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How	To	Use	Correlations	To	
Find	Stories	In	The	Data	
May
2019
	
	
Ray	Poynter	
NewMR
Today’s	Plot	
1.  What	is	correlation?	
2.  The	causes	of	correlation	
3.  Finding	stories	with	correlation	
4.  Beyond	correlation	
5.  Question	and	Answer
Correlation	
• Measures	the	linear	association	between	2	metric	scales	
•  There	are	correlation	measures	for	nonmetric	scales	
• It	produces	numbers	between	-1	and	+1	
•  Where:	+1	is	perfect	correlation,	0	is	no	correlation,	and	-1	is	perfect	
negative	correlation	
• We	use	the	letter	r	to	refer	to	the	most	common	form	of	the	
correlation	coefficient	
• We	often	square	the	correlation	coefficient	to	get	r‑squared,	
which	we	often	express	as	a	percentage
Perfect	Correlation	
When	we	drive	a	car,	the	amount	of	fuel	in	the	tank	is	negatively	
correlated	with	how	far	we	have	driven	–	until	we	add	more	fuel.
Strong	Correlation	
•  Correlation	coefficients	are	not	intuitive	
•  We	often	use	r-squared,	r2,	the	variance	
•  r-squared	is	the	proportion	of	the	total	variance	that	is	shared	
•  0.9	*	0.9	is	0.81	(often	written	81%)	
•  81%	of	the	variance	is	shared	–	and	19%	is	not
A	typical	strong	correlation	
•  In	the	real	world,	0.7	(or	-0.7)	is	a	strong	relationship	
•  r2	for	0.7	(AND	-0.7)	is	51%	
•  51%	of	the	total	variation	is	shared	(and	49%	is	not)
Notable	correlations	
•  In	the	real	world,	0.5	(or	-0.5)	might	be	interesting	
•  r2	for	0.5	(AND	-0.5)	is	25%	
•  25%	of	the	total	variation	is	shared	(and	75%	is	not)
No	(linear)	relationship	
•  In	the	real	world,	0	is	pretty	rare	
•  The	process	of	measurement	often	creates	some	correlation	
•  Selecting	questions	for	a	study	often	implies	association
Today’s	Plot	
1.  What	is	correlation?	
2.  The	causes	of	correlation	
3.  Finding	stories	with	correlation	
4.  Beyond	correlation	
5.  Question	and	Answer
What	‘causes’	correlation	
“Correlation	does	not	imply	causality”	
	
If	X	is	correlated	with	Y	then	we	can	usually	say	
•  X	causes	Y,	or	
•  Y	causes	X,	or	
•  X	and	Y	are	both	caused	by	a	common	agent	Z,	or	
•  X	and	Y	both	cause	each	other	in	a	feedback	system,	or	
•  It	is	just	chance	
	
But	if	X	is	correlated	with	Y,	we	should	investigate	why
Smoking	and	Lung	Cancer	
• 1950,	UK,	Richard	Doll	and	Austin	Bradford	Hill	
conducted	statistical	research	for	the	Medical	
Research	Council	
• Discovered	a	correlation	between	the	amount	
of	tobacco	smoked	and	lung	cancer	
• Published	findings	and	warnings	in	British	
Medical	Journal	in	1950	
• A	1954	British	Doctors	Study	confirmed	the	
correlation,	leading	to	UK	Government	advice	
that	smoking	and	Cancer	were	related	
• Proof	had	to	wait	until	the	science	could	show	
the	causative	mechanism.	
Richard	Doll	
Austin	Bradford	Hill
What	‘causes’	correlation	
“Correlation	does	not	imply	causality”	
	
If	X	is	correlated	with	Y	then	we	can	usually	say	
•  X	causes	Y,	or	
•  Y	causes	X,	or	
•  X	and	Y	are	both	caused	by	a	common	agent	Z,	or	
•  X	and	Y	both	cause	each	other	in	a	feedback	system,	or	
•  It	is	just	chance	
	
But	if	X	is	correlated	with	Y,	we	should	investigate	why
Lots	of	spurious	correlations	
http://www.tylervigen.com/spurious-correlations
Spurious	Correlations	r=0.79	
r2=63%
Today’s	Plot	
1.  What	is	correlation?	
2.  The	causes	of	correlation	
3.  Finding	stories	with	correlation	
4.  Beyond	correlation	
5.  Question	and	Answer
Knowing	where	to	look	
Correlation	can	help	make	the	map	(the	data)	more	readable
Knowing	where	to	look	
Correlation	can	help	make	the	map	(the	data)	more	readable
Satisfaction	with	features	and	the	link	to	NPS
Correlation	between	NPS	
and	feature	satisfaction	
NPS	 Correlation	
Bed	 0.80	
Restaurant	 0.58	
Price	 0.39	
TV	 0.26	
Check	in	 0.43	
Check	out	 0.40	
Location	 0.62	
Internet	 0.27	
Bathroom	 0.31	
Mini-bar	 0.20	
NPS	 Correlation	
Bed	 0.80	
Location	 0.62	
Restaurant	 0.58	
Check	in	 0.43	
Check	out	 0.40	
Price	 0.39	
Bathroom	 0.31	
Internet	 0.27	
TV	 0.26	
Mini-bar	 0.20	
With	story	finding,	sorting	is	key
The	ratios	between	the	features	
r-squared	
NPS	 R-squared	
Bed	 64%	
Location	 39%	
Restaurant	 34%	
Check	in	 19%	
Check	out	 16%	
Price	 15%	
Bathroom	 10%	
Internet	 7%	
TV	 7%	
Mini-bar	 4%
‘Drivers’	of	Choice	–	Derived	Importance	
High	Satisfaction	Low	Satisfaction	
High	Importance	Low	Importance	
Bed	
Location	
Restaurant	
Check	In	
Check	out	
Price	
Bathroom	
Internet	
TV	
Mini-bar
The	ratios	between	the	features	
r-squared	
NPS	 R-squared	
Bed	 64%	
Location	 39%	
Restaurant	 34%	
Check	in	 19%	
Check	out	 16%	
Price	 15%	
Bathroom	 10%	
Internet	 7%	
TV	 7%	
Mini-bar	 4%	
Add	the	r-squared	values	together	=	214%	
Why?	
Correlations	between	the	scores	of	the	features	
Multicollinearity
Multicollinearity	
NPS	 Bed	
Resta-
urant	 Price	 TV	
Check		
in	
Check	
out	
Loca-
tion	
Inter-
net	
Bath-
room	
Mini	
bar	
NPS	 1.00	 0.80	 0.58	 0.39	 0.26	 0.43	 0.40	 0.62	 0.27	 0.31	 0.20	
Bed	 0.80	 1.00	 0.56	 0.41	 0.21	 0.43	 0.41	 0.41	 0.32	 0.45	 0.19	
Restaurant	 0.58	 0.56	 1.00	 0.02	 0.05	 0.52	 0.45	 0.49	 -0.01	 0.30	 0.22	
Price	 0.39	 0.41	 0.02	 1.00	 0.41	 -0.08	 0.03	 0.08	 0.15	 0.00	 0.03	
TV	 0.26	 0.21	 0.05	 0.41	 1.00	 -0.09	 0.01	 -0.05	 0.53	 -0.07	 0.33	
Check	in	 0.43	 0.43	 0.52	 -0.08	 -0.09	 1.00	 0.71	 0.30	 0.14	 0.16	 0.07	
Check	out	 0.40	 0.41	 0.45	 0.03	 0.01	 0.71	 1.00	 0.55	 0.11	 0.23	 0.16	
Location	 0.62	 0.41	 0.49	 0.08	 -0.05	 0.30	 0.55	 1.00	 0.05	 -0.02	 0.13	
Internet	 0.27	 0.32	 -0.01	 0.15	 0.53	 0.14	 0.11	 0.05	 1.00	 -0.19	 0.10	
Bathroom	 0.31	 0.45	 0.30	 0.00	 -0.07	 0.16	 0.23	 -0.02	 -0.19	 1.00	 -0.02	
Mini-bar	 0.20	 0.19	 0.22	 0.03	 0.33	 0.07	 0.16	 0.13	 0.10	 -0.02	 1.00
Today’s	Plot	
1.  What	is	correlation?	
2.  The	causes	of	correlation	
3.  Finding	stories	with	correlation	
4.  Beyond	correlation	
5.  Question	and	Answer
Factor	Analysis	
Factor	Solution Factor	1 Factor	2 Factor	3 Factor	4
Check	In 0.87 0.07 0.05 0.08
TV 0.83 -0.01 -0.06 0.02
Check	Out 0.71 0.08 -0.01 -0.09
Bed 0.70 0.21 0.04 0.32
Bathroom 0.09 0.98 0.11 -0.04
Mini	bar 0.16 0.97 0.05 0.04
Price -0.05 0.28 0.84 -0.14
Restaurant -0.04 -0.05 0.76 0.21
Location 0.19 -0.03 0.62 -0.53
Internet 0.16 -0.02 0.04 0.87
Variance 29%	 20%	 15%	 11%	
Cumulative	Variance 29%	 49%	 64%	 75%	
NewMR	Webinar	-	Introduction	to	Factor	Analysis	
https://newmr.org/blog/introduction-to-factor-analysis/
Drivers	of	choice,	importance	etc	
• Correlation	
•  Easy,	stable,	but	less	rigourous	–	a	gateway	drug	for	Advanced	Analytics	
• Regression	
• Shapley	Values	
• Latent	Class	
• Conjoint	Analysis	
• Path	Analysis
Correlation	versus	Regression	
y	=	2x	+	1	
R²	=	0.67028	
0	
5	
10	
15	
20	
25	
0	 1	 2	 3	 4	 5	 6	 7	 8	 9	
Correlation	shows	the	goodness	of	fit	
y	=	2x	+	1	
R²	=	1	
0	
5	
10	
15	
20	
25	
0	 1	 2	 3	 4	 5	 6	 7	 8	 9	
Regression	shows	the	scale	of	the	
relationship
Uses	of	correlation	
• To	show	patterns	in	the	data,	associations	between	items	
and	between	attributes	
• As	a	measure	of	importance,	attributes	that	correlate	with	
an	outcome	(e.g.	satisfaction)	might	be	more	important	
• To	suggest	areas	of	investigation	–	the	link	between	smoking	
and	lung	cancer	started	as	a	correlation,	leading	to	the	
discovery	of	the	causal	link	
• In	the	form	of	r-squared	to	assess	the	quality	of	model	–	
usually	in	terms	of	consistency	rather	than	validity
Thank	You	
Ray	Poynter	
NewMR	
Connect	with	me	via	
Twitter: 	@RayPoynter	
LinkedIn:		linkedin.com/in/raypoynter
Q	&	A	
May
2019
	
	
Ray Poynter
#NewMR	Sponsors	
May
2019
	
	
Communication	
Gold	
Silver

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