Transcript Slide 1
Spearmans Rank
Statistical Analysis to show
Relationship Strength.
Results from a survey looking investigating the price of
items in relation to the shops distance from a major
tourist attraction
Rank distance
- Rank price
Convenience
Store
Distance from
CAM (m)
1
2
3
4
5
6
7
8
9
10
50
175
270
375
425
580
710
790
890
980
Rank distance
10
9
8
7
6
5
4
3
2
1
Price of 50cl
bottle (€)
Rank price
1.80
1.20
2.00
1.00
1.00
1.20
0.80
0.60
1.00
0.85
2
3.5
1
6
6
3.5
9
10
6
8
Difference
between ranks
(d)
8
5.5
7
1
0
1.5
-5
-7
-4
-7
d² = 285.5
d²
64
30.25
49
1
0
2.25
25
49
16
49
SPEARMAN’S RANK CORRELATION COEFFICIENT
It says …
rs 1
It allows us to …
6 d
2
n( n 1)
2
Compare the
RANK ORDER
of TWO Data Sets
The total of
6x
Spearman’s Rank
Correlation
Coefficient
rs 1
6 d
2
The DIFFERENCES
between the RANKS
assigned to each
‘price’ SQUARED
n( n 1)
2
The Number of
different ‘sites’
This example is based on a survey looking at price & distance
The Maths
• The top line of the equation
• d² (rank difference 2) = 285.5.
• Multiplying this by 6 gives 1713.
rs 1
6 d
2
n n
3
• Now for the bottom line of the equation.
• n (the number of sites) =10.
• n³ - n :1000 – 10 = 990
• R = 1 - (1713/990)
• R: 1 - 1.73 = -0.73
• What does this R value of -0.73 mean?
• The closer R is to +1 or -1, the stronger the likely correlation. Perfect
positive correlation is +1 and a perfect negative correlation is -1. The
R value of -0.73 suggests a fairly strong negative relationship.
What is it showing?
Total Agreement
rs close to 1
Overall Neither
Agree or Disagree
rs close to 0
Total Disagreement
rs close to -1
The significance of the relationship!
• The R value of -0.73 must be looked up on the
Spearman Rank significance table.
• 'degrees of freedom' : This is the number of pairs in
your sample minus 2 (n-2).
• 8 (10 - 2).
• Using the r value (y axis) the degrees of freedom value
(x axis)plot the position of the graph (next page).
Tasks
• Work through the example on p.636
(Waugh), fill in the table & check that
you understand how each column is
calculated.
• Complete the tasks on the next 2 slides
and
A student Surveyed the ages, in years, and the prices, in £’s, of ten second hand cars of a
particular type, in a local paper and obtained the data in the table below:
Age, years
6
2
9
5
13
4
7
8
3
10
Price, £’s
2790
5990
850
3100
650
3350
3790
1350
4590
990
What can you say about the relationship between the age and price of cars …
Data
Age
Ranks
Price
Age
Differences
Price
d
d2
Use the graph (p.637) to
determine the significance
of the relationship.
A student has been shown photographs of eight different people
and asked to estimate their ages …
The results are shown …
Actual age in years
54
88
22
70
30
15
47
6
Estimated Age
45
70
35
62
24
19
56
11
Data
Actual
Estimate
Ranks
Actual
Estimat
e
Differences
d
d2
What is the significance
of the relationship?