normalized
AHP thru Example
2.1544
1.1447
0.4055
1 2 5
1/2 1 3
1/5 1/3 1
3.0037
3.0037
3.0037
3.0037AVERAGE =
CR = 0.0032
Step IV - Review inconsistency

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Possibilities with AHP
‣ Estimate story points
‣ pick up 3-4 homogenous stories and throw 1-2 stories
with known story points; and apply AHP
‣ can improve accuracy further by applying AHP separately
for UX, Coding, DB, ... Testing and use weighted sum to
arrive at story points
‣ Prioritize themes or backlog
‣ Improve SAW by computing criteria weights using AHP
‣ consider using contextually & semantically applicable
adjectives/adverbs instead of numeric ranks for
alternatives; and use AHP to determine rank (or priority)
of such adjectives.

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Q & A
possibilities are limitless!
Sanjaya Kumar Saxena
@sanjayaksaxena
sanjaya@graype.in
Rachna Chakraborty
@R4CHN4
rachna@graype.in
GrayPE Systems (P) Limited
www.graype.in
Contact:

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Thank you!
References:
[1] Agile Estimation & Planning by Mike Cohn
[2] Fundamentals of Decision Making with the Analytic Hierarchy Process by Thomas L Saaty
[3] http://www.discover6sigma.org/cat/statistics/