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?